Global geomagnetic macreld modelsfor the past 3000 years transient

or permanent deg ux lobes

By Catherine G Constable1 Catherine L Johnson2

an d Steven P Lund3

1Institute for Geophysics and Planetary Physics Scripps Institution ofOceanography University of California at San Diego La Jolla

CA 92093-0225 USA (cconstableucsdedu)2Department of Terrestrial Magnetism Carnegie Institution of Washington

5241 Broad Branch Road Washington DC 200015 USA (cjohnsondtmciwedu)3Department of Earth Sciences University of Southern California

Los Angeles CA 90089-0740 USA (slunduscedu)

PSVMOD10 is a compilation of globally distributed palaeodirectional data fromarchaeomagnetic artefacts lava regows and lake sediments at 24 sites evaluated at100 year intervals from 1000 BC to AD 1800 We estimate uncertainty in thesemeasures of declination and inclination by comparison with predictions from stan-dard historical models in time-intervals of overlap and use the 100-year samples andtheir associated uncertainties to construct a sequence of minimum structure globalgeomagnetic shy eld models Global predictions of radial magnetic shy eld at the coremantle boundary (CMB) as well as inclination and declination anomalies at theEarthrsquos surface provide an unprecedented view of geomagnetic secular variationsover the past 3000 years and demonstrate a consistent evolution of the shy eld withtime Resolution of the models is poorest in the Southern Hemisphere where onlysix of the 24 sites are located several with incomplete temporal coverage Low-reguxregions seen in the historical shy eld near the North Pole are poorly resolved but theNorthern Hemisphere regux lobes are clearly visible in the models These lobes arenot shy xed in position and intensity but they only rarely venture into the Pacishy chemisphere The Pacishy c region is seen to have experienced signishy cant secular vari-ation a strong negative inclination anomaly in the region like that seen in 05 Mamodels persists from 1000 BC until AD 1000 and then gradually evolves into thesmaller positive anomaly seen today On average between 1000 BC and AD 1800the non-axial-dipole contribution to the radial magnetic shy eld at the coremantleboundary is largest in the north-central Pacishy c and beneath Central Asia withclear non-zonal contributions At the Earthrsquos surface average inclination anoma-lies are large and negative in the central Pacishy c and most positive slightly to theeast of Central Africa Inclination anomalies decrease with increasing latitude Aver-age declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and Eastern AsiaSecular variation at the Earthrsquos surface is quantishy ed by standard deviation of incli-nation and declination about their average values and at the CMB by standarddeviation in radial magnetic shy eld All three show signishy cant geographical variations

Phil Trans R Soc Lond A (2000) 358 9911008

991

c 2000 The Royal Society

992 C G Constable C L Johnson and S P Lund

but appear incompatible with the idea that secular variation in the Pacishy c hemi-sphere is permanently attenuated by greatly enhanced conductivity in D00 beneaththe region

Keywords geomagnetic secular variation palaeomagnetismgeomagnetic macreld modelling

1 Introduction

Analyses of the historical record of the geomagnetic shy eld provide an ever-improving(see Jackson et al this issue) view of the geomagnetic secular variation at theEarthrsquos surface as well as images of the radial component of the shy eld downwardcontinued to the coremantle boundary (CMB) This record is well characterized forthe time-interval AD 18401980 by the UFM1 model time-varying shy eld of Bloxhamamp Jackson (1992) Historical measurements are sparse before AD 1600 so for aglobal perspective we must turn to the palaeomagnetic and archaeomagnetic recordConsiderable enotort has been devoted to assembling datasets that span the last 5 Myr(Quidelleur et al 1994 Johnson amp Constable 1996 McElhinny amp McFadden 1997)and a number of shy eld models have been published using lava regow directional data aswell as those from marine sediments and the limited palaeointensity measurementsavailable for lava regows (Gubbins amp Kelly 1993 Kelly amp Gubbins 1997 Carlut ampCourtillot 1998 McElhinny et al 1996a b Johnson amp Constable 1995 1997 1998Schneider amp Kent 1988 1990)

The intermediate time-scales of hundreds to thousands of years have to datereceived less attention in terms of global modelling because of more stringent agecontrol requirements (compared with the temporal control needed for data spanninglonger time intervals) and because the palaeomagnetic time-series used must be con-sistent over continent-sized regions Regional studies have been published by Lund(1996) and more recently two globally distributed datasets have been compiledDaly amp Le Gonot (1996) have produced model time-series from globally distributedarchaeomagnetic observations for the last 2000 years these have been the subject ofstudy by Hongre et al (1998) Lund amp Constable (2000) have produced model time-series (PSVMOD10) of declination and inclination evaluated at 100-year intervalsfrom 1000 BC to AD 1800 This compilation is not restricted to archaeomagneticrecords but includes lake sediments and lava regows where there are appropriatequality and age controls PSVMOD10 is used here to produce a series of 29 mag-netic shy eld models at 100-year intervals Both the dataset and resulting models areaccessible on the World Wide Web at httpmahiucsdeducathyHolocene or viaanonymous ftp at ozzyucsdedu

The models presented in this paper are compared with some derived earlier fromboth historical and longer-term palaeomagnetic data Figure 1 shows predictionsfrom UFM1 (Bloxham amp Jackson 1992) averaged over the time-interval AD 18401980 LSN1 a time-averaged shy eld model derived from 05 Ma lava regow directionaldata (Johnson amp Constable 1997) and ALS3K a time-averaged model for the past3000 years derived from PSVMOD10 (Johnson amp Constable 1998) The shy rst columnshows the radial component of the magnetic shy eld at the CMB while the secondcolumn is the non-axial-dipole part of the radial component this second column isuseful because the dominant axial dipole tends to obscure structure in the rest of

Phil Trans R Soc Lond A (2000)

992 C G Constable C L Johnson and S P Lund

but appear incompatible with the idea that secular variation in the Pacishy c hemi-sphere is permanently attenuated by greatly enhanced conductivity in D00 beneaththe region

Keywords geomagnetic secular variation palaeomagnetismgeomagnetic macreld modelling

1 Introduction

Analyses of the historical record of the geomagnetic shy eld provide an ever-improving(see Jackson et al this issue) view of the geomagnetic secular variation at theEarthrsquos surface as well as images of the radial component of the shy eld downwardcontinued to the coremantle boundary (CMB) This record is well characterized forthe time-interval AD 18401980 by the UFM1 model time-varying shy eld of Bloxhamamp Jackson (1992) Historical measurements are sparse before AD 1600 so for aglobal perspective we must turn to the palaeomagnetic and archaeomagnetic recordConsiderable enotort has been devoted to assembling datasets that span the last 5 Myr(Quidelleur et al 1994 Johnson amp Constable 1996 McElhinny amp McFadden 1997)and a number of shy eld models have been published using lava regow directional data aswell as those from marine sediments and the limited palaeointensity measurementsavailable for lava regows (Gubbins amp Kelly 1993 Kelly amp Gubbins 1997 Carlut ampCourtillot 1998 McElhinny et al 1996a b Johnson amp Constable 1995 1997 1998Schneider amp Kent 1988 1990)

The intermediate time-scales of hundreds to thousands of years have to datereceived less attention in terms of global modelling because of more stringent agecontrol requirements (compared with the temporal control needed for data spanninglonger time intervals) and because the palaeomagnetic time-series used must be con-sistent over continent-sized regions Regional studies have been published by Lund(1996) and more recently two globally distributed datasets have been compiledDaly amp Le Gonot (1996) have produced model time-series from globally distributedarchaeomagnetic observations for the last 2000 years these have been the subject ofstudy by Hongre et al (1998) Lund amp Constable (2000) have produced model time-series (PSVMOD10) of declination and inclination evaluated at 100-year intervalsfrom 1000 BC to AD 1800 This compilation is not restricted to archaeomagneticrecords but includes lake sediments and lava regows where there are appropriatequality and age controls PSVMOD10 is used here to produce a series of 29 mag-netic shy eld models at 100-year intervals Both the dataset and resulting models areaccessible on the World Wide Web at httpmahiucsdeducathyHolocene or viaanonymous ftp at ozzyucsdedu

The models presented in this paper are compared with some derived earlier fromboth historical and longer-term palaeomagnetic data Figure 1 shows predictionsfrom UFM1 (Bloxham amp Jackson 1992) averaged over the time-interval AD 18401980 LSN1 a time-averaged shy eld model derived from 05 Ma lava regow directionaldata (Johnson amp Constable 1997) and ALS3K a time-averaged model for the past3000 years derived from PSVMOD10 (Johnson amp Constable 1998) The shy rst columnshows the radial component of the magnetic shy eld at the CMB while the secondcolumn is the non-axial-dipole part of the radial component this second column isuseful because the dominant axial dipole tends to obscure structure in the rest of

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 993

the shy eld particularly when it has been averaged over thousands of years The thirdcolumn of shy gure 1 is the inclination anomaly (the dinoterence between the predictedinclination and that of a geocentric axial dipole for the site) and the rightmostcolumn is the average declination In our new models we have not used intensityinformation thus we have estimates of the shy eld models to within an arbitrary scalarmultiplier (disregarding other issues of non-uniqueness see Proctor amp Gubbins (1990)and Hulot et al (1997)) We resolve this ambiguity by arbitrarily setting g0

1 to be30 T a value representative of the present shy eld

The historical shy eld has been described in detail in Bloxham et al (1989) Theradial shy eld at the CMB (shy gure 1a) contains four main static regux lobes that make amajor contribution to the dipole part of the shy eld Minor changes occur in the lobesover the 140-year period but no persistent drift There is a region of low regux overthe North and possibly also the South geographic Pole The regux concentration inthe central Pacishy c appears remarkably stable as does a large low-regux region to thenorth and northwest of it Persistent small changes occur to the east of the centralPacishy c concentration but there is little large-scale drift in the Pacishy c hemisphereThe low-regux patch near Easter Island also appears permanent on this time-scale Incontrast with the Pacishy c hemisphere the Atlantic hemisphere shows large reverse-regux patches beneath the Southern Atlantic and Indian Oceans that change rapidlywith time and drift westward The average shy eld over this time is approximatelyantisymmetric about the Equator with the exception of the central Pacishy c regux con-centration (note from 1b that this remains somewhat true even when the stronglyantisymmetric dipole contribution to the shy eld is removed) The Northern Hemi-sphere regux lobes are also seen in the non-axial-dipole Br Walker amp Backus (1996)have shown that the present non-dipole shy eld as measured by

RB2

r d2S in the Pacishy chemisphere is anomalously low compared with that in the Atlantic The inclinationanomaly (shy gure 1c) ranges from 240 to 264 with largest magnitude in equa-torial to mid-southern latitudes except in the Pacishy c region where it is generallysmaller than elsewhere Average declinations are largest near the poles (a geometricenotect) dominantly positive over the Pacishy c region much of the Americas centralAsia and Australia but negative in Europe Africa the Atlantic and Indian OceansAlthough declination anomalies are small in the central Pacishy c as well as over easternAsia it does not seem that they are exceptional when compared with some otherlocations

In contrast to the historical model ALS3K and LSN1 show only small but none-theless signishy cant departures from predictions of the geocentric axial-dipole hypoth-esis Over 3000 years secular variation results in average inclination and declinationanomalies (shy gure 1g h) that exhibit about half the range seen in UFM1 Interest-ingly the spatial structure of these anomalies is also quite dinoterent indicating thatmany of the features seen in UFM1 are far from permanent The largest inclinationanomalies over this time-interval are strong negative anomalies in the central Pacishy cand the declination anomaly has a completely dinoterent structure Although there isa strong suggestion of the static regux lobes in the radial magnetic shy eld they arenot well resolved by the model Johnson amp Constable (1998) showed that 1980 datasimilar to PSVMOD10 in distribution and accuracy inverted for the 1980 shy eld willresolve structure like that in ALS3K when regux lobes are present We note here thatALS3K was derived from temporal averages of the directional data this average willinevitably be somewhat biased by gaps in the available time-series for PSVMOD10

Phil Trans R Soc Lond A (2000)

994 C G Constable C L Johnson and S P Lund

(a) UFM1 average Br

ndash375ndash225ndash75

75225375

(e) ALS3K Br

(i) LSN1 Br

(b) UFM1 average Br NAD

( f) ALS3K Br NAD

(j) LSN1 Br NAD (l) LSN1 declination

(h) ALS3K declination

(d) UFM1 averagedeclination

(k) LSN1 inclinationanomaly

(g) ALS3K inclinationanomaly

(c) UFM1 averageinclination anomaly

ndash10ndash6ndash2

04812

Figure 1 Radial magnetic macreld at CMB (Br ) radial non-axial-dipole magnetic macreld atCMB (Br NAD ) inclination anomalies and declination for UFM1 after averaging over theAD 18401980 time-interval (a)(d) for ALS3K (e)(h) and for LSN1 (i)(l) Radial macreldmaps are in mT (contour interval 75 mT) inclination anomaly and declination maps are indegrees (contour interval 2 )

The 05 Ma model LSN1 is more attenuated in structure than ALS3K reregectingthat over long time-intervals the geomagnetic shy eld structure is closer to that pre-dicted from an axial dipole Nonetheless there is non-zonal (longitudinal) structurein the shy eld the observations cannot be adequately shy tted by a purely axisymmetricmodel Simulations show that the Northern Hemisphere regux lobes are dimacr cult todetect in inversions of 1980 data similar to the 05 Ma normal polarity dataset indistribution and accuracy Thus it remains plausible from ALS3K and LSN1 that theregux lobes are indeed quasi-permanent features in the geomagnetic shy eld Predictionsfrom the minimum structure model LSN1 show predominantly negative inclinationanomalies ranging from 8 in the central Pacishy c to +2 in the southeastern Pacishy cLarge inclination anomalies tend to be in the equatorial and mid-latitude regionswhich is also where the sampling sites are most concentrated Declination anomaliesare generally positive over Europe Africa and Western Asia as well as in much ofthe Pacishy c Johnson amp Constable (1998) drew attention to similarities in the averageradial magnetic shy eld at the CMB in the Pacishy c region in ALS3K and LSN1 in thesurface shy eld this is manifest in the signishy cant negative inclination anomaly Declina-tion predictions are less similar This should not be surprising since the declinationis most sensitive to Br in regions on the CMB that are displaced by 22 in longitudefrom the sampling site (see for example Johnson amp Constable 1997 1998) andsampling of the CMB by the ALS3K and LSN1 datasets is quite dinoterent (Johnsonamp Constable 1998)

Part of the motivation for developing the models described above is a longstandingquestion about the geomagnetic shy eld recently enunciated by Gubbins (1998) in theform of two competing theories Theory 1 holds that since we mostly see westwarddrift at the Earthrsquos surface during historical times non-axisymmetric parts of theshy eld will be averaged out over time to leave a purely axisymmetric average (see

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 995

for example McElhinny et al 1996b Carlut amp Courtillot 1998) Theory 2 drawson recent analyses of historical secular variation (Bloxham et al 1989 Bloxham ampJackson 1992) in which it is observed that westward drift is conshy ned to one partof the core surface there is no tendency to drift through a full rotation and littlesecular variation in the Pacishy c This may be interpreted as evidence that the core isinreguenced by the solid mantle resulting in a non-axisymmetric contribution to thetime-averaged geomagnetic shy eld Over 5 Myr or even 3 kyr the departures of thetime-averaged shy eld from axisymmetry are small and because of limitations in thedatasets both theory 1 and theory 2 remain plausible interpretations of the time-averaged shy eld structure (Carlut amp Courtillot 1998 Gubbins amp Kelly 1993 Kelly ampGubbins 1997 Johnson amp Constable 1995 1997 1998) However the dataset to bedescribed in the next section allows the development of models at 100-year intervalsJudging from UFM1 the signal over such 100-year time-intervals should be largein comparison with the results of shy gure 1el and despite the rather sparse globaldistribution of sites there remains the facility to track any possible evolution of theregux lobes and apparently unusual Pacishy c secular variation The resolution of thislongstanding question of the inreguence of the lower mantle on the geodynamo fromthe perspective of shy eld behaviour consistent with palaeomagnetic data is importantThree-dimensional numerical simulations of the geodynamo investigating dinoterentspatial variations in heat regow across the CMB are already being carried out (Glatz-maier et al 1999 Bloxham 1998) and independent investigations focusing on theproperties of palaeomagnetic datasets provide important ground truthing for suchsimulations Furthermore if heat-regow patterns across the CMB inreguence geodynamoprocesses there are implications for the geomagnetic shy eld over longer time-scalesthan the past 5 Myr since the thermal structure of the lower mantle has certainlychanged over time-scales of 107 to 108 yr (Richards amp Engebretson 1992 Lithgow-Bertelloni amp Richards 1998) Greatly enhanced electrical conductivity in D00 beneaththe Pacishy c region (see for example Runcorn 1992) has also been considered as apossible mechanism for attenuating geomagnetic secular variations at the Earthrsquossurface and inreguences on virtual geomagnetic pole (VGP) paths during reversalsFurther examinations of the inreguence of electromagnetic torques on the mantle dueto the poloidal shy eld led initially to suggestions that heterogeneity in mantle conduc-tivity is a plausible mechanism (Arnou et al 1996) to inreguence the trajectory of theVGP during reversals Later work with a more complete consideration of the problemled to a reversal of this opinion (Brito et al 1999) Most recently Holme (2000) hasargued that the conductance required for such a mechanism is inconsistent with theobserved coremantle angular momentum exchange on decadal time-scales

