the e¡ect of dq on pkp(ab3df) travel time residuals and possible implications for...

The e¡ect of DQ on PKP(AB3DF) travel time residuals andpossible implications for inner core structure

Ludovic Breger *, Hrvoje Tkalcic, Barbara RomanowiczSeismological Laboratory, University of California, Berkeley, 215 Mc Cone Hall, Berkeley, CA 94720, USA

Received 29 June 1999; accepted 10 November 1999

Abstract

The hypothesis that the deep inner core is anisotropic is based on PKP travel time observations at large distances andrelies on a small number of very anomalous measurements for paths quasi-parallel to the Earth's rotation axis. Here, weanalyze a global dataset of PKP(AB3DF) travel times residuals, and discuss their significant dispersion ( þ 2 s), andcoherent large scale patterns. We show that the trends observed for quasi-equatorial paths are consistent withpredictions from recent tomographic mantle models, when the latter are modified to account for strong heterogeneity atthe base of the mantle under the Pacific Ocean and Africa, as documented in several recent studies. Likewise, for polarpaths, we show that a large part of the signal could be explained by deep mantle structure. The effects of complexstructure in the deep mantle on PKP(AB3DF) travel times should be carefully considered in order to reliably estimatethe anisotropic structure of the central part of the inner core. ß 2000 Elsevier Science B.V. All rights reserved.

Keywords: seismology; core; mantle; body wave; propagation

1. Introduction

Fifteen years ago, Poupinet et al. [1] showedthat waves turning in the inner core (PKIKP,PKP(DF) or simply DF) and travelling parallelto the Earth's rotation axis were on average 1^2s faster than those propagating along the equato-rial plane. These observations were later inter-preted in terms of inner core anisotropy [2], whichcould simultaneously explain the anomalous split-ting of core sensitive free oscillations [3]. Thispioneer work was followed by many studies con-

¢rming and re¢ning this interpretation [4^13].Although the existence of cylindrical anisotropy,with an average strength of about 3^3.5%, in theinner core now seems widely accepted, there is noconsensus on the details of its distribution. Thereare indications that it may be weaker near thesurface than towards the center of the innercore, and that it may be laterally varying. Nota-bly, some recent results suggest that there mightbe anisotropy in only one hemisphere of the innercore [14], and even that the top 250 km may beisotropic [15], which is hard to reconcile with nor-mal mode data, which require anisotropy to bepresent in the top third of the inner core [8,11,16].

In order to study inner core structure using thephase PKP(DF), outer core sensitive phasesPKP(BC) and PKP(AB) (Fig. 1A) are generally

* Corresponding author.E-mail: [email protected]

EPSL 5327 3-1-00 Cyaan Magenta Geel Zwart

Earth and Planetary Science Letters 175 (2000) 133^143

www.elsevier.com/locate/epsl

Abstract

1. Introduction

Abstract

1. Introduction

Abstract

1. Introduction

used as reference phases. Di¡erential travel timesPKP(BC3DF) and PKP(AB3DF) have the ad-vantage of reducing earthquake mislocation andorigin time errors, near-source and near-receiverstructure, and are, in principle, less sensitive thanabsolute times to large scale deep mantle struc-ture. Breger et al. [17] showed recently thatPKP(BC3DF) di¡erential residuals were incom-patible with a simple model of inner core aniso-tropy, and suggested that their complex behaviorcould be explained by a complex inner core struc-ture, but also proposed that contamination ofPKP(BC3DF) residuals by DQ heterogeneitycould have been generally underestimated andsuggested deep mantle structure as a complemen-tary, or even alternative explanation. On the other

hand, PKP(AB3DF) di¡erential travel times ob-tained at large distances (150^180³) are particu-larly valuable, since at those distances PKP(DF)uniquely samples the central part of the innercore. Although it has been often recognized thatmantle heterogeneity contributes to the large scat-ter observed in the PKP(AB3DF) travel time re-siduals [18^20], so far, it has been assumed thatthe large scale trend observed, namely an increaseof residual as the path approaches the Earth'srotation axis, is best explained in terms of thee¡ect of inner core anisotropy on the PKP(DF)phase [6,9].