In what follows we brieregy review the PSVMOD10 dataset described in detailby Lund amp Constable (2000) and the methodology for constructing models (alsodescribed elsewhere see Johnson amp Constable (1995 1997)) We present `snapshotsrsquoof the geomagnetic shy eld|models at 100-year intervals|and discuss the evolutionand secular variations of features observed both at the CMB and at the Earthrsquossurface

2 The PSVMOD10 dataset

PSVMOD10 consists of model time-series at 24 globally distributed sites (locationsindicated by the triangles on shy gure 1eh each of which contribute palaeomagnetic

Phil Trans R Soc Lond A (2000)

996 C G Constable C L Johnson and S P Lund

Table 1 Sites contributing to the macreld models for the periods 1000 BC to AD 1800

code latitude longitude class

WUS 350 N 2500 E 1A

JPN 350 N 1350 E 1A

SEU 400 N 200 E 1A

UKR 500 N 300 E 1A

WUR 500 N 00 E 1A

HAW 200 N 2050 E 1B

MAM 170 N 2650 E 1B

PRC 350 N 1150 E 1B

CAU 400 N 450 E 1C

NZE 358 S 1749 E 2A

AUS 380 S 1450 E 2B

MON 460 N 1060 E 2C

BAI 524 N 1061 E 3A

FIS 426 N 2414 E 3A

ICE 660 N 3370 E 3A

KEI 382 S 1429 E 3A

LEB 419 N 2801 E 3A

LLO 561 N 3553 E 3A

LSC 450 N 2672 E 3A

POU 413 S 1752 E 3A

VUK 634 N 286 E 3B

ARG 410 S 2885 E 3B

EAC 173 S 1061 E 3B

TUR 26 N 366 E 3C

records of declination and inclination at 100-year intervals when available) Eachtime-series was developed from composite archaeomagnetic or sediment palaeosecularvariation data with independent good-quality age control Where 14C dating was usedin the original studies the time-scale has been transformed to calendar years usingthe calibration of Clark (1975) Lund amp Constable (2000) classishy ed data for eachtime-series as follows

Class 1 archaeomagnetic directional records with sumacr cient data to characterize thepattern of shy eld variability

Class 2 fragmentary archaeomagnetic data (inclination-only short-duration largedata gaps)

Class 3 sediment directional records

It is assumed that the lower the number of the record type the better the dataquality Relative data quality within each record type was also indicated by a letterbetween A and D with A indicating the best quality records We note that theseclassishy cations are purely qualitative and in attempting to assign numerical uncer-tainties to PSVMOD10 for use in our later inversions we have made an independentassessment based on comparisons with historical data Table 1 gives the site loca-tions and the classishy cation codes for each site and the temporal completeness of the

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 997

2000

1500

1000

500 0

ndash500

ndash1000

age (ndashBC+AD)

wus

arg

aus

bai

cau

eac

fis

haw

ice

jpn

kei

leb

llo

Isc

mam

mon

nze

pou

prc

seu

tur

ukr

vuk

wur

Figure 2 Temporal sampling at each site a triangle (circle) at the time point indicates theexistence of a 100-year sample of declination (inclination) at the indicated site

Phil Trans R Soc Lond A (2000)

998 C G Constable C L Johnson and S P Lund

records is shown in shy gure 2 where a triangle at a given time above the site codeindicates the existence of a 100-year sample for declination and a circle indicatesinclination The 100-year sample is not a direct average of the shy eld direction overthe 100-year interval but an evaluation at the indicated time based on a compositecurve from multiple observations In general each `datumrsquo represents something likea 2030-year average of the shy eld depending somewhat on the dating resolution andthe general quality of the record Age uncertainty is generally larger for sedimentsthan for archaeomagnetic sites We note that the coverage in the Southern Hemi-sphere is very sparse for some time-intervals a point to be kept in mind in evaluatingthe models derived in the next section

Lund amp Constable (2000) discuss the possible causes of uncertainty in the PSV-MOD10 directions in some detail There are shy ve sources of uncertainty in our obser-vations

(i) error in the shy eld direction recorded by the rock sample on acquisition of depo-sitional or thermal remanence

(ii) contamination of the direction from the core shy eld by local magnetic shy eld anoma-lies

(iii) uncertainty in the age at which magnetic remanence was acquired

(iv) orientation errors during sampling and

(v) inadequate magnetic cleaning in the palaeomagnetic laboratory such that thecharacteristic remanence direction may not be recovered

The combined inreguence of these processes can be estimated by comparing PSV-MOD10 with corresponding predictions from Bloxham amp Jacksonrsquos (1992) UFM inthe post-AD 1690 time period Sixteen sites have directions for AD 1800 and 20 forAD 1700 the archaeomagnetic sites tend to have more complete records in the veryrecent past because the top of lake-sediment cores is often disturbed in the coringprocess Absolute orientation of the archaeomagnetic samples also tends to be moreaccurate because it is rare for absolute records of declination to be acquired duringcoring The average deviation for all sites from UFM is close to zero and usingthe available comparisons standard errors of 25 were assigned to both declinationand inclination measurements derived from archaeomagnetic sources while for lakesediments standard errors of 35 and 50 were assigned to inclination and decli-nation respectively Experimentation suggests that in general the largest source ofuncertainty in our observations is the secular variation itself which combined withuncertainties in age can contribute the major part of the observed deviation fromUFM predictions

Lund amp Constable (2000) plot average declination and inclination anomalies forPSVMOD10 relative to a geocentric axial dipole and compare them with similarsite residuals for both UFM and LSN1 The signal in PSVMOD10 is generally inter-mediate in magnitude between that in UFM and LSN1 reregecting the time-scale overwhich the various records are averaged All models show coherent spatial structuresin the residuals over areas several thousand kilometres across but there are some sig-nishy cant dinoterences between these structures over the three time-intervals representedhere For example at TUR in Kenya PSVMOD10 exhibits a positive inclination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 999

Table 2

iteration starting macrnal variance model

epoch no RMS RMS reduction norm

AD 1800 05 302 100 890 130

AD 1700 07 240 100 826 193

AD 1600 14 238 100 823 328

AD 1500 08 220 152 523 140

AD 1400 11 199 127 593 166

AD 1300 09 208 130 609 136

AD 1200 07 266 138 731 192

AD 1100 07 308 142 787 306

AD 1000 07 319 139 810 213

AD 900 09 289 144 752 165

AD 800 09 233 123 721 108

AD 700 09 254 157 618 215

AD 600 09 279 190 536 185

AD 500 11 251 154 624 158

AD 400 09 226 145 588 144

AD 300 08 212 135 594 167

AD 200 06 217 141 578 129

AD 100 09 200 131 571 174

AD 0 08 228 167 464 209

100 BC 07 243 179 457 167

200 BC 17 232 155 554 215

300 BC 07 289 180 612 202

400 BC 05 309 179 664 181

500 BC 07 397 215 707 241

600 BC 07 453 214 777 318

700 BC 03 528 293 692 298

800 BC 03 526 251 772 350

900 BC 04 471 236 749 274

1000 BC 05 372 187 747 205

anomaly while both LSN1 and UFM show negative values While we cannot rule outthe possibility of some systematic errors in PSVMOD10 and we can certainly lookfor improved geographic and temporal coverage in the future the analyses of Lundamp Constable (2000) demonstrate good regional coherence and general reliability ofthe time-series

3 Models

The detailed evaluation of the archaeomagnetic dataset described in Lund amp Con-stable (2000) and summarized in the previous section permits the investigation ofthe evolution of the global geomagnetic shy eld over the past 3000 years Figure 1 showsthat the recent time-averaged structure of the shy eld as seen in UFM1 is quite dinoter-ent from that for the past 3 kyr and thus we might expect signishy cant changes inglobal shy eld behaviour Spherical harmonic models of the geomagnetic shy eld were con-

Phil Trans R Soc Lond A (2000)

1000 C G Constable C L Johnson and S P Lund

structed at 100-year intervals using data from as many sites as are available (shy gure 2)at each time-interval The modelling procedure follows that used in the generationof time-averaged shy eld models for the periods 05 Ma and 03 Ka and details can befound elsewhere (Johnson amp Constable 1995 1997 1998) The scalar geomagneticpotential is described in terms of a spherical harmonic expansion and thus ourmeasurements of declination and inclination are nonlinearly related to the sphericalharmonic coemacr cients which are the model parameters We use an iterative nonlinearinversion procedure modishy ed for geomagnetic shy eld modelling from Constable et al rsquos(1987) Occamrsquos inversion algorithm our models are regularized by minimizing themean square value of the non-axial-dipole part of the radial magnetic shy eld (Br) atthe CMB while shy tting the data to a specishy ed tolerance As discussed by Johnsonamp Constable (1997) in the context of constructing LSN1 our model choice dependscritically upon the minimum acceptable misshy t to our observations designated in theprevious section Under the assumption that these uncertainties are independentzero-mean Gaussian variables the target misshy t of the model to our data will corre-spond to the expected value of Agrave 2

N which is N when the misshy t is normalized by thedata uncertainties In practice the target value for the misshy t was not always attain-able without generating overly complicated shy eld models we therefore compromiseand select models with a plausible degree of roughness and a slightly higher misshy tto the observations The necessity for this probably indicates that our use of UFM tocalibrate the uncertainties in PSVMOD10 is not adequate to deal with variations indata quality as they extend further into the past Table 2 lists the initial RMS signalin the data (measured relative to GAD and normalized by the standard error) theRMS of the shy nal model the percentage variance reduction the roughness of theshy nal model (model norm) for each epoch and the iteration at which the preferredmodel was achieved The variance reductions achieved range from 46 to 89 andare typically ca 70 The model norm does not contain the axial-dipole contributionto the roughness and is normalized relative to that contribution

The sequence of models from 1000 BC to AD 1800 is presented in shy gure 3 using thesame format as in shy gure 1 note however that the non-axial-dipole contribution to Br

at the CMB (BrNAD) is on a dinoterent colour scale There is clearly a coherent temporal

evolution of these shy eld models with structures persisting for hundreds of years andgradually evolving into new features Since each model is a snapshot in time andindependent of the data in adjacent temporal slots this reregects well on the quality ofthe observations and the care taken in selecting them There is signishy cant evolvingnon-zonal structure in the shy eld models whose character appears quite distinct in thedinoterent representations of the shy eld Br at the CMB is dominated by the axial-dipoleshy eld contribution but changes in shy eld structure can be seen these are revealed moreclearly in the second column of shy gures from which the axial-dipole contribution hasbeen subtracted From this we see that from 1000 BC until 600 BC the regux lobe overAsia was dominant and there was a positive anomaly in BrNAD

over western NorthAmerica extending across the Pacishy c past Hawaii The North American regux lobe isonly occasionally visible during this time Southern Hemisphere shy eld structure is verysmooth reregecting the paucity of data there Large negative inclination anomaliesin the central Pacishy c region and positive ones centred in the Indian Ocean areassociated with these structures The focus of these inclination anomalies in dinoterentgeographic regions from the radial shy eld anomalies reregects the dinoterent CMB samplingkernels for the radial shy eld inclination and declination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1001

Br 1000 BCndash375ndash225ndash7575225375

Br 900 BC

Br 800 BC

Br 700 BC

Br 600 BC

Br NAD 1000 BCndash160

ndash80

0

80

160

Br NAD 900 BC

Br NAD 800 BC

Br NAD 700 BC

Br NAD 600 BC

inclination anomaly 1000 BCndash12ndash8ndash404812

inclination anomaly 900 BC

inclination anomaly 800 BC

inclination anomaly 700 BC

inclination anomaly 600 BC

declination 1000 BC

declination 900 BC

declination 800 BC

declination 700 BC

declination 600 BC

(i)

Br 500 BCndash375ndash225ndash7575225375

Br 400 BC

Br 300 BC

Br 200 BC

Br 100 BC

Br NAD 500 BCndash160

ndash80

0

80

160

Br NAD 400 BC

Br NAD 300 BC

Br NAD 200 BC

Br NAD 100 BC

inclination anomaly 500 BCndash12ndash8ndash404812

inclination anomaly 400 BC

inclination anomaly 300 BC

inclination anomaly 200 BC

inclination anomaly 100 BC

declination 500 BC

declination 400 BC

declination 300 BC

declination 200 BC

declination 100 BC

(ii)

Figure 3 Snapshots of Br (75 mT contour interval) Br NAD (40 mT contour interval) inclinationanomaly at the Earthrsquo s surface and declination (contour interval 2 ) for models every 100 yearsfrom 1000 BC to AD 1800 Colour bars sit to the right of the parameter plotted except for thedeclination which has the same scale as the inclination

Phil Trans R Soc Lond A (2000)

1002 C G Constable C L Johnson and S P Lund

Br 0 ADndash375ndash225ndash7575225375

Br 100 AD

Br 200 AD

Br 300 AD

Br 400 AD

Br NAD 0 ADndash160

ndash80

0

80

160

Br NAD 100 AD

Br NAD 200 AD

Br NAD 300 AD

Br NAD 400 AD

inclination anomaly 0 ADndash12ndash8ndash404812

inclination anomaly 100 AD

inclination anomaly 200 AD

inclination anomaly 300 AD

inclination anomaly 400 AD

declination 0 AD

declination 100 AD

declination 200 AD

declination 300 AD

declination 400 AD

(iii)

Br 500 ADndash375ndash225ndash7575225375

Br 600 AD

Br 700 AD

Br 800 AD

Br 900 AD

Br NAD 500 ADndash160

ndash80

0

80

160

Br NAD 600 AD

Br NAD 700 AD

Br NAD 800 AD

Br NAD 900 AD

inclination anomaly 500 ADndash12ndash8ndash404812

inclination anomaly 600 AD

inclination anomaly 700 AD

inclination anomaly 800 AD

inclination anomaly 900 AD

declination 500 AD

declination 600 AD

declination 700 AD

declination 800 AD

declination 900 AD

(iv)

Figure 3 (Cont)

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

994 C G Constable C L Johnson and S P Lund

(a) UFM1 average Br

ndash375ndash225ndash75

75225375

(e) ALS3K Br

(i) LSN1 Br

(b) UFM1 average Br NAD

( f) ALS3K Br NAD

(j) LSN1 Br NAD (l) LSN1 declination

(h) ALS3K declination

(d) UFM1 averagedeclination

(k) LSN1 inclinationanomaly

(g) ALS3K inclinationanomaly

(c) UFM1 averageinclination anomaly

ndash10ndash6ndash2

04812

Figure 1 Radial magnetic macreld at CMB (Br ) radial non-axial-dipole magnetic macreld atCMB (Br NAD ) inclination anomalies and declination for UFM1 after averaging over theAD 18401980 time-interval (a)(d) for ALS3K (e)(h) and for LSN1 (i)(l) Radial macreldmaps are in mT (contour interval 75 mT) inclination anomaly and declination maps are indegrees (contour interval 2 )

The 05 Ma model LSN1 is more attenuated in structure than ALS3K reregectingthat over long time-intervals the geomagnetic shy eld structure is closer to that pre-dicted from an axial dipole Nonetheless there is non-zonal (longitudinal) structurein the shy eld the observations cannot be adequately shy tted by a purely axisymmetricmodel Simulations show that the Northern Hemisphere regux lobes are dimacr cult todetect in inversions of 1980 data similar to the 05 Ma normal polarity dataset indistribution and accuracy Thus it remains plausible from ALS3K and LSN1 that theregux lobes are indeed quasi-permanent features in the geomagnetic shy eld Predictionsfrom the minimum structure model LSN1 show predominantly negative inclinationanomalies ranging from 8 in the central Pacishy c to +2 in the southeastern Pacishy cLarge inclination anomalies tend to be in the equatorial and mid-latitude regionswhich is also where the sampling sites are most concentrated Declination anomaliesare generally positive over Europe Africa and Western Asia as well as in much ofthe Pacishy c Johnson amp Constable (1998) drew attention to similarities in the averageradial magnetic shy eld at the CMB in the Pacishy c region in ALS3K and LSN1 in thesurface shy eld this is manifest in the signishy cant negative inclination anomaly Declina-tion predictions are less similar This should not be surprising since the declinationis most sensitive to Br in regions on the CMB that are displaced by 22 in longitudefrom the sampling site (see for example Johnson amp Constable 1997 1998) andsampling of the CMB by the ALS3K and LSN1 datasets is quite dinoterent (Johnsonamp Constable 1998)

Part of the motivation for developing the models described above is a longstandingquestion about the geomagnetic shy eld recently enunciated by Gubbins (1998) in theform of two competing theories Theory 1 holds that since we mostly see westwarddrift at the Earthrsquos surface during historical times non-axisymmetric parts of theshy eld will be averaged out over time to leave a purely axisymmetric average (see

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 995

for example McElhinny et al 1996b Carlut amp Courtillot 1998) Theory 2 drawson recent analyses of historical secular variation (Bloxham et al 1989 Bloxham ampJackson 1992) in which it is observed that westward drift is conshy ned to one partof the core surface there is no tendency to drift through a full rotation and littlesecular variation in the Pacishy c This may be interpreted as evidence that the core isinreguenced by the solid mantle resulting in a non-axisymmetric contribution to thetime-averaged geomagnetic shy eld Over 5 Myr or even 3 kyr the departures of thetime-averaged shy eld from axisymmetry are small and because of limitations in thedatasets both theory 1 and theory 2 remain plausible interpretations of the time-averaged shy eld structure (Carlut amp Courtillot 1998 Gubbins amp Kelly 1993 Kelly ampGubbins 1997 Johnson amp Constable 1995 1997 1998) However the dataset to bedescribed in the next section allows the development of models at 100-year intervalsJudging from UFM1 the signal over such 100-year time-intervals should be largein comparison with the results of shy gure 1el and despite the rather sparse globaldistribution of sites there remains the facility to track any possible evolution of theregux lobes and apparently unusual Pacishy c secular variation The resolution of thislongstanding question of the inreguence of the lower mantle on the geodynamo fromthe perspective of shy eld behaviour consistent with palaeomagnetic data is importantThree-dimensional numerical simulations of the geodynamo investigating dinoterentspatial variations in heat regow across the CMB are already being carried out (Glatz-maier et al 1999 Bloxham 1998) and independent investigations focusing on theproperties of palaeomagnetic datasets provide important ground truthing for suchsimulations Furthermore if heat-regow patterns across the CMB inreguence geodynamoprocesses there are implications for the geomagnetic shy eld over longer time-scalesthan the past 5 Myr since the thermal structure of the lower mantle has certainlychanged over time-scales of 107 to 108 yr (Richards amp Engebretson 1992 Lithgow-Bertelloni amp Richards 1998) Greatly enhanced electrical conductivity in D00 beneaththe Pacishy c region (see for example Runcorn 1992) has also been considered as apossible mechanism for attenuating geomagnetic secular variations at the Earthrsquossurface and inreguences on virtual geomagnetic pole (VGP) paths during reversalsFurther examinations of the inreguence of electromagnetic torques on the mantle dueto the poloidal shy eld led initially to suggestions that heterogeneity in mantle conduc-tivity is a plausible mechanism (Arnou et al 1996) to inreguence the trajectory of theVGP during reversals Later work with a more complete consideration of the problemled to a reversal of this opinion (Brito et al 1999) Most recently Holme (2000) hasargued that the conductance required for such a mechanism is inconsistent with theobserved coremantle angular momentum exchange on decadal time-scales

In what follows we brieregy review the PSVMOD10 dataset described in detailby Lund amp Constable (2000) and the methodology for constructing models (alsodescribed elsewhere see Johnson amp Constable (1995 1997)) We present `snapshotsrsquoof the geomagnetic shy eld|models at 100-year intervals|and discuss the evolutionand secular variations of features observed both at the CMB and at the Earthrsquossurface

2 The PSVMOD10 dataset

PSVMOD10 consists of model time-series at 24 globally distributed sites (locationsindicated by the triangles on shy gure 1eh each of which contribute palaeomagnetic

Phil Trans R Soc Lond A (2000)

996 C G Constable C L Johnson and S P Lund

Table 1 Sites contributing to the macreld models for the periods 1000 BC to AD 1800

code latitude longitude class

WUS 350 N 2500 E 1A

JPN 350 N 1350 E 1A

SEU 400 N 200 E 1A

UKR 500 N 300 E 1A

WUR 500 N 00 E 1A

HAW 200 N 2050 E 1B

MAM 170 N 2650 E 1B

PRC 350 N 1150 E 1B

CAU 400 N 450 E 1C

NZE 358 S 1749 E 2A

AUS 380 S 1450 E 2B

MON 460 N 1060 E 2C

BAI 524 N 1061 E 3A

FIS 426 N 2414 E 3A

ICE 660 N 3370 E 3A

KEI 382 S 1429 E 3A

LEB 419 N 2801 E 3A

LLO 561 N 3553 E 3A

LSC 450 N 2672 E 3A

POU 413 S 1752 E 3A

VUK 634 N 286 E 3B

ARG 410 S 2885 E 3B

EAC 173 S 1061 E 3B

TUR 26 N 366 E 3C

records of declination and inclination at 100-year intervals when available) Eachtime-series was developed from composite archaeomagnetic or sediment palaeosecularvariation data with independent good-quality age control Where 14C dating was usedin the original studies the time-scale has been transformed to calendar years usingthe calibration of Clark (1975) Lund amp Constable (2000) classishy ed data for eachtime-series as follows

Class 1 archaeomagnetic directional records with sumacr cient data to characterize thepattern of shy eld variability

Class 2 fragmentary archaeomagnetic data (inclination-only short-duration largedata gaps)

Class 3 sediment directional records

It is assumed that the lower the number of the record type the better the dataquality Relative data quality within each record type was also indicated by a letterbetween A and D with A indicating the best quality records We note that theseclassishy cations are purely qualitative and in attempting to assign numerical uncer-tainties to PSVMOD10 for use in our later inversions we have made an independentassessment based on comparisons with historical data Table 1 gives the site loca-tions and the classishy cation codes for each site and the temporal completeness of the

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 997

2000

1500

1000

500 0

ndash500

ndash1000

age (ndashBC+AD)

wus

arg

aus

bai

cau

eac

fis

haw

ice

jpn

kei

leb

llo

Isc

mam

mon

nze

pou

prc

seu

tur

ukr

vuk

wur

Figure 2 Temporal sampling at each site a triangle (circle) at the time point indicates theexistence of a 100-year sample of declination (inclination) at the indicated site

Phil Trans R Soc Lond A (2000)

998 C G Constable C L Johnson and S P Lund

records is shown in shy gure 2 where a triangle at a given time above the site codeindicates the existence of a 100-year sample for declination and a circle indicatesinclination The 100-year sample is not a direct average of the shy eld direction overthe 100-year interval but an evaluation at the indicated time based on a compositecurve from multiple observations In general each `datumrsquo represents something likea 2030-year average of the shy eld depending somewhat on the dating resolution andthe general quality of the record Age uncertainty is generally larger for sedimentsthan for archaeomagnetic sites We note that the coverage in the Southern Hemi-sphere is very sparse for some time-intervals a point to be kept in mind in evaluatingthe models derived in the next section

Lund amp Constable (2000) discuss the possible causes of uncertainty in the PSV-MOD10 directions in some detail There are shy ve sources of uncertainty in our obser-vations

(i) error in the shy eld direction recorded by the rock sample on acquisition of depo-sitional or thermal remanence

(ii) contamination of the direction from the core shy eld by local magnetic shy eld anoma-lies

(iii) uncertainty in the age at which magnetic remanence was acquired

(iv) orientation errors during sampling and

(v) inadequate magnetic cleaning in the palaeomagnetic laboratory such that thecharacteristic remanence direction may not be recovered

The combined inreguence of these processes can be estimated by comparing PSV-MOD10 with corresponding predictions from Bloxham amp Jacksonrsquos (1992) UFM inthe post-AD 1690 time period Sixteen sites have directions for AD 1800 and 20 forAD 1700 the archaeomagnetic sites tend to have more complete records in the veryrecent past because the top of lake-sediment cores is often disturbed in the coringprocess Absolute orientation of the archaeomagnetic samples also tends to be moreaccurate because it is rare for absolute records of declination to be acquired duringcoring The average deviation for all sites from UFM is close to zero and usingthe available comparisons standard errors of 25 were assigned to both declinationand inclination measurements derived from archaeomagnetic sources while for lakesediments standard errors of 35 and 50 were assigned to inclination and decli-nation respectively Experimentation suggests that in general the largest source ofuncertainty in our observations is the secular variation itself which combined withuncertainties in age can contribute the major part of the observed deviation fromUFM predictions

Lund amp Constable (2000) plot average declination and inclination anomalies forPSVMOD10 relative to a geocentric axial dipole and compare them with similarsite residuals for both UFM and LSN1 The signal in PSVMOD10 is generally inter-mediate in magnitude between that in UFM and LSN1 reregecting the time-scale overwhich the various records are averaged All models show coherent spatial structuresin the residuals over areas several thousand kilometres across but there are some sig-nishy cant dinoterences between these structures over the three time-intervals representedhere For example at TUR in Kenya PSVMOD10 exhibits a positive inclination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 999

Table 2

iteration starting macrnal variance model

epoch no RMS RMS reduction norm

AD 1800 05 302 100 890 130

AD 1700 07 240 100 826 193

AD 1600 14 238 100 823 328

AD 1500 08 220 152 523 140

AD 1400 11 199 127 593 166

AD 1300 09 208 130 609 136

AD 1200 07 266 138 731 192

AD 1100 07 308 142 787 306

AD 1000 07 319 139 810 213

AD 900 09 289 144 752 165

AD 800 09 233 123 721 108

AD 700 09 254 157 618 215

AD 600 09 279 190 536 185

AD 500 11 251 154 624 158

AD 400 09 226 145 588 144

AD 300 08 212 135 594 167

AD 200 06 217 141 578 129

AD 100 09 200 131 571 174

AD 0 08 228 167 464 209

100 BC 07 243 179 457 167

200 BC 17 232 155 554 215

300 BC 07 289 180 612 202

400 BC 05 309 179 664 181

500 BC 07 397 215 707 241

600 BC 07 453 214 777 318

700 BC 03 528 293 692 298

800 BC 03 526 251 772 350

900 BC 04 471 236 749 274

1000 BC 05 372 187 747 205

anomaly while both LSN1 and UFM show negative values While we cannot rule outthe possibility of some systematic errors in PSVMOD10 and we can certainly lookfor improved geographic and temporal coverage in the future the analyses of Lundamp Constable (2000) demonstrate good regional coherence and general reliability ofthe time-series

3 Models

The detailed evaluation of the archaeomagnetic dataset described in Lund amp Con-stable (2000) and summarized in the previous section permits the investigation ofthe evolution of the global geomagnetic shy eld over the past 3000 years Figure 1 showsthat the recent time-averaged structure of the shy eld as seen in UFM1 is quite dinoter-ent from that for the past 3 kyr and thus we might expect signishy cant changes inglobal shy eld behaviour Spherical harmonic models of the geomagnetic shy eld were con-

Phil Trans R Soc Lond A (2000)

1000 C G Constable C L Johnson and S P Lund

structed at 100-year intervals using data from as many sites as are available (shy gure 2)at each time-interval The modelling procedure follows that used in the generationof time-averaged shy eld models for the periods 05 Ma and 03 Ka and details can befound elsewhere (Johnson amp Constable 1995 1997 1998) The scalar geomagneticpotential is described in terms of a spherical harmonic expansion and thus ourmeasurements of declination and inclination are nonlinearly related to the sphericalharmonic coemacr cients which are the model parameters We use an iterative nonlinearinversion procedure modishy ed for geomagnetic shy eld modelling from Constable et al rsquos(1987) Occamrsquos inversion algorithm our models are regularized by minimizing themean square value of the non-axial-dipole part of the radial magnetic shy eld (Br) atthe CMB while shy tting the data to a specishy ed tolerance As discussed by Johnsonamp Constable (1997) in the context of constructing LSN1 our model choice dependscritically upon the minimum acceptable misshy t to our observations designated in theprevious section Under the assumption that these uncertainties are independentzero-mean Gaussian variables the target misshy t of the model to our data will corre-spond to the expected value of Agrave 2

N which is N when the misshy t is normalized by thedata uncertainties In practice the target value for the misshy t was not always attain-able without generating overly complicated shy eld models we therefore compromiseand select models with a plausible degree of roughness and a slightly higher misshy tto the observations The necessity for this probably indicates that our use of UFM tocalibrate the uncertainties in PSVMOD10 is not adequate to deal with variations indata quality as they extend further into the past Table 2 lists the initial RMS signalin the data (measured relative to GAD and normalized by the standard error) theRMS of the shy nal model the percentage variance reduction the roughness of theshy nal model (model norm) for each epoch and the iteration at which the preferredmodel was achieved The variance reductions achieved range from 46 to 89 andare typically ca 70 The model norm does not contain the axial-dipole contributionto the roughness and is normalized relative to that contribution

The sequence of models from 1000 BC to AD 1800 is presented in shy gure 3 using thesame format as in shy gure 1 note however that the non-axial-dipole contribution to Br

at the CMB (BrNAD) is on a dinoterent colour scale There is clearly a coherent temporal

evolution of these shy eld models with structures persisting for hundreds of years andgradually evolving into new features Since each model is a snapshot in time andindependent of the data in adjacent temporal slots this reregects well on the quality ofthe observations and the care taken in selecting them There is signishy cant evolvingnon-zonal structure in the shy eld models whose character appears quite distinct in thedinoterent representations of the shy eld Br at the CMB is dominated by the axial-dipoleshy eld contribution but changes in shy eld structure can be seen these are revealed moreclearly in the second column of shy gures from which the axial-dipole contribution hasbeen subtracted From this we see that from 1000 BC until 600 BC the regux lobe overAsia was dominant and there was a positive anomaly in BrNAD

over western NorthAmerica extending across the Pacishy c past Hawaii The North American regux lobe isonly occasionally visible during this time Southern Hemisphere shy eld structure is verysmooth reregecting the paucity of data there Large negative inclination anomaliesin the central Pacishy c region and positive ones centred in the Indian Ocean areassociated with these structures The focus of these inclination anomalies in dinoterentgeographic regions from the radial shy eld anomalies reregects the dinoterent CMB samplingkernels for the radial shy eld inclination and declination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1001

Br 1000 BCndash375ndash225ndash7575225375

Br 900 BC

Br 800 BC

Br 700 BC

Br 600 BC

Br NAD 1000 BCndash160

ndash80

0

80

160

Br NAD 900 BC

Br NAD 800 BC

Br NAD 700 BC

Br NAD 600 BC

inclination anomaly 1000 BCndash12ndash8ndash404812

inclination anomaly 900 BC

inclination anomaly 800 BC

inclination anomaly 700 BC

inclination anomaly 600 BC

declination 1000 BC

declination 900 BC

declination 800 BC

declination 700 BC

declination 600 BC

(i)

Br 500 BCndash375ndash225ndash7575225375

Br 400 BC

Br 300 BC

Br 200 BC

Br 100 BC

Br NAD 500 BCndash160

ndash80

0

80

160

Br NAD 400 BC

Br NAD 300 BC

Br NAD 200 BC

Br NAD 100 BC

inclination anomaly 500 BCndash12ndash8ndash404812

inclination anomaly 400 BC

inclination anomaly 300 BC

inclination anomaly 200 BC

inclination anomaly 100 BC

declination 500 BC

declination 400 BC

declination 300 BC

declination 200 BC

declination 100 BC

(ii)

Figure 3 Snapshots of Br (75 mT contour interval) Br NAD (40 mT contour interval) inclinationanomaly at the Earthrsquo s surface and declination (contour interval 2 ) for models every 100 yearsfrom 1000 BC to AD 1800 Colour bars sit to the right of the parameter plotted except for thedeclination which has the same scale as the inclination

Phil Trans R Soc Lond A (2000)

1002 C G Constable C L Johnson and S P Lund

Br 0 ADndash375ndash225ndash7575225375

Br 100 AD

Br 200 AD

Br 300 AD

Br 400 AD

Br NAD 0 ADndash160

ndash80

0

80

160

Br NAD 100 AD

Br NAD 200 AD

Br NAD 300 AD

Br NAD 400 AD

inclination anomaly 0 ADndash12ndash8ndash404812

inclination anomaly 100 AD

inclination anomaly 200 AD

inclination anomaly 300 AD

inclination anomaly 400 AD

declination 0 AD

declination 100 AD

declination 200 AD

declination 300 AD

declination 400 AD

(iii)

Br 500 ADndash375ndash225ndash7575225375

Br 600 AD

Br 700 AD

Br 800 AD

Br 900 AD

Br NAD 500 ADndash160

ndash80

0

80

160

Br NAD 600 AD

Br NAD 700 AD

Br NAD 800 AD

Br NAD 900 AD

inclination anomaly 500 ADndash12ndash8ndash404812

inclination anomaly 600 AD

inclination anomaly 700 AD

inclination anomaly 800 AD

inclination anomaly 900 AD

declination 500 AD

declination 600 AD

declination 700 AD

declination 800 AD

declination 900 AD

(iv)

Figure 3 (Cont)