We have assembled a dataset of 335PKP(AB3DF) di¡erential travel times which wemeasured on the vertical component of Geoscope,

Fig. 1. (A) Schematic representation of the wavepaths of PKP(DF), PKP(AB), and PKP(BC) discussed in this study. (B) Earth-quakes (stars), stations (triangles), and projections of the raypaths analyzed. We used 137 events from 1987 to 1998, and 57 sta-tions. Our dataset consists of our own measurements and data from [6]. The geographical distribution is representative of cur-rently available data. Note the large number of quasi-equatorial paths (hs 45³, green lines), but the reduced number of quasi-polar paths (h6 45³, red lines).

L. Breger et al. / Earth and Planetary Science Letters 175 (2000) 133^143134

IRIS, GRSN, and Mednet broadband recordsand combined them with the previously assembledcollection of [6]. PKP(AB3DF) di¡erential timeswere determined by overlapping the PKP(AB)waveform with the Hilbert transform ofPKP(DF). Residuals were computed with respectto the Preliminary Reference Earth Model [21].Standard ellipticity corrections [22] were applied.The global coverage provided by this dataset issimilar to that of other studies, with a large num-ber of quasi-equatorial paths but considerablyfewer paths approaching the Earth's rotationaxis (Fig. 1B).

2. AB33DF di¡erential residuals as a function ofpolar angle

Plots of AB3DF residuals as a function of epi-central distance and angle with respect to the ro-tation axis (Fig. 2a,b) are consistent with resultsfrom previous studies [6,9]. In particular, thetrend with angle (hereafter called h) is as expectedfor a simple model of constant cylindrical innercore anisotropy. The dispersion observed aroundthat trend is of the order of þ 2.5 s, which is alsoconsistent with earlier work [6,9,18^20] and ismuch larger than measurement uncertainty. Thedistribution of AB3DF data as a function of an-gle h is very non-uniform (Fig. 3a). There are onlya small number of data points for h between 0and 30³, and most of these correspond to earth-quakes in the South Sandwich Islands region. In-terestingly, the distribution of mean AB3DFtravel time anomalies as a function of h (Fig.3b) indicates that the largest anomalies corre-spond to the poorest sampling. In order to obtaina rough estimate of the contribution of mantlestructure to AB3DF residuals, we computed syn-thetic anomalies based on a recent tomographicmodel. We used Grand's [23] recent S-velocitymodel and converted it to P, assuming dln(Vs)/dln(Vp) = 2. Although it has been shown that Pand S anomalies do not always vary in proportion[24], an S-velocity model was preferred to a P-velocity velocity model for several reasons. First,there is reasonably good agreement between re-cent S-velocity tomographic models in the lower-

most mantle [23,25^27]. The low harmonic de-grees are in particular very similar whichsuggests that S models now give a good descrip-tion of large scale DQ heterogeneity. S-velocitymodels were also recently shown to give a ratheraccurate description of the shape of heterogeneityin the deep mantle beneath the Central Paci¢c[28], and Africa [29] `plumes'. These two regionsare particularly important because they are, sofar, the two most anomalous domains of DQ. P-velocity models of the deep mantle, on the otherhand, are still rather di¡erent [30^33], and su¡erfrom uneven coverage in DQ in oceanic regions,which are of most interest in the present study.We veri¢ed that the distribution of P-velocityanomalies predicted by a model recently derivedspeci¢cally for DQ [32] was compatible with thatpredicted using our S derived P model, whichsuggests that this approach is reasonable. We

Fig. 2. AB3DF di¡erential travel time residuals as a func-tion of epicentral distance (a) and angle h of the path in theinner core with respect to the rotation axis (b). Typical meas-urement errors are in the order of 0.1^0.2 s, and error barswould have the height of diamonds. The best ¢tting seconddegree polynomial in cos2h (solid line) is shown in (b) tooutline the observed trend. Such a trend is expected, at ¢xeddistance, for models of constant cylindrical anisotropy in theinner core. (c and d): Same as (a) and (b) after correctionfor the MMM model. Mean residuals are 1.05 and 0.67 s, re-spectively before and after correction using MMM. Notethat a few large residuals at low h remain unexplained. Thesecorrespond to South Sandwich Islands paths to stationsCOL and BILL. The complexity of these particular pathshas been noted previously, for instance, BC3DF residualsdi¡ering by more than 2 s for neighboring stations [14,17].

L. Breger et al. / Earth and Planetary Science Letters 175 (2000) 133^143 135

have computed synthetic travel time residuals us-ing ray theory. The ray tracing was done in thespherically symmetric PREM model [21]. For afew paths, we have veri¢