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 995

for example McElhinny et al 1996b Carlut amp Courtillot 1998) Theory 2 drawson recent analyses of historical secular variation (Bloxham et al 1989 Bloxham ampJackson 1992) in which it is observed that westward drift is conshy ned to one partof the core surface there is no tendency to drift through a full rotation and littlesecular variation in the Pacishy c This may be interpreted as evidence that the core isinreguenced by the solid mantle resulting in a non-axisymmetric contribution to thetime-averaged geomagnetic shy eld Over 5 Myr or even 3 kyr the departures of thetime-averaged shy eld from axisymmetry are small and because of limitations in thedatasets both theory 1 and theory 2 remain plausible interpretations of the time-averaged shy eld structure (Carlut amp Courtillot 1998 Gubbins amp Kelly 1993 Kelly ampGubbins 1997 Johnson amp Constable 1995 1997 1998) However the dataset to bedescribed in the next section allows the development of models at 100-year intervalsJudging from UFM1 the signal over such 100-year time-intervals should be largein comparison with the results of shy gure 1el and despite the rather sparse globaldistribution of sites there remains the facility to track any possible evolution of theregux lobes and apparently unusual Pacishy c secular variation The resolution of thislongstanding question of the inreguence of the lower mantle on the geodynamo fromthe perspective of shy eld behaviour consistent with palaeomagnetic data is importantThree-dimensional numerical simulations of the geodynamo investigating dinoterentspatial variations in heat regow across the CMB are already being carried out (Glatz-maier et al 1999 Bloxham 1998) and independent investigations focusing on theproperties of palaeomagnetic datasets provide important ground truthing for suchsimulations Furthermore if heat-regow patterns across the CMB inreguence geodynamoprocesses there are implications for the geomagnetic shy eld over longer time-scalesthan the past 5 Myr since the thermal structure of the lower mantle has certainlychanged over time-scales of 107 to 108 yr (Richards amp Engebretson 1992 Lithgow-Bertelloni amp Richards 1998) Greatly enhanced electrical conductivity in D00 beneaththe Pacishy c region (see for example Runcorn 1992) has also been considered as apossible mechanism for attenuating geomagnetic secular variations at the Earthrsquossurface and inreguences on virtual geomagnetic pole (VGP) paths during reversalsFurther examinations of the inreguence of electromagnetic torques on the mantle dueto the poloidal shy eld led initially to suggestions that heterogeneity in mantle conduc-tivity is a plausible mechanism (Arnou et al 1996) to inreguence the trajectory of theVGP during reversals Later work with a more complete consideration of the problemled to a reversal of this opinion (Brito et al 1999) Most recently Holme (2000) hasargued that the conductance required for such a mechanism is inconsistent with theobserved coremantle angular momentum exchange on decadal time-scales

In what follows we brieregy review the PSVMOD10 dataset described in detailby Lund amp Constable (2000) and the methodology for constructing models (alsodescribed elsewhere see Johnson amp Constable (1995 1997)) We present `snapshotsrsquoof the geomagnetic shy eld|models at 100-year intervals|and discuss the evolutionand secular variations of features observed both at the CMB and at the Earthrsquossurface

2 The PSVMOD10 dataset

PSVMOD10 consists of model time-series at 24 globally distributed sites (locationsindicated by the triangles on shy gure 1eh each of which contribute palaeomagnetic

Phil Trans R Soc Lond A (2000)

996 C G Constable C L Johnson and S P Lund

Table 1 Sites contributing to the macreld models for the periods 1000 BC to AD 1800

code latitude longitude class

WUS 350 N 2500 E 1A

JPN 350 N 1350 E 1A

SEU 400 N 200 E 1A

UKR 500 N 300 E 1A

WUR 500 N 00 E 1A

HAW 200 N 2050 E 1B

MAM 170 N 2650 E 1B

PRC 350 N 1150 E 1B

CAU 400 N 450 E 1C

NZE 358 S 1749 E 2A

AUS 380 S 1450 E 2B

MON 460 N 1060 E 2C

BAI 524 N 1061 E 3A

FIS 426 N 2414 E 3A

ICE 660 N 3370 E 3A

KEI 382 S 1429 E 3A

LEB 419 N 2801 E 3A

LLO 561 N 3553 E 3A

LSC 450 N 2672 E 3A

POU 413 S 1752 E 3A

VUK 634 N 286 E 3B

ARG 410 S 2885 E 3B

EAC 173 S 1061 E 3B

TUR 26 N 366 E 3C

records of declination and inclination at 100-year intervals when available) Eachtime-series was developed from composite archaeomagnetic or sediment palaeosecularvariation data with independent good-quality age control Where 14C dating was usedin the original studies the time-scale has been transformed to calendar years usingthe calibration of Clark (1975) Lund amp Constable (2000) classishy ed data for eachtime-series as follows

Class 1 archaeomagnetic directional records with sumacr cient data to characterize thepattern of shy eld variability

Class 2 fragmentary archaeomagnetic data (inclination-only short-duration largedata gaps)

Class 3 sediment directional records

It is assumed that the lower the number of the record type the better the dataquality Relative data quality within each record type was also indicated by a letterbetween A and D with A indicating the best quality records We note that theseclassishy cations are purely qualitative and in attempting to assign numerical uncer-tainties to PSVMOD10 for use in our later inversions we have made an independentassessment based on comparisons with historical data Table 1 gives the site loca-tions and the classishy cation codes for each site and the temporal completeness of the

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 997

2000

1500

1000

500 0

ndash500

ndash1000

age (ndashBC+AD)

wus

arg

aus

bai

cau

eac

fis

haw

ice

jpn

kei

leb

llo

Isc

mam

mon

nze

pou

prc

seu

tur

ukr

vuk

wur

Figure 2 Temporal sampling at each site a triangle (circle) at the time point indicates theexistence of a 100-year sample of declination (inclination) at the indicated site

Phil Trans R Soc Lond A (2000)

998 C G Constable C L Johnson and S P Lund

records is shown in shy gure 2 where a triangle at a given time above the site codeindicates the existence of a 100-year sample for declination and a circle indicatesinclination The 100-year sample is not a direct average of the shy eld direction overthe 100-year interval but an evaluation at the indicated time based on a compositecurve from multiple observations In general each `datumrsquo represents something likea 2030-year average of the shy eld depending somewhat on the dating resolution andthe general quality of the record Age uncertainty is generally larger for sedimentsthan for archaeomagnetic sites We note that the coverage in the Southern Hemi-sphere is very sparse for some time-intervals a point to be kept in mind in evaluatingthe models derived in the next section

Lund amp Constable (2000) discuss the possible causes of uncertainty in the PSV-MOD10 directions in some detail There are shy ve sources of uncertainty in our obser-vations

(i) error in the shy eld direction recorded by the rock sample on acquisition of depo-sitional or thermal remanence

(ii) contamination of the direction from the core shy eld by local magnetic shy eld anoma-lies

(iii) uncertainty in the age at which magnetic remanence was acquired

(iv) orientation errors during sampling and

(v) inadequate magnetic cleaning in the palaeomagnetic laboratory such that thecharacteristic remanence direction may not be recovered

The combined inreguence of these processes can be estimated by comparing PSV-MOD10 with corresponding predictions from Bloxham amp Jacksonrsquos (1992) UFM inthe post-AD 1690 time period Sixteen sites have directions for AD 1800 and 20 forAD 1700 the archaeomagnetic sites tend to have more complete records in the veryrecent past because the top of lake-sediment cores is often disturbed in the coringprocess Absolute orientation of the archaeomagnetic samples also tends to be moreaccurate because it is rare for absolute records of declination to be acquired duringcoring The average deviation for all sites from UFM is close to zero and usingthe available comparisons standard errors of 25 were assigned to both declinationand inclination measurements derived from archaeomagnetic sources while for lakesediments standard errors of 35 and 50 were assigned to inclination and decli-nation respectively Experimentation suggests that in general the largest source ofuncertainty in our observations is the secular variation itself which combined withuncertainties in age can contribute the major part of the observed deviation fromUFM predictions

Lund amp Constable (2000) plot average declination and inclination anomalies forPSVMOD10 relative to a geocentric axial dipole and compare them with similarsite residuals for both UFM and LSN1 The signal in PSVMOD10 is generally inter-mediate in magnitude between that in UFM and LSN1 reregecting the time-scale overwhich the various records are averaged All models show coherent spatial structuresin the residuals over areas several thousand kilometres across but there are some sig-nishy cant dinoterences between these structures over the three time-intervals representedhere For example at TUR in Kenya PSVMOD10 exhibits a positive inclination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 999

Table 2

iteration starting macrnal variance model

epoch no RMS RMS reduction norm

AD 1800 05 302 100 890 130

AD 1700 07 240 100 826 193

AD 1600 14 238 100 823 328

AD 1500 08 220 152 523 140

AD 1400 11 199 127 593 166

AD 1300 09 208 130 609 136

AD 1200 07 266 138 731 192

AD 1100 07 308 142 787 306

AD 1000 07 319 139 810 213

AD 900 09 289 144 752 165

AD 800 09 233 123 721 108

AD 700 09 254 157 618 215

AD 600 09 279 190 536 185

AD 500 11 251 154 624 158

AD 400 09 226 145 588 144

AD 300 08 212 135 594 167

AD 200 06 217 141 578 129

AD 100 09 200 131 571 174

AD 0 08 228 167 464 209

100 BC 07 243 179 457 167

200 BC 17 232 155 554 215

300 BC 07 289 180 612 202

400 BC 05 309 179 664 181

500 BC 07 397 215 707 241

600 BC 07 453 214 777 318

700 BC 03 528 293 692 298

800 BC 03 526 251 772 350

900 BC 04 471 236 749 274

1000 BC 05 372 187 747 205

anomaly while both LSN1 and UFM show negative values While we cannot rule outthe possibility of some systematic errors in PSVMOD10 and we can certainly lookfor improved geographic and temporal coverage in the future the analyses of Lundamp Constable (2000) demonstrate good regional coherence and general reliability ofthe time-series

3 Models

The detailed evaluation of the archaeomagnetic dataset described in Lund amp Con-stable (2000) and summarized in the previous section permits the investigation ofthe evolution of the global geomagnetic shy eld over the past 3000 years Figure 1 showsthat the recent time-averaged structure of the shy eld as seen in UFM1 is quite dinoter-ent from that for the past 3 kyr and thus we might expect signishy cant changes inglobal shy eld behaviour Spherical harmonic models of the geomagnetic shy eld were con-

Phil Trans R Soc Lond A (2000)

1000 C G Constable C L Johnson and S P Lund

structed at 100-year intervals using data from as many sites as are available (shy gure 2)at each time-interval The modelling procedure follows that used in the generationof time-averaged shy eld models for the periods 05 Ma and 03 Ka and details can befound elsewhere (Johnson amp Constable 1995 1997 1998) The scalar geomagneticpotential is described in terms of a spherical harmonic expansion and thus ourmeasurements of declination and inclination are nonlinearly related to the sphericalharmonic coemacr cients which are the model parameters We use an iterative nonlinearinversion procedure modishy ed for geomagnetic shy eld modelling from Constable et al rsquos(1987) Occamrsquos inversion algorithm our models are regularized by minimizing themean square value of the non-axial-dipole part of the radial magnetic shy eld (Br) atthe CMB while shy tting the data to a specishy ed tolerance As discussed by Johnsonamp Constable (1997) in the context of constructing LSN1 our model choice dependscritically upon the minimum acceptable misshy t to our observations designated in theprevious section Under the assumption that these uncertainties are independentzero-mean Gaussian variables the target misshy t of the model to our data will corre-spond to the expected value of Agrave 2

N which is N when the misshy t is normalized by thedata uncertainties In practice the target value for the misshy t was not always attain-able without generating overly complicated shy eld models we therefore compromiseand select models with a plausible degree of roughness and a slightly higher misshy tto the observations The necessity for this probably indicates that our use of UFM tocalibrate the uncertainties in PSVMOD10 is not adequate to deal with variations indata quality as they extend further into the past Table 2 lists the initial RMS signalin the data (measured relative to GAD and normalized by the standard error) theRMS of the shy nal model the percentage variance reduction the roughness of theshy nal model (model norm) for each epoch and the iteration at which the preferredmodel was achieved The variance reductions achieved range from 46 to 89 andare typically ca 70 The model norm does not contain the axial-dipole contributionto the roughness and is normalized relative to that contribution

The sequence of models from 1000 BC to AD 1800 is presented in shy gure 3 using thesame format as in shy gure 1 note however that the non-axial-dipole contribution to Br

at the CMB (BrNAD) is on a dinoterent colour scale There is clearly a coherent temporal

evolution of these shy eld models with structures persisting for hundreds of years andgradually evolving into new features Since each model is a snapshot in time andindependent of the data in adjacent temporal slots this reregects well on the quality ofthe observations and the care taken in selecting them There is signishy cant evolvingnon-zonal structure in the shy eld models whose character appears quite distinct in thedinoterent representations of the shy eld Br at the CMB is dominated by the axial-dipoleshy eld contribution but changes in shy eld structure can be seen these are revealed moreclearly in the second column of shy gures from which the axial-dipole contribution hasbeen subtracted From this we see that from 1000 BC until 600 BC the regux lobe overAsia was dominant and there was a positive anomaly in BrNAD

over western NorthAmerica extending across the Pacishy c past Hawaii The North American regux lobe isonly occasionally visible during this time Southern Hemisphere shy eld structure is verysmooth reregecting the paucity of data there Large negative inclination anomaliesin the central Pacishy c region and positive ones centred in the Indian Ocean areassociated with these structures The focus of these inclination anomalies in dinoterentgeographic regions from the radial shy eld anomalies reregects the dinoterent CMB samplingkernels for the radial shy eld inclination and declination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1001

Br 1000 BCndash375ndash225ndash7575225375

Br 900 BC

Br 800 BC

Br 700 BC

Br 600 BC

Br NAD 1000 BCndash160

ndash80

0

80

160

Br NAD 900 BC

Br NAD 800 BC

Br NAD 700 BC

Br NAD 600 BC

inclination anomaly 1000 BCndash12ndash8ndash404812

inclination anomaly 900 BC

inclination anomaly 800 BC

inclination anomaly 700 BC

inclination anomaly 600 BC

declination 1000 BC

declination 900 BC

declination 800 BC

declination 700 BC

declination 600 BC

(i)

Br 500 BCndash375ndash225ndash7575225375

Br 400 BC

Br 300 BC

Br 200 BC

Br 100 BC

Br NAD 500 BCndash160

ndash80

0

80

160

Br NAD 400 BC

Br NAD 300 BC

Br NAD 200 BC

Br NAD 100 BC

inclination anomaly 500 BCndash12ndash8ndash404812

inclination anomaly 400 BC

inclination anomaly 300 BC

inclination anomaly 200 BC

inclination anomaly 100 BC

declination 500 BC

declination 400 BC

declination 300 BC

declination 200 BC

declination 100 BC

(ii)

Figure 3 Snapshots of Br (75 mT contour interval) Br NAD (40 mT contour interval) inclinationanomaly at the Earthrsquo s surface and declination (contour interval 2 ) for models every 100 yearsfrom 1000 BC to AD 1800 Colour bars sit to the right of the parameter plotted except for thedeclination which has the same scale as the inclination

Phil Trans R Soc Lond A (2000)

1002 C G Constable C L Johnson and S P Lund

Br 0 ADndash375ndash225ndash7575225375

Br 100 AD

Br 200 AD

Br 300 AD

Br 400 AD

Br NAD 0 ADndash160

ndash80

0

80

160

Br NAD 100 AD

Br NAD 200 AD

Br NAD 300 AD

Br NAD 400 AD

inclination anomaly 0 ADndash12ndash8ndash404812

inclination anomaly 100 AD

inclination anomaly 200 AD

inclination anomaly 300 AD

inclination anomaly 400 AD

declination 0 AD

declination 100 AD

declination 200 AD

declination 300 AD

declination 400 AD

(iii)

Br 500 ADndash375ndash225ndash7575225375

Br 600 AD

Br 700 AD

Br 800 AD

Br 900 AD

Br NAD 500 ADndash160

ndash80

0

80

160

Br NAD 600 AD

Br NAD 700 AD

Br NAD 800 AD

Br NAD 900 AD

inclination anomaly 500 ADndash12ndash8ndash404812

inclination anomaly 600 AD

inclination anomaly 700 AD

inclination anomaly 800 AD

inclination anomaly 900 AD

declination 500 AD

declination 600 AD

declination 700 AD

declination 800 AD

declination 900 AD

(iv)

Figure 3 (Cont)

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

996 C G Constable C L Johnson and S P Lund

Table 1 Sites contributing to the macreld models for the periods 1000 BC to AD 1800

code latitude longitude class

WUS 350 N 2500 E 1A

JPN 350 N 1350 E 1A

SEU 400 N 200 E 1A

UKR 500 N 300 E 1A

WUR 500 N 00 E 1A

HAW 200 N 2050 E 1B

MAM 170 N 2650 E 1B

PRC 350 N 1150 E 1B

CAU 400 N 450 E 1C

NZE 358 S 1749 E 2A

AUS 380 S 1450 E 2B

MON 460 N 1060 E 2C

BAI 524 N 1061 E 3A

FIS 426 N 2414 E 3A

ICE 660 N 3370 E 3A

KEI 382 S 1429 E 3A

LEB 419 N 2801 E 3A

LLO 561 N 3553 E 3A

LSC 450 N 2672 E 3A

POU 413 S 1752 E 3A

VUK 634 N 286 E 3B

ARG 410 S 2885 E 3B

EAC 173 S 1061 E 3B

TUR 26 N 366 E 3C

records of declination and inclination at 100-year intervals when available) Eachtime-series was developed from composite archaeomagnetic or sediment palaeosecularvariation data with independent good-quality age control Where 14C dating was usedin the original studies the time-scale has been transformed to calendar years usingthe calibration of Clark (1975) Lund amp Constable (2000) classishy ed data for eachtime-series as follows

Class 1 archaeomagnetic directional records with sumacr cient data to characterize thepattern of shy eld variability

Class 2 fragmentary archaeomagnetic data (inclination-only short-duration largedata gaps)

Class 3 sediment directional records

It is assumed that the lower the number of the record type the better the dataquality Relative data quality within each record type was also indicated by a letterbetween A and D with A indicating the best quality records We note that theseclassishy cations are purely qualitative and in attempting to assign numerical uncer-tainties to PSVMOD10 for use in our later inversions we have made an independentassessment based on comparisons with historical data Table 1 gives the site loca-tions and the classishy cation codes for each site and the temporal completeness of the

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 997

2000

1500

1000

500 0

ndash500

ndash1000

age (ndashBC+AD)

wus

arg

aus

bai

cau

eac

fis

haw

ice

jpn

kei

leb

llo

Isc

mam

mon

nze

pou

prc

seu

tur

ukr

vuk

wur

Figure 2 Temporal sampling at each site a triangle (circle) at the time point indicates theexistence of a 100-year sample of declination (inclination) at the indicated site

Phil Trans R Soc Lond A (2000)

998 C G Constable C L Johnson and S P Lund

records is shown in shy gure 2 where a triangle at a given time above the site codeindicates the existence of a 100-year sample for declination and a circle indicatesinclination The 100-year sample is not a direct average of the shy eld direction overthe 100-year interval but an evaluation at the indicated time based on a compositecurve from multiple observations In general each `datumrsquo represents something likea 2030-year average of the shy eld depending somewhat on the dating resolution andthe general quality of the record Age uncertainty is generally larger for sedimentsthan for archaeomagnetic sites We note that the coverage in the Southern Hemi-sphere is very sparse for some time-intervals a point to be kept in mind in evaluatingthe models derived in the next section

Lund amp Constable (2000) discuss the possible causes of uncertainty in the PSV-MOD10 directions in some detail There are shy ve sources of uncertainty in our obser-vations

(i) error in the shy eld direction recorded by the rock sample on acquisition of depo-sitional or thermal remanence

(ii) contamination of the direction from the core shy eld by local magnetic shy eld anoma-lies

(iii) uncertainty in the age at which magnetic remanence was acquired

(iv) orientation errors during sampling and

(v) inadequate magnetic cleaning in the palaeomagnetic laboratory such that thecharacteristic remanence direction may not be recovered

The combined inreguence of these processes can be estimated by comparing PSV-MOD10 with corresponding predictions from Bloxham amp Jacksonrsquos (1992) UFM inthe post-AD 1690 time period Sixteen sites have directions for AD 1800 and 20 forAD 1700 the archaeomagnetic sites tend to have more complete records in the veryrecent past because the top of lake-sediment cores is often disturbed in the coringprocess Absolute orientation of the archaeomagnetic samples also tends to be moreaccurate because it is rare for absolute records of declination to be acquired duringcoring The average deviation for all sites from UFM is close to zero and usingthe available comparisons standard errors of 25 were assigned to both declinationand inclination measurements derived from archaeomagnetic sources while for lakesediments standard errors of 35 and 50 were assigned to inclination and decli-nation respectively Experimentation suggests that in general the largest source ofuncertainty in our observations is the secular variation itself which combined withuncertainties in age can contribute the major part of the observed deviation fromUFM predictions

Lund amp Constable (2000) plot average declination and inclination anomalies forPSVMOD10 relative to a geocentric axial dipole and compare them with similarsite residuals for both UFM and LSN1 The signal in PSVMOD10 is generally inter-mediate in magnitude between that in UFM and LSN1 reregecting the time-scale overwhich the various records are averaged All models show coherent spatial structuresin the residuals over areas several thousand kilometres across but there are some sig-nishy cant dinoterences between these structures over the three time-intervals representedhere For example at TUR in Kenya PSVMOD10 exhibits a positive inclination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 999

Table 2

iteration starting macrnal variance model

epoch no RMS RMS reduction norm

AD 1800 05 302 100 890 130

AD 1700 07 240 100 826 193

AD 1600 14 238 100 823 328

AD 1500 08 220 152 523 140

AD 1400 11 199 127 593 166

AD 1300 09 208 130 609 136

AD 1200 07 266 138 731 192

AD 1100 07 308 142 787 306

AD 1000 07 319 139 810 213

AD 900 09 289 144 752 165

AD 800 09 233 123 721 108

AD 700 09 254 157 618 215

AD 600 09 279 190 536 185

AD 500 11 251 154 624 158

AD 400 09 226 145 588 144

AD 300 08 212 135 594 167

AD 200 06 217 141 578 129

AD 100 09 200 131 571 174

AD 0 08 228 167 464 209

100 BC 07 243 179 457 167

200 BC 17 232 155 554 215

300 BC 07 289 180 612 202

400 BC 05 309 179 664 181

500 BC 07 397 215 707 241

600 BC 07 453 214 777 318

700 BC 03 528 293 692 298

800 BC 03 526 251 772 350

900 BC 04 471 236 749 274

1000 BC 05 372 187 747 205

anomaly while both LSN1 and UFM show negative values While we cannot rule outthe possibility of some systematic errors in PSVMOD10 and we can certainly lookfor improved geographic and temporal coverage in the future the analyses of Lundamp Constable (2000) demonstrate good regional coherence and general reliability ofthe time-series

3 Models

The detailed evaluation of the archaeomagnetic dataset described in Lund amp Con-stable (2000) and summarized in the previous section permits the investigation ofthe evolution of the global geomagnetic shy eld over the past 3000 years Figure 1 showsthat the recent time-averaged structure of the shy eld as seen in UFM1 is quite dinoter-ent from that for the past 3 kyr and thus we might expect signishy cant changes inglobal shy eld behaviour Spherical harmonic models of the geomagnetic shy eld were con-

Phil Trans R Soc Lond A (2000)

1000 C G Constable C L Johnson and S P Lund

structed at 100-year intervals using data from as many sites as are available (shy gure 2)at each time-interval The modelling procedure follows that used in the generationof time-averaged shy eld models for the periods 05 Ma and 03 Ka and details can befound elsewhere (Johnson amp Constable 1995 1997 1998) The scalar geomagneticpotential is described in terms of a spherical harmonic expansion and thus ourmeasurements of declination and inclination are nonlinearly related to the sphericalharmonic coemacr cients which are the model parameters We use an iterative nonlinearinversion procedure modishy ed for geomagnetic shy eld modelling from Constable et al rsquos(1987) Occamrsquos inversion algorithm our models are regularized by minimizing themean square value of the non-axial-dipole part of the radial magnetic shy eld (Br) atthe CMB while shy tting the data to a specishy ed tolerance As discussed by Johnsonamp Constable (1997) in the context of constructing LSN1 our model choice dependscritically upon the minimum acceptable misshy t to our observations designated in theprevious section Under the assumption that these uncertainties are independentzero-mean Gaussian variables the target misshy t of the model to our data will corre-spond to the expected value of Agrave 2

N which is N when the misshy t is normalized by thedata uncertainties In practice the target value for the misshy t was not always attain-able without generating overly complicated shy eld models we therefore compromiseand select models with a plausible degree of roughness and a slightly higher misshy tto the observations The necessity for this probably indicates that our use of UFM tocalibrate the uncertainties in PSVMOD10 is not adequate to deal with variations indata quality as they extend further into the past Table 2 lists the initial RMS signalin the data (measured relative to GAD and normalized by the standard error) theRMS of the shy nal model the percentage variance reduction the roughness of theshy nal model (model norm) for each epoch and the iteration at which the preferredmodel was achieved The variance reductions achieved range from 46 to 89 andare typically ca 70 The model norm does not contain the axial-dipole contributionto the roughness and is normalized relative to that contribution

The sequence of models from 1000 BC to AD 1800 is presented in shy gure 3 using thesame format as in shy gure 1 note however that the non-axial-dipole contribution to Br

at the CMB (BrNAD) is on a dinoterent colour scale There is clearly a coherent temporal

evolution of these shy eld models with structures persisting for hundreds of years andgradually evolving into new features Since each model is a snapshot in time andindependent of the data in adjacent temporal slots this reregects well on the quality ofthe observations and the care taken in selecting them There is signishy cant evolvingnon-zonal structure in the shy eld models whose character appears quite distinct in thedinoterent representations of the shy eld Br at the CMB is dominated by the axial-dipoleshy eld contribution but changes in shy eld structure can be seen these are revealed moreclearly in the second column of shy gures from which the axial-dipole contribution hasbeen subtracted From this we see that from 1000 BC until 600 BC the regux lobe overAsia was dominant and there was a positive anomaly in BrNAD

over western NorthAmerica extending across the Pacishy c past Hawaii The North American regux lobe isonly occasionally visible during this time Southern Hemisphere shy eld structure is verysmooth reregecting the paucity of data there Large negative inclination anomaliesin the central Pacishy c region and positive ones centred in the Indian Ocean areassociated with these structures The focus of these inclination anomalies in dinoterentgeographic regions from the radial shy eld anomalies reregects the dinoterent CMB samplingkernels for the radial shy eld inclination and declination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1001

Br 1000 BCndash375ndash225ndash7575225375

Br 900 BC

Br 800 BC

Br 700 BC

Br 600 BC

Br NAD 1000 BCndash160

ndash80

0

80

160

Br NAD 900 BC

Br NAD 800 BC

Br NAD 700 BC

Br NAD 600 BC

inclination anomaly 1000 BCndash12ndash8ndash404812

inclination anomaly 900 BC

inclination anomaly 800 BC

inclination anomaly 700 BC

inclination anomaly 600 BC

declination 1000 BC

declination 900 BC

declination 800 BC

declination 700 BC

declination 600 BC

(i)

Br 500 BCndash375ndash225ndash7575225375

Br 400 BC

Br 300 BC

Br 200 BC

Br 100 BC

Br NAD 500 BCndash160

ndash80

0

80

160

Br NAD 400 BC

Br NAD 300 BC

Br NAD 200 BC

Br NAD 100 BC

inclination anomaly 500 BCndash12ndash8ndash404812

inclination anomaly 400 BC

inclination anomaly 300 BC

inclination anomaly 200 BC

inclination anomaly 100 BC

declination 500 BC

declination 400 BC

declination 300 BC

declination 200 BC

declination 100 BC

(ii)

Figure 3 Snapshots of Br (75 mT contour interval) Br NAD (40 mT contour interval) inclinationanomaly at the Earthrsquo s surface and declination (contour interval 2 ) for models every 100 yearsfrom 1000 BC to AD 1800 Colour bars sit to the right of the parameter plotted except for thedeclination which has the same scale as the inclination

Phil Trans R Soc Lond A (2000)

1002 C G Constable C L Johnson and S P Lund

Br 0 ADndash375ndash225ndash7575225375

Br 100 AD

Br 200 AD

Br 300 AD

Br 400 AD

Br NAD 0 ADndash160

ndash80

0

80

160

Br NAD 100 AD

Br NAD 200 AD

Br NAD 300 AD

Br NAD 400 AD

inclination anomaly 0 ADndash12ndash8ndash404812

inclination anomaly 100 AD

inclination anomaly 200 AD

inclination anomaly 300 AD

inclination anomaly 400 AD

declination 0 AD

declination 100 AD

declination 200 AD

declination 300 AD

declination 400 AD

(iii)

Br 500 ADndash375ndash225ndash7575225375

Br 600 AD

Br 700 AD

Br 800 AD

Br 900 AD

Br NAD 500 ADndash160

ndash80

0

80

160

Br NAD 600 AD

Br NAD 700 AD

Br NAD 800 AD

Br NAD 900 AD

inclination anomaly 500 ADndash12ndash8ndash404812

inclination anomaly 600 AD

inclination anomaly 700 AD

inclination anomaly 800 AD

inclination anomaly 900 AD

declination 500 AD

declination 600 AD

declination 700 AD

declination 800 AD

declination 900 AD

(iv)

Figure 3 (Cont)

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 997

2000

1500

1000

500 0

ndash500

ndash1000

age (ndashBC+AD)

wus

arg

aus

bai

cau

eac

fis

haw

ice

jpn

kei

leb

llo

Isc

mam

mon

nze

pou

prc

seu

tur

ukr

vuk

wur

Figure 2 Temporal sampling at each site a triangle (circle) at the time point indicates theexistence of a 100-year sample of declination (inclination) at the indicated site

Phil Trans R Soc Lond A (2000)

998 C G Constable C L Johnson and S P Lund

records is shown in shy gure 2 where a triangle at a given time above the site codeindicates the existence of a 100-year sample for declination and a circle indicatesinclination The 100-year sample is not a direct average of the shy eld direction overthe 100-year interval but an evaluation at the indicated time based on a compositecurve from multiple observations In general each `datumrsquo represents something likea 2030-year average of the shy eld depending somewhat on the dating resolution andthe general quality of the record Age uncertainty is generally larger for sedimentsthan for archaeomagnetic sites We note that the coverage in the Southern Hemi-sphere is very sparse for some time-intervals a point to be kept in mind in evaluatingthe models derived in the next section

Lund amp Constable (2000) discuss the possible causes of uncertainty in the PSV-MOD10 directions in some detail There are shy ve sources of uncertainty in our obser-vations

(i) error in the shy eld direction recorded by the rock sample on acquisition of depo-sitional or thermal remanence

(ii) contamination of the direction from the core shy eld by local magnetic shy eld anoma-lies

(iii) uncertainty in the age at which magnetic remanence was acquired

(iv) orientation errors during sampling and

(v) inadequate magnetic cleaning in the palaeomagnetic laboratory such that thecharacteristic remanence direction may not be recovered

The combined inreguence of these processes can be estimated by comparing PSV-MOD10 with corresponding predictions from Bloxham amp Jacksonrsquos (1992) UFM inthe post-AD 1690 time period Sixteen sites have directions for AD 1800 and 20 forAD 1700 the archaeomagnetic sites tend to have more complete records in the veryrecent past because the top of lake-sediment cores is often disturbed in the coringprocess Absolute orientation of the archaeomagnetic samples also tends to be moreaccurate because it is rare for absolute records of declination to be acquired duringcoring The average deviation for all sites from UFM is close to zero and usingthe available comparisons standard errors of 25 were assigned to both declinationand inclination measurements derived from archaeomagnetic sources while for lakesediments standard errors of 35 and 50 were assigned to inclination and decli-nation respectively Experimentation suggests that in general the largest source ofuncertainty in our observations is the secular variation itself which combined withuncertainties in age can contribute the major part of the observed deviation fromUFM predictions

Lund amp Constable (2000) plot average declination and inclination anomalies forPSVMOD10 relative to a geocentric axial dipole and compare them with similarsite residuals for both UFM and LSN1 The signal in PSVMOD10 is generally inter-mediate in magnitude between that in UFM and LSN1 reregecting the time-scale overwhich the various records are averaged All models show coherent spatial structuresin the residuals over areas several thousand kilometres across but there are some sig-nishy cant dinoterences between these structures over the three time-intervals representedhere For example at TUR in Kenya PSVMOD10 exhibits a positive inclination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 999

Table 2

iteration starting macrnal variance model

epoch no RMS RMS reduction norm

AD 1800 05 302 100 890 130

AD 1700 07 240 100 826 193

AD 1600 14 238 100 823 328

AD 1500 08 220 152 523 140

AD 1400 11 199 127 593 166

AD 1300 09 208 130 609 136

AD 1200 07 266 138 731 192

AD 1100 07 308 142 787 306

AD 1000 07 319 139 810 213

AD 900 09 289 144 752 165

AD 800 09 233 123 721 108

AD 700 09 254 157 618 215

AD 600 09 279 190 536 185

AD 500 11 251 154 624 158

AD 400 09 226 145 588 144

AD 300 08 212 135 594 167

AD 200 06 217 141 578 129

AD 100 09 200 131 571 174

AD 0 08 228 167 464 209

100 BC 07 243 179 457 167

200 BC 17 232 155 554 215

300 BC 07 289 180 612 202

400 BC 05 309 179 664 181

500 BC 07 397 215 707 241

600 BC 07 453 214 777 318

700 BC 03 528 293 692 298

800 BC 03 526 251 772 350

900 BC 04 471 236 749 274

1000 BC 05 372 187 747 205

anomaly while both LSN1 and UFM show negative values While we cannot rule outthe possibility of some systematic errors in PSVMOD10 and we can certainly lookfor improved geographic and temporal coverage in the future the analyses of Lundamp Constable (2000) demonstrate good regional coherence and general reliability ofthe time-series

3 Models

The detailed evaluation of the archaeomagnetic dataset described in Lund amp Con-stable (2000) and summarized in the previous section permits the investigation ofthe evolution of the global geomagnetic shy eld over the past 3000 years Figure 1 showsthat the recent time-averaged structure of the shy eld as seen in UFM1 is quite dinoter-ent from that for the past 3 kyr and thus we might expect signishy cant changes inglobal shy eld behaviour Spherical harmonic models of the geomagnetic shy eld were con-

Phil Trans R Soc Lond A (2000)

1000 C G Constable C L Johnson and S P Lund

structed at 100-year intervals using data from as many sites as are available (shy gure 2)at each time-interval The modelling procedure follows that used in the generationof time-averaged shy eld models for the periods 05 Ma and 03 Ka and details can befound elsewhere (Johnson amp Constable 1995 1997 1998) The scalar geomagneticpotential is described in terms of a spherical harmonic expansion and thus ourmeasurements of declination and inclination are nonlinearly related to the sphericalharmonic coemacr cients which are the model parameters We use an iterative nonlinearinversion procedure modishy ed for geomagnetic shy eld modelling from Constable et al rsquos(1987) Occamrsquos inversion algorithm our models are regularized by minimizing themean square value of the non-axial-dipole part of the radial magnetic shy eld (Br) atthe CMB while shy tting the data to a specishy ed tolerance As discussed by Johnsonamp Constable (1997) in the context of constructing LSN1 our model choice dependscritically upon the minimum acceptable misshy t to our observations designated in theprevious section Under the assumption that these uncertainties are independentzero-mean Gaussian variables the target misshy t of the model to our data will corre-spond to the expected value of Agrave 2

N which is N when the misshy t is normalized by thedata uncertainties In practice the target value for the misshy t was not always attain-able without generating overly complicated shy eld models we therefore compromiseand select models with a plausible degree of roughness and a slightly higher misshy tto the observations The necessity for this probably indicates that our use of UFM tocalibrate the uncertainties in PSVMOD10 is not adequate to deal with variations indata quality as they extend further into the past Table 2 lists the initial RMS signalin the data (measured relative to GAD and normalized by the standard error) theRMS of the shy nal model the percentage variance reduction the roughness of theshy nal model (model norm) for each epoch and the iteration at which the preferredmodel was achieved The variance reductions achieved range from 46 to 89 andare typically ca 70 The model norm does not contain the axial-dipole contributionto the roughness and is normalized relative to that contribution

The sequence of models from 1000 BC to AD 1800 is presented in shy gure 3 using thesame format as in shy gure 1 note however that the non-axial-dipole contribution to Br

at the CMB (BrNAD) is on a dinoterent colour scale There is clearly a coherent temporal

evolution of these shy eld models with structures persisting for hundreds of years andgradually evolving into new features Since each model is a snapshot in time andindependent of the data in adjacent temporal slots this reregects well on the quality ofthe observations and the care taken in selecting them There is signishy cant evolvingnon-zonal structure in the shy eld models whose character appears quite distinct in thedinoterent representations of the shy eld Br at the CMB is dominated by the axial-dipoleshy eld contribution but changes in shy eld structure can be seen these are revealed moreclearly in the second column of shy gures from which the axial-dipole contribution hasbeen subtracted From this we see that from 1000 BC until 600 BC the regux lobe overAsia was dominant and there was a positive anomaly in BrNAD

over western NorthAmerica extending across the Pacishy c past Hawaii The North American regux lobe isonly occasionally visible during this time Southern Hemisphere shy eld structure is verysmooth reregecting the paucity of data there Large negative inclination anomaliesin the central Pacishy c region and positive ones centred in the Indian Ocean areassociated with these structures The focus of these inclination anomalies in dinoterentgeographic regions from the radial shy eld anomalies reregects the dinoterent CMB samplingkernels for the radial shy eld inclination and declination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1001

Br 1000 BCndash375ndash225ndash7575225375

Br 900 BC

Br 800 BC

Br 700 BC

Br 600 BC

Br NAD 1000 BCndash160

ndash80

0

80

160

Br NAD 900 BC

Br NAD 800 BC

Br NAD 700 BC

Br NAD 600 BC

inclination anomaly 1000 BCndash12ndash8ndash404812

inclination anomaly 900 BC

inclination anomaly 800 BC

inclination anomaly 700 BC

inclination anomaly 600 BC

declination 1000 BC

declination 900 BC

declination 800 BC

declination 700 BC

declination 600 BC

(i)

Br 500 BCndash375ndash225ndash7575225375

Br 400 BC

Br 300 BC

Br 200 BC

Br 100 BC

Br NAD 500 BCndash160

ndash80

0

80

160

Br NAD 400 BC

Br NAD 300 BC

Br NAD 200 BC

Br NAD 100 BC

inclination anomaly 500 BCndash12ndash8ndash404812

inclination anomaly 400 BC

inclination anomaly 300 BC

inclination anomaly 200 BC

inclination anomaly 100 BC

declination 500 BC

declination 400 BC

declination 300 BC

declination 200 BC

declination 100 BC

(ii)

Figure 3 Snapshots of Br (75 mT contour interval) Br NAD (40 mT contour interval) inclinationanomaly at the Earthrsquo s surface and declination (contour interval 2 ) for models every 100 yearsfrom 1000 BC to AD 1800 Colour bars sit to the right of the parameter plotted except for thedeclination which has the same scale as the inclination

Phil Trans R Soc Lond A (2000)

1002 C G Constable C L Johnson and S P Lund

Br 0 ADndash375ndash225ndash7575225375

Br 100 AD

Br 200 AD

Br 300 AD

Br 400 AD

Br NAD 0 ADndash160

ndash80

0

80

160

Br NAD 100 AD

Br NAD 200 AD

Br NAD 300 AD

Br NAD 400 AD

inclination anomaly 0 ADndash12ndash8ndash404812

inclination anomaly 100 AD

inclination anomaly 200 AD

inclination anomaly 300 AD

inclination anomaly 400 AD

declination 0 AD

declination 100 AD

declination 200 AD

declination 300 AD

declination 400 AD

(iii)

Br 500 ADndash375ndash225ndash7575225375

Br 600 AD

Br 700 AD

Br 800 AD

Br 900 AD

Br NAD 500 ADndash160

ndash80

0

80

160

Br NAD 600 AD

Br NAD 700 AD

Br NAD 800 AD

Br NAD 900 AD

inclination anomaly 500 ADndash12ndash8ndash404812

inclination anomaly 600 AD

inclination anomaly 700 AD

inclination anomaly 800 AD

inclination anomaly 900 AD

declination 500 AD

declination 600 AD

declination 700 AD

declination 800 AD

declination 900 AD

(iv)

Figure 3 (Cont)

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

998 C G Constable C L Johnson and S P Lund

records is shown in shy gure 2 where a triangle at a given time above the site codeindicates the existence of a 100-year sample for declination and a circle indicatesinclination The 100-year sample is not a direct average of the shy eld direction overthe 100-year interval but an evaluation at the indicated time based on a compositecurve from multiple observations In general each `datumrsquo represents something likea 2030-year average of the shy eld depending somewhat on the dating resolution andthe general quality of the record Age uncertainty is generally larger for sedimentsthan for archaeomagnetic sites We note that the coverage in the Southern Hemi-sphere is very sparse for some time-intervals a point to be kept in mind in evaluatingthe models derived in the next section

Lund amp Constable (2000) discuss the possible causes of uncertainty in the PSV-MOD10 directions in some detail There are shy ve sources of uncertainty in our obser-vations

(i) error in the shy eld direction recorded by the rock sample on acquisition of depo-sitional or thermal remanence

(ii) contamination of the direction from the core shy eld by local magnetic shy eld anoma-lies

(iii) uncertainty in the age at which magnetic remanence was acquired

(iv) orientation errors during sampling and

(v) inadequate magnetic cleaning in the palaeomagnetic laboratory such that thecharacteristic remanence direction may not be recovered

The combined inreguence of these processes can be estimated by comparing PSV-MOD10 with corresponding predictions from Bloxham amp Jacksonrsquos (1992) UFM inthe post-AD 1690 time period Sixteen sites have directions for AD 1800 and 20 forAD 1700 the archaeomagnetic sites tend to have more complete records in the veryrecent past because the top of lake-sediment cores is often disturbed in the coringprocess Absolute orientation of the archaeomagnetic samples also tends to be moreaccurate because it is rare for absolute records of declination to be acquired duringcoring The average deviation for all sites from UFM is close to zero and usingthe available comparisons standard errors of 25 were assigned to both declinationand inclination measurements derived from archaeomagnetic sources while for lakesediments standard errors of 35 and 50 were assigned to inclination and decli-nation respectively Experimentation suggests that in general the largest source ofuncertainty in our observations is the secular variation itself which combined withuncertainties in age can contribute the major part of the observed deviation fromUFM predictions

Lund amp Constable (2000) plot average declination and inclination anomalies forPSVMOD10 relative to a geocentric axial dipole and compare them with similarsite residuals for both UFM and LSN1 The signal in PSVMOD10 is generally inter-mediate in magnitude between that in UFM and LSN1 reregecting the time-scale overwhich the various records are averaged All models show coherent spatial structuresin the residuals over areas several thousand kilometres across but there are some sig-nishy cant dinoterences between these structures over the three time-intervals representedhere For example at TUR in Kenya PSVMOD10 exhibits a positive inclination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 999

Table 2

iteration starting macrnal variance model

epoch no RMS RMS reduction norm

AD 1800 05 302 100 890 130

AD 1700 07 240 100 826 193

AD 1600 14 238 100 823 328

AD 1500 08 220 152 523 140

AD 1400 11 199 127 593 166

AD 1300 09 208 130 609 136

AD 1200 07 266 138 731 192

AD 1100 07 308 142 787 306

AD 1000 07 319 139 810 213

AD 900 09 289 144 752 165

AD 800 09 233 123 721 108

AD 700 09 254 157 618 215

AD 600 09 279 190 536 185

AD 500 11 251 154 624 158

AD 400 09 226 145 588 144

AD 300 08 212 135 594 167

AD 200 06 217 141 578 129

AD 100 09 200 131 571 174

AD 0 08 228 167 464 209

100 BC 07 243 179 457 167

200 BC 17 232 155 554 215

300 BC 07 289 180 612 202

400 BC 05 309 179 664 181

500 BC 07 397 215 707 241

600 BC 07 453 214 777 318

700 BC 03 528 293 692 298

800 BC 03 526 251 772 350

900 BC 04 471 236 749 274

1000 BC 05 372 187 747 205

anomaly while both LSN1 and UFM show negative values While we cannot rule outthe possibility of some systematic errors in PSVMOD10 and we can certainly lookfor improved geographic and temporal coverage in the future the analyses of Lundamp Constable (2000) demonstrate good regional coherence and general reliability ofthe time-series

3 Models

The detailed evaluation of the archaeomagnetic dataset described in Lund amp Con-stable (2000) and summarized in the previous section permits the investigation ofthe evolution of the global geomagnetic shy eld over the past 3000 years Figure 1 showsthat the recent time-averaged structure of the shy eld as seen in UFM1 is quite dinoter-ent from that for the past 3 kyr and thus we might expect signishy cant changes inglobal shy eld behaviour Spherical harmonic models of the geomagnetic shy eld were con-

Phil Trans R Soc Lond A (2000)

1000 C G Constable C L Johnson and S P Lund

structed at 100-year intervals using data from as many sites as are available (shy gure 2)at each time-interval The modelling procedure follows that used in the generationof time-averaged shy eld models for the periods 05 Ma and 03 Ka and details can befound elsewhere (Johnson amp Constable 1995 1997 1998) The scalar geomagneticpotential is described in terms of a spherical harmonic expansion and thus ourmeasurements of declination and inclination are nonlinearly related to the sphericalharmonic coemacr cients which are the model parameters We use an iterative nonlinearinversion procedure modishy ed for geomagnetic shy eld modelling from Constable et al rsquos(1987) Occamrsquos inversion algorithm our models are regularized by minimizing themean square value of the non-axial-dipole part of the radial magnetic shy eld (Br) atthe CMB while shy tting the data to a specishy ed tolerance As discussed by Johnsonamp Constable (1997) in the context of constructing LSN1 our model choice dependscritically upon the minimum acceptable misshy t to our observations designated in theprevious section Under the assumption that these uncertainties are independentzero-mean Gaussian variables the target misshy t of the model to our data will corre-spond to the expected value of Agrave 2

N which is N when the misshy t is normalized by thedata uncertainties In practice the target value for the misshy t was not always attain-able without generating overly complicated shy eld models we therefore compromiseand select models with a plausible degree of roughness and a slightly higher misshy tto the observations The necessity for this probably indicates that our use of UFM tocalibrate the uncertainties in PSVMOD10 is not adequate to deal with variations indata quality as they extend further into the past Table 2 lists the initial RMS signalin the data (measured relative to GAD and normalized by the standard error) theRMS of the shy nal model the percentage variance reduction the roughness of theshy nal model (model norm) for each epoch and the iteration at which the preferredmodel was achieved The variance reductions achieved range from 46 to 89 andare typically ca 70 The model norm does not contain the axial-dipole contributionto the roughness and is normalized relative to that contribution

The sequence of models from 1000 BC to AD 1800 is presented in shy gure 3 using thesame format as in shy gure 1 note however that the non-axial-dipole contribution to Br

at the CMB (BrNAD) is on a dinoterent colour scale There is clearly a coherent temporal

evolution of these shy eld models with structures persisting for hundreds of years andgradually evolving into new features Since each model is a snapshot in time andindependent of the data in adjacent temporal slots this reregects well on the quality ofthe observations and the care taken in selecting them There is signishy cant evolvingnon-zonal structure in the shy eld models whose character appears quite distinct in thedinoterent representations of the shy eld Br at the CMB is dominated by the axial-dipoleshy eld contribution but changes in shy eld structure can be seen these are revealed moreclearly in the second column of shy gures from which the axial-dipole contribution hasbeen subtracted From this we see that from 1000 BC until 600 BC the regux lobe overAsia was dominant and there was a positive anomaly in BrNAD

over western NorthAmerica extending across the Pacishy c past Hawaii The North American regux lobe isonly occasionally visible during this time Southern Hemisphere shy eld structure is verysmooth reregecting the paucity of data there Large negative inclination anomaliesin the central Pacishy c region and positive ones centred in the Indian Ocean areassociated with these structures The focus of these inclination anomalies in dinoterentgeographic regions from the radial shy eld anomalies reregects the dinoterent CMB samplingkernels for the radial shy eld inclination and declination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1001

Br 1000 BCndash375ndash225ndash7575225375

Br 900 BC

Br 800 BC

Br 700 BC

Br 600 BC

Br NAD 1000 BCndash160

ndash80

0

80

160

Br NAD 900 BC

Br NAD 800 BC

Br NAD 700 BC

Br NAD 600 BC

inclination anomaly 1000 BCndash12ndash8ndash404812

inclination anomaly 900 BC

inclination anomaly 800 BC

inclination anomaly 700 BC

inclination anomaly 600 BC

declination 1000 BC

declination 900 BC

declination 800 BC

declination 700 BC

declination 600 BC

(i)

Br 500 BCndash375ndash225ndash7575225375

Br 400 BC

Br 300 BC

Br 200 BC

Br 100 BC

Br NAD 500 BCndash160

ndash80

0

80

160

Br NAD 400 BC

Br NAD 300 BC

Br NAD 200 BC

Br NAD 100 BC

inclination anomaly 500 BCndash12ndash8ndash404812

inclination anomaly 400 BC

inclination anomaly 300 BC

inclination anomaly 200 BC

inclination anomaly 100 BC

declination 500 BC

declination 400 BC

declination 300 BC

declination 200 BC

declination 100 BC

(ii)

Figure 3 Snapshots of Br (75 mT contour interval) Br NAD (40 mT contour interval) inclinationanomaly at the Earthrsquo s surface and declination (contour interval 2 ) for models every 100 yearsfrom 1000 BC to AD 1800 Colour bars sit to the right of the parameter plotted except for thedeclination which has the same scale as the inclination

Phil Trans R Soc Lond A (2000)

1002 C G Constable C L Johnson and S P Lund

Br 0 ADndash375ndash225ndash7575225375

Br 100 AD

Br 200 AD

Br 300 AD

Br 400 AD

Br NAD 0 ADndash160

ndash80

0

80

160

Br NAD 100 AD

Br NAD 200 AD

Br NAD 300 AD

Br NAD 400 AD

inclination anomaly 0 ADndash12ndash8ndash404812

inclination anomaly 100 AD

inclination anomaly 200 AD

inclination anomaly 300 AD

inclination anomaly 400 AD

declination 0 AD

declination 100 AD

declination 200 AD

declination 300 AD

declination 400 AD

(iii)

Br 500 ADndash375ndash225ndash7575225375

Br 600 AD

Br 700 AD

Br 800 AD

Br 900 AD

Br NAD 500 ADndash160

ndash80

0

80

160

Br NAD 600 AD

Br NAD 700 AD

Br NAD 800 AD

Br NAD 900 AD

inclination anomaly 500 ADndash12ndash8ndash404812

inclination anomaly 600 AD

inclination anomaly 700 AD

inclination anomaly 800 AD

inclination anomaly 900 AD

declination 500 AD

declination 600 AD

declination 700 AD

declination 800 AD

declination 900 AD

(iv)

Figure 3 (Cont)

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 999

Table 2

iteration starting macrnal variance model

epoch no RMS RMS reduction norm

AD 1800 05 302 100 890 130

AD 1700 07 240 100 826 193

AD 1600 14 238 100 823 328

AD 1500 08 220 152 523 140

AD 1400 11 199 127 593 166

AD 1300 09 208 130 609 136

AD 1200 07 266 138 731 192

AD 1100 07 308 142 787 306

AD 1000 07 319 139 810 213

AD 900 09 289 144 752 165

AD 800 09 233 123 721 108

AD 700 09 254 157 618 215

AD 600 09 279 190 536 185

AD 500 11 251 154 624 158

AD 400 09 226 145 588 144

AD 300 08 212 135 594 167

AD 200 06 217 141 578 129

AD 100 09 200 131 571 174

AD 0 08 228 167 464 209

100 BC 07 243 179 457 167

200 BC 17 232 155 554 215

300 BC 07 289 180 612 202

400 BC 05 309 179 664 181

500 BC 07 397 215 707 241

600 BC 07 453 214 777 318

700 BC 03 528 293 692 298

800 BC 03 526 251 772 350

900 BC 04 471 236 749 274

1000 BC 05 372 187 747 205

anomaly while both LSN1 and UFM show negative values While we cannot rule outthe possibility of some systematic errors in PSVMOD10 and we can certainly lookfor improved geographic and temporal coverage in the future the analyses of Lundamp Constable (2000) demonstrate good regional coherence and general reliability ofthe time-series

3 Models

The detailed evaluation of the archaeomagnetic dataset described in Lund amp Con-stable (2000) and summarized in the previous section permits the investigation ofthe evolution of the global geomagnetic shy eld over the past 3000 years Figure 1 showsthat the recent time-averaged structure of the shy eld as seen in UFM1 is quite dinoter-ent from that for the past 3 kyr and thus we might expect signishy cant changes inglobal shy eld behaviour Spherical harmonic models of the geomagnetic shy eld were con-

Phil Trans R Soc Lond A (2000)

1000 C G Constable C L Johnson and S P Lund

structed at 100-year intervals using data from as many sites as are available (shy gure 2)at each time-interval The modelling procedure follows that used in the generationof time-averaged shy eld models for the periods 05 Ma and 03 Ka and details can befound elsewhere (Johnson amp Constable 1995 1997 1998) The scalar geomagneticpotential is described in terms of a spherical harmonic expansion and thus ourmeasurements of declination and inclination are nonlinearly related to the sphericalharmonic coemacr cients which are the model parameters We use an iterative nonlinearinversion procedure modishy ed for geomagnetic shy eld modelling from Constable et al rsquos(1987) Occamrsquos inversion algorithm our models are regularized by minimizing themean square value of the non-axial-dipole part of the radial magnetic shy eld (Br) atthe CMB while shy tting the data to a specishy ed tolerance As discussed by Johnsonamp Constable (1997) in the context of constructing LSN1 our model choice dependscritically upon the minimum acceptable misshy t to our observations designated in theprevious section Under the assumption that these uncertainties are independentzero-mean Gaussian variables the target misshy t of the model to our data will corre-spond to the expected value of Agrave 2

N which is N when the misshy t is normalized by thedata uncertainties In practice the target value for the misshy t was not always attain-able without generating overly complicated shy eld models we therefore compromiseand select models with a plausible degree of roughness and a slightly higher misshy tto the observations The necessity for this probably indicates that our use of UFM tocalibrate the uncertainties in PSVMOD10 is not adequate to deal with variations indata quality as they extend further into the past Table 2 lists the initial RMS signalin the data (measured relative to GAD and normalized by the standard error) theRMS of the shy nal model the percentage variance reduction the roughness of theshy nal model (model norm) for each epoch and the iteration at which the preferredmodel was achieved The variance reductions achieved range from 46 to 89 andare typically ca 70 The model norm does not contain the axial-dipole contributionto the roughness and is normalized relative to that contribution

The sequence of models from 1000 BC to AD 1800 is presented in shy gure 3 using thesame format as in shy gure 1 note however that the non-axial-dipole contribution to Br

at the CMB (BrNAD) is on a dinoterent colour scale There is clearly a coherent temporal

evolution of these shy eld models with structures persisting for hundreds of years andgradually evolving into new features Since each model is a snapshot in time andindependent of the data in adjacent temporal slots this reregects well on the quality ofthe observations and the care taken in selecting them There is signishy cant evolvingnon-zonal structure in the shy eld models whose character appears quite distinct in thedinoterent representations of the shy eld Br at the CMB is dominated by the axial-dipoleshy eld contribution but changes in shy eld structure can be seen these are revealed moreclearly in the second column of shy gures from which the axial-dipole contribution hasbeen subtracted From this we see that from 1000 BC until 600 BC the regux lobe overAsia was dominant and there was a positive anomaly in BrNAD

over western NorthAmerica extending across the Pacishy c past Hawaii The North American regux lobe isonly occasionally visible during this time Southern Hemisphere shy eld structure is verysmooth reregecting the paucity of data there Large negative inclination anomaliesin the central Pacishy c region and positive ones centred in the Indian Ocean areassociated with these structures The focus of these inclination anomalies in dinoterentgeographic regions from the radial shy eld anomalies reregects the dinoterent CMB samplingkernels for the radial shy eld inclination and declination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1001

Br 1000 BCndash375ndash225ndash7575225375

Br 900 BC

Br 800 BC

Br 700 BC

Br 600 BC

Br NAD 1000 BCndash160

ndash80

0

80

160

Br NAD 900 BC

Br NAD 800 BC

Br NAD 700 BC

Br NAD 600 BC

inclination anomaly 1000 BCndash12ndash8ndash404812

inclination anomaly 900 BC

inclination anomaly 800 BC

inclination anomaly 700 BC

inclination anomaly 600 BC

declination 1000 BC

declination 900 BC

declination 800 BC

declination 700 BC

declination 600 BC

(i)

Br 500 BCndash375ndash225ndash7575225375

Br 400 BC

Br 300 BC

Br 200 BC

Br 100 BC

Br NAD 500 BCndash160

ndash80

0

80

160

Br NAD 400 BC

Br NAD 300 BC

Br NAD 200 BC

Br NAD 100 BC

inclination anomaly 500 BCndash12ndash8ndash404812

inclination anomaly 400 BC

inclination anomaly 300 BC

inclination anomaly 200 BC

inclination anomaly 100 BC

declination 500 BC

declination 400 BC

declination 300 BC

declination 200 BC

declination 100 BC

(ii)

Figure 3 Snapshots of Br (75 mT contour interval) Br NAD (40 mT contour interval) inclinationanomaly at the Earthrsquo s surface and declination (contour interval 2 ) for models every 100 yearsfrom 1000 BC to AD 1800 Colour bars sit to the right of the parameter plotted except for thedeclination which has the same scale as the inclination

Phil Trans R Soc Lond A (2000)

1002 C G Constable C L Johnson and S P Lund

Br 0 ADndash375ndash225ndash7575225375

Br 100 AD

Br 200 AD

Br 300 AD

Br 400 AD

Br NAD 0 ADndash160

ndash80

0

80

160

Br NAD 100 AD

Br NAD 200 AD

Br NAD 300 AD

Br NAD 400 AD

inclination anomaly 0 ADndash12ndash8ndash404812

inclination anomaly 100 AD

inclination anomaly 200 AD

inclination anomaly 300 AD

inclination anomaly 400 AD

declination 0 AD

declination 100 AD

declination 200 AD

declination 300 AD

declination 400 AD

(iii)

Br 500 ADndash375ndash225ndash7575225375

Br 600 AD

Br 700 AD

Br 800 AD

Br 900 AD

Br NAD 500 ADndash160

ndash80

0

80

160

Br NAD 600 AD

Br NAD 700 AD

Br NAD 800 AD

Br NAD 900 AD

inclination anomaly 500 ADndash12ndash8ndash404812

inclination anomaly 600 AD

inclination anomaly 700 AD

inclination anomaly 800 AD

inclination anomaly 900 AD

declination 500 AD

declination 600 AD

declination 700 AD

declination 800 AD

declination 900 AD

(iv)

Figure 3 (Cont)

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

1000 C G Constable C L Johnson and S P Lund

structed at 100-year intervals using data from as many sites as are available (shy gure 2)at each time-interval The modelling procedure follows that used in the generationof time-averaged shy eld models for the periods 05 Ma and 03 Ka and details can befound elsewhere (Johnson amp Constable 1995 1997 1998) The scalar geomagneticpotential is described in terms of a spherical harmonic expansion and thus ourmeasurements of declination and inclination are nonlinearly related to the sphericalharmonic coemacr cients which are the model parameters We use an iterative nonlinearinversion procedure modishy ed for geomagnetic shy eld modelling from Constable et al rsquos(1987) Occamrsquos inversion algorithm our models are regularized by minimizing themean square value of the non-axial-dipole part of the radial magnetic shy eld (Br) atthe CMB while shy tting the data to a specishy ed tolerance As discussed by Johnsonamp Constable (1997) in the context of constructing LSN1 our model choice dependscritically upon the minimum acceptable misshy t to our observations designated in theprevious section Under the assumption that these uncertainties are independentzero-mean Gaussian variables the target misshy t of the model to our data will corre-spond to the expected value of Agrave 2

N which is N when the misshy t is normalized by thedata uncertainties In practice the target value for the misshy t was not always attain-able without generating overly complicated shy eld models we therefore compromiseand select models with a plausible degree of roughness and a slightly higher misshy tto the observations The necessity for this probably indicates that our use of UFM tocalibrate the uncertainties in PSVMOD10 is not adequate to deal with variations indata quality as they extend further into the past Table 2 lists the initial RMS signalin the data (measured relative to GAD and normalized by the standard error) theRMS of the shy nal model the percentage variance reduction the roughness of theshy nal model (model norm) for each epoch and the iteration at which the preferredmodel was achieved The variance reductions achieved range from 46 to 89 andare typically ca 70 The model norm does not contain the axial-dipole contributionto the roughness and is normalized relative to that contribution

The sequence of models from 1000 BC to AD 1800 is presented in shy gure 3 using thesame format as in shy gure 1 note however that the non-axial-dipole contribution to Br

at the CMB (BrNAD) is on a dinoterent colour scale There is clearly a coherent temporal

evolution of these shy eld models with structures persisting for hundreds of years andgradually evolving into new features Since each model is a snapshot in time andindependent of the data in adjacent temporal slots this reregects well on the quality ofthe observations and the care taken in selecting them There is signishy cant evolvingnon-zonal structure in the shy eld models whose character appears quite distinct in thedinoterent representations of the shy eld Br at the CMB is dominated by the axial-dipoleshy eld contribution but changes in shy eld structure can be seen these are revealed moreclearly in the second column of shy gures from which the axial-dipole contribution hasbeen subtracted From this we see that from 1000 BC until 600 BC the regux lobe overAsia was dominant and there was a positive anomaly in BrNAD

over western NorthAmerica extending across the Pacishy c past Hawaii The North American regux lobe isonly occasionally visible during this time Southern Hemisphere shy eld structure is verysmooth reregecting the paucity of data there Large negative inclination anomaliesin the central Pacishy c region and positive ones centred in the Indian Ocean areassociated with these structures The focus of these inclination anomalies in dinoterentgeographic regions from the radial shy eld anomalies reregects the dinoterent CMB samplingkernels for the radial shy eld inclination and declination

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1001

Br 1000 BCndash375ndash225ndash7575225375

Br 900 BC

Br 800 BC

Br 700 BC

Br 600 BC

Br NAD 1000 BCndash160

ndash80

0

80

160

Br NAD 900 BC

Br NAD 800 BC

Br NAD 700 BC

Br NAD 600 BC

inclination anomaly 1000 BCndash12ndash8ndash404812

inclination anomaly 900 BC

inclination anomaly 800 BC

inclination anomaly 700 BC

inclination anomaly 600 BC

declination 1000 BC

declination 900 BC

declination 800 BC

declination 700 BC

declination 600 BC

(i)

Br 500 BCndash375ndash225ndash7575225375

Br 400 BC

Br 300 BC

Br 200 BC

Br 100 BC

Br NAD 500 BCndash160

ndash80

0

80

160

Br NAD 400 BC

Br NAD 300 BC

Br NAD 200 BC

Br NAD 100 BC

inclination anomaly 500 BCndash12ndash8ndash404812

inclination anomaly 400 BC

inclination anomaly 300 BC

inclination anomaly 200 BC

inclination anomaly 100 BC

declination 500 BC

declination 400 BC

declination 300 BC

declination 200 BC

declination 100 BC

(ii)

Figure 3 Snapshots of Br (75 mT contour interval) Br NAD (40 mT contour interval) inclinationanomaly at the Earthrsquo s surface and declination (contour interval 2 ) for models every 100 yearsfrom 1000 BC to AD 1800 Colour bars sit to the right of the parameter plotted except for thedeclination which has the same scale as the inclination

Phil Trans R Soc Lond A (2000)

1002 C G Constable C L Johnson and S P Lund

Br 0 ADndash375ndash225ndash7575225375

Br 100 AD

Br 200 AD

Br 300 AD

Br 400 AD

Br NAD 0 ADndash160

ndash80

0

80

160

Br NAD 100 AD

Br NAD 200 AD

Br NAD 300 AD

Br NAD 400 AD

inclination anomaly 0 ADndash12ndash8ndash404812

inclination anomaly 100 AD

inclination anomaly 200 AD

inclination anomaly 300 AD

inclination anomaly 400 AD

declination 0 AD

declination 100 AD

declination 200 AD

declination 300 AD

declination 400 AD

(iii)

Br 500 ADndash375ndash225ndash7575225375

Br 600 AD

Br 700 AD

Br 800 AD

Br 900 AD

Br NAD 500 ADndash160

ndash80

0

80

160

Br NAD 600 AD

Br NAD 700 AD

Br NAD 800 AD

Br NAD 900 AD

inclination anomaly 500 ADndash12ndash8ndash404812

inclination anomaly 600 AD

inclination anomaly 700 AD

inclination anomaly 800 AD

inclination anomaly 900 AD

declination 500 AD

declination 600 AD

declination 700 AD

declination 800 AD

declination 900 AD

(iv)

Figure 3 (Cont)

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1001

Br 1000 BCndash375ndash225ndash7575225375

Br 900 BC

Br 800 BC

Br 700 BC

Br 600 BC

Br NAD 1000 BCndash160

ndash80

0

80

160

Br NAD 900 BC

Br NAD 800 BC

Br NAD 700 BC

Br NAD 600 BC

inclination anomaly 1000 BCndash12ndash8ndash404812

inclination anomaly 900 BC

inclination anomaly 800 BC

inclination anomaly 700 BC

inclination anomaly 600 BC

declination 1000 BC

declination 900 BC

declination 800 BC

declination 700 BC

declination 600 BC

(i)

Br 500 BCndash375ndash225ndash7575225375

Br 400 BC

Br 300 BC

Br 200 BC

Br 100 BC

Br NAD 500 BCndash160

ndash80

0

80

160

Br NAD 400 BC

Br NAD 300 BC

Br NAD 200 BC

Br NAD 100 BC

inclination anomaly 500 BCndash12ndash8ndash404812

inclination anomaly 400 BC

inclination anomaly 300 BC

inclination anomaly 200 BC

inclination anomaly 100 BC

declination 500 BC

declination 400 BC

declination 300 BC

declination 200 BC

declination 100 BC

(ii)

Figure 3 Snapshots of Br (75 mT contour interval) Br NAD (40 mT contour interval) inclinationanomaly at the Earthrsquo s surface and declination (contour interval 2 ) for models every 100 yearsfrom 1000 BC to AD 1800 Colour bars sit to the right of the parameter plotted except for thedeclination which has the same scale as the inclination

Phil Trans R Soc Lond A (2000)

1002 C G Constable C L Johnson and S P Lund

Br 0 ADndash375ndash225ndash7575225375

Br 100 AD

Br 200 AD

Br 300 AD

Br 400 AD

Br NAD 0 ADndash160

ndash80

0

80

160

Br NAD 100 AD

Br NAD 200 AD

Br NAD 300 AD

Br NAD 400 AD

inclination anomaly 0 ADndash12ndash8ndash404812

inclination anomaly 100 AD

inclination anomaly 200 AD

inclination anomaly 300 AD

inclination anomaly 400 AD

declination 0 AD

declination 100 AD

declination 200 AD

declination 300 AD

declination 400 AD

(iii)

Br 500 ADndash375ndash225ndash7575225375

Br 600 AD

Br 700 AD

Br 800 AD

Br 900 AD

Br NAD 500 ADndash160

ndash80

0

80

160

Br NAD 600 AD

Br NAD 700 AD

Br NAD 800 AD

Br NAD 900 AD

inclination anomaly 500 ADndash12ndash8ndash404812

inclination anomaly 600 AD

inclination anomaly 700 AD

inclination anomaly 800 AD

inclination anomaly 900 AD

declination 500 AD

declination 600 AD

declination 700 AD

declination 800 AD

declination 900 AD

(iv)

Figure 3 (Cont)

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

1002 C G Constable C L Johnson and S P Lund

Br 0 ADndash375ndash225ndash7575225375

Br 100 AD

Br 200 AD

Br 300 AD

Br 400 AD

Br NAD 0 ADndash160

ndash80

0

80

160

Br NAD 100 AD

Br NAD 200 AD

Br NAD 300 AD

Br NAD 400 AD

inclination anomaly 0 ADndash12ndash8ndash404812

inclination anomaly 100 AD

inclination anomaly 200 AD

inclination anomaly 300 AD

inclination anomaly 400 AD

declination 0 AD

declination 100 AD

declination 200 AD

declination 300 AD

declination 400 AD

(iii)

Br 500 ADndash375ndash225ndash7575225375

Br 600 AD

Br 700 AD

Br 800 AD

Br 900 AD

Br NAD 500 ADndash160

ndash80

0

80

160

Br NAD 600 AD

Br NAD 700 AD

Br NAD 800 AD

Br NAD 900 AD

inclination anomaly 500 ADndash12ndash8ndash404812

inclination anomaly 600 AD

inclination anomaly 700 AD

inclination anomaly 800 AD

inclination anomaly 900 AD

declination 500 AD

declination 600 AD

declination 700 AD

declination 800 AD

declination 900 AD

(iv)

Figure 3 (Cont)

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1003

Br 1000 ADndash375ndash225ndash7575225375

Br 1100 AD

Br 1200 AD

Br 1300 AD

Br 1400 AD

Br NAD 1000 ADndash160

ndash80

0

80

160

Br NAD 1100 AD

Br NAD 1200 AD

Br NAD 1300 AD

Br NAD 1400 AD

inclination anomaly 1000 ADndash12ndash8ndash404812

inclination anomaly 1100 AD

inclination anomaly 1200 AD

inclination anomaly 1300 AD

inclination anomaly 1400 AD

declination 1000 AD

declination 1100 AD

declination 1200 AD

declination 1300 AD

declination 1400 AD

(v)

Br 1500 ADndash375ndash225ndash7575225375

Br 1600 AD

Br 1700 AD

Br 1800 AD

Br NAD 1500 ADndash160

ndash80

0

80

160

Br NAD 1600 AD

Br NAD 1700 AD

Br NAD 1800 AD

inclination anomaly 1500 ADndash12ndash8ndash404812

inclination anomaly 1600 AD

inclination anomaly 1700 AD

inclination anomaly 1800 AD

declination 1500 AD

declination 1600 AD

declination 1700 AD

declination 1800 AD

(vi)

Figure 3 (Cont)

At about 500 BC the inreguence of the Asian regux lobe begins to wane the positivefocus of BrNAD

shifts to the western Pacishy c but still encompasses the region beneathHawaii and a negative lobe develops over North America with a shy nger extending intothe Atlantic region A negative focus centred northwest of New Zealand developsperhaps because of evolving shy eld structure although it may reregect the addition of

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

1004 C G Constable C L Johnson and S P Lund

New Zealand lake-sediment data to the available dataset (see shy gure 2) Negative incli-nation anomalies weaken somewhat and spread into eastern Asia and the Atlanticforming a pair of foci over India and the Pacishy c by 100 BC By 100 BC the NorthAmerican regux lobe in BrNAD

is weakening the lobe then brieregy ventures over Asiaand then extends down into the western Pacishy c all the while preserving a positiveanomaly in the central Pacishy c During this time the negative inclination anomalycentred on Hawaii persists but is surrounded by developing regions of positivity overAustralasia and the Americas Note however that the magnitude of the inclinationanomalies over the Americas and Asia is considerably reduced relative to earliertimes Around AD 400 the North American regux lobe re-asserts itself there followsa trade-onot of relative power in the regux lobes with extension of a third lobe downover Africa through AD 1000 Associated with this the positive anomaly beneathHawaii begins to weaken ultimately to be replaced by a weaker negative anomalyaround AD 1600 As this occurs the Pacishy c inclination anomaly structure changestoo with the negative anomaly evolving to two foci on Hawaii and MesoAmerica(AD 700) the Hawaiian anomaly gradually dying down becoming weakly positivearound AD 1100 as a strong negative MesoAmericanAtlantic inclination anomalydevelops Strongest positive inclination anomalies move eastward from Africa intothe equatorial Indian Ocean from AD 900 to AD 1200 By AD 1300 these anomaliesdiminish change sign and at AD 1500 there is a strong negative anomaly over Aus-tralasia with a positive one (not as pronounced) in Africa and the Atlantic graduallymoving over South America as time evolves

Overall we can see from shy gure 3 that BrNADand inclination anomalies tend to

change together at equatorial and mid-latitudes as expected from the way in whichthey sample the CMB However inclination is much less sensitive to variations in Br

at high latitudes thus changes in position and relative magnitude of the regux lobestend to be manifest as lower-latitude changes in inclination anomaly In contrast thelargest values of declination occur at high latitudes There is some tendency for linesof zero declination to fall close to the territory occupied by the regux lobes at highlatitude This is to be expected if the regux lobes form the major contribution to thedipole part of the geomagnetic shy eld It is also clear that at times when one regux lobeclearly dominates the shy eld structure for example between 1000 BC and 500 BC thedeclination pattern is much less complex than when a pair of lobes is visible

It is evident from shy gure 3 that the regux lobes are not restricted to the NorthAmerican and Siberian locations that dominate the historical shy eld models FromAD 200 to AD 300 they invade the western Pacishy c and from 900 AD to 1000 ADand again from AD 1500 to AD 1700 there are large negative anomalies in BrNAD

over African longitudes However the central Pacishy c seems to be exempt from suchinvasions although there is substantial secular variation in the region

4 Synthesis of results

We summarize the information contained in the 29 models of shy gure 3 by calculatingthe average properties of the shy eld over the past 3 kyr and the variability about thismean In shy gure 4 we present the average and standard deviation about the meanfor each of the non-axial-dipole radial magnetic shy eld at the CMB the inclinationanomalies and the declinations for the 29 time samples shown in shy gure 3 The aver-ages of shy gure 4a c e dinoter somewhat from those presented for ALS3K in shy gure 1

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1005

(a) average Br NAD

ndash160ndash80080160

(b) standard deviation in Br

1632486480

(c) average inclination anomalyndash12ndash8ndash404812

(d) standard deviation in inclination

246810

(e) average declinationndash12ndash8ndash404812

(f) standard deviation in declination

246810

Figure 4 Average and standard deviation for Br NAD (a) (b) inclination anomalies (c) (d) anddeclination for the models of macrgure 3 Br NAD is in mT inclination and declination in degrees

this reregects the fact that ALS3K was constructed using the time-averaged data anddinoterent data uncertainties assigned earlier in our assessment of the Lund amp Con-stable (2000) dataset rather than averaging the predictions of the shy eld models aftertheir construction Figure 2 shows that a number of sites (particularly in the South-ern Hemisphere) are missing data at a signishy cant fraction of the possible times Inthe individual 100-year interval models the absent sites will result in a strongerinreguence of the regularization implicit in the modelling procedure this regulariza-tion attempts to make the model more like that for a geocentric axial dipole Thedinoterences between shy gures 1fh and 4a c e reregect the increasingly smooth modelsresulting from these data dropouts

On average between 1000 BC and AD 1800 the Asian regux lobe dominates at north-ernmost latitudes the positive anomaly in BrNAD

beneath Hawaii is also persistentas is a smaller anomaly beneath Japan At the Earthrsquos surface average inclinationanomalies are large and negative in the central Pacishy c and most positive slightly tothe east of Central Africa Inclination anomalies decrease with increasing latitudeAverage declinations are smallest in equatorial regions again with strong longitudinalvariations largest negative departures are centred over Australia and eastern Asia

Intensity of secular variation at the Earthrsquos surface is quantishy ed here by standarddeviation of the model inclinations and declinations about their average values andat the CMB by standard deviation in radial magnetic shy eld These globally vary-ing measures of secular variation can be compared with predictions from statisticalpalaeosecular variation models like those of Constable amp Johnson (1999) althoughwe should keep in mind the temporal and spatial limitations of the data coverage

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

1006 C G Constable C L Johnson and S P Lund

Figure 4b shows the geographic variation in standard deviations in Br at theCMB The Southern Hemisphere is generally much less active than the NorthernHemisphere probably a reregection of the much better northerly data coverage John-son amp Constable (1998) show that the data used here have adequate coverage forsampling the radial magnetic shy eld at the CMB between ca 40 S and 80 N whenall sites are present More interestingly there are regions with good data coverage inthe Northern Hemisphere over central North America and eastern Asia with com-paratively little variation These and other Northern Hemisphere features may wellrepresent geographic variations in the secular variation at the CMB over the past3 kyr Peaks in variation in Br occur just south of the locations of the Siberian andNorth American regux lobes with a lesser maximum near the African lobe The regionbeneath and slightly south of Hawaii is also a hotbed of activity The relative impor-tance of the Australasian region may be exaggerated by poor sampling elsewhere inthe Southern Hemisphere

Turning now to standard deviation in inclination in shy gure 4d we see generallylarger values near the Equator as predicted by palaeosecular variation (PSV) modelCJ98 with a general decrease towards the poles Again there is less variability inthe Southern Hemisphere Signishy cant non-zonal structure is evident in the three fociof inclination anomalies strung in a broad band around the Equator centred in thenorthern Indian Ocean southeast of Hawaii and the central Atlantic These anoma-lies are similar to the structure predicted by the non-zonal version of Constable ampJohnsonrsquos (1999) statistical model for PSV (CJ98nz) One of them even occurs in thesame position although the simple non-zonal structure assumed for CJ98nz (basedon excess variance in h1

2 terms of the spherical harmonic expansion) is probably notan adequate representation for shy eld variability given that the regux lobes in the 03 kyr interval are not conshy ned to North America and Asia These peaks in SV forinclination show a general correspondence with those in BrNAD

in shy gure 4b and seemto show a trilobate structure approximately coinciding with the positions occupiedby regux lobes in shy gure 3 Declination variations (shy gure 4f) also appear trilobate butin contrast are almost out of phase with Br and inclination reregecting the fact thatthe kernel for declination changes sampling Br at the CMB is most strongly peakedat longitudes displaced 22 from the site

5 Conclusions

The above discussion and shy gures 3 and 4 indicate substantive secular variation inthe Pacishy c hemisphere over the 03 kyr period and suggest that the historically lowsecular variation in the Pacishy c compared with that in the Atlantic is a short-livedphenomenon Indeed the standard deviations in inclination anomaly declinationand BrNAD

are typically larger in magnitude than the average departures from anaxial-dipole shy eld These observations lay to rest the idea (eg Runcorn 1992) thatan excellent conductor at or near the CMB throughout the Pacishy c region perma-nently attenuates the magnetic shy eld changes occurring in the core shy eld and preventssuch changes from being propagated to the Earthrsquos surface From these models wecan conclude that the North American and Siberian regux lobes cannot be consid-ered permanent features however we do see that a dominant regux lobe is almostalways present somewhere in the Northern Hemisphere and that the Asian positiondominates the average for the past 3 kyr The fact that these lobes do not occur in

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

Global geomagnetic macreld models for the past 3000 years 1007

the central Pacishy c combined with the non-zonal structures seen in the measures ofsecular variation in shy gure 4b d f leaves the possibility for geographic variations inheat regux at the CMB inreguencing the structure of the geomagnetic shy eld wide open

The models presented in shy gures 3 and 4 can be obtained by anonymous ftp fromozzyucsdedu from the directory pubHoloceneModels

This work was funded by NSF grants EAR 95-26890 EAR 95-26682 and EAR 93-04186

References

Arnou J M Buttles J L Neumann G A amp Olson P 1996 Electromagnetic coremantlecoupling and paleomagnetic reversal paths Geophys Res Lett 23 27052708

Bloxham J 1998 Geodynamo modelling the paleosecular variation and thermal coremantleinteractions Eos 79 F232

Bloxham J amp Jackson A 1992 Time-dependent mapping of the magnetic macreld at the coremantle boundary J Geophys Res 97 19 53719 563

Bloxham J Gubbins D amp Jackson A 1989 Geomagnetic secular variation Phil Trans RSoc Lond A 329 415502

Brito D Arnou J amp Olson P 1999 Can heterogeneous coremantle electromagnetic couplingcontrol geomagnetic reversals Phys Earth Planet Interiors 112 159170

Carlut J amp Courtillot V 1998 How complex is the time-averaged geomagnetic macreld over thelast 5 million years Geophys J Int 134 527544

Clark R M 1975 A calibration curve for radiocarbon dates Antiquity XLIX 251266

Constable C G amp Johnson C L 1999 Anisotropic paleosecular variation models implicationsfor geomagnetic macreld observables Phys Earth Planet Interiors 115 3551

Constable S C Parker R L amp Constable C G 1987 Occamrsquo s inversion a practical algorithmfor generating smooth models from electromagnetic sounding data Geophys 52 289300

Daly L amp LeGoreg M 1996 An updated and homogeneous world secular variation database 1Smoothing of the archeomagnetic results Phys Earth Planet Interiors 93 159190

Glatzmaier G A Coe R S Hongre L amp Roberts P H 1999 The role of the Earthrsquo s mantlein controlling the frequency of geomagnetic reversals Nature 401 885890

Gubbins D 1998 Interpreting the plaeomagnetic macreld In The core mantle boundary region (edM Gurnis M E Wysession E Knittle amp B Bureg ett) pp 167182 Geodynamics vol 28American Geophysical Union

Gubbins D amp Kelly P 1993 Persistent patterns in the geomagnetic macreld over the past 25 MyrNature 365 829832

Holme R 2000 Electromagnetic coremantle coupling III Laterally varying mantle conduc-tance Phys Earth Planet Interiors 117 329344

Hongre L Hulot G amp Khokhlov A 1998 An analysis of the geomagnetic macreld over the past2000 years Phys Earth Planet Interiors 106 311335

Hulot G Khokhlov A amp Le Mouel J L 1997 Uniqueness of a mainly dipolar magnetic macreldrecovered from directional data Geophys J Int 129 347354

Johnson C L amp Constable C G 1995 The time-averaged geomagnetic macreld as recorded bylava deg ows over the past 5 Myr Geophys J Int 122 489519

Johnson C L amp Constable C G 1996 Paleosecular variation recorded by lava deg ows over thelast 5 Myr Phil Trans R Soc Lond A 354 89141

Johnson C L amp Constable C G 1997 The time-averaged geomagnetic macreld global and regionalbiases for 05 Ma Geophys J Int 131 643666

Johnson C L amp Constable C G 1998 Persistently anomalous Pacimacrc geomagnetic macreldsGeophys Res Lett 25 10111014

Phil Trans R Soc Lond A (2000)

1008 C G Constable C L Johnson and S P Lund

Kelly P amp Gubbins D 1997 The geomagnetic macreld over the past 5 Myr Geophys J Int 128315330

Lithgow-Bertelloni C amp Richards M A 1998 The dynamics of cenozoic and mesozoic platemotions Rev Geophys 36 2778

Lund S P 1996 A comparison of holocene paleomagnetic secular variation records from NorthAmerica J Geophys Res 101 80078024

Lund S P amp Constable C G 2000 Global geomagnetic secular variation for the past 3000 yearsGeophys J Int (In preparation)

McElhinny M W amp McFadden P L 1997 Paleosecular variation for the past 5 Myr based ona new generalized database Geophys J Int 131 240252

McElhinny M W McFadden P L amp Merrill R T 1996a The time averaged paleomagneticmacreld 05 Ma J Geophys Res 101 25 00725 027

McElhinny M W McFadden P L amp Merrill R T 1996b The myth of the Pacimacrc dipolewindow Earth Planet Sci Lett 143 1322

Proctor M R E amp Gubbins D 1990 Analysis of geomagnetic directional data Geophys JInt 100 6977

Quidelleur X Valet J-P Courtillot V amp Hulot G 1994 Long-term geometry of the geomag-netic macreld for the last 5 million years an updated secular variation database from volcanicsequences Geophys Res Lett 21 16391642

Richards M A amp Engebretson D C 1992 Large scale mantle convection and the history ofsubduction Nature 355 437440

Runcorn S K 1992 Polar path in geomagnetic reversals Nature 356 654656

Schneider D A amp Kent D V 1988 Inclination anomalies from Indian Ocean sediments andthe possibility of a standing non-dipole macreld J Geophys Res 93 11 62111 630

Schneider D A amp Kent D V 1990 The time-averaged paleomagnetic macreld Rev Geophys 287196

Walker A D amp Backus G E 1996 On the direg erence between the average values of B2r in the

Atlantic and Pacimacrc hemispheres Geophys Res Lett 23 19651968

Phil Trans R Soc Lond A (2000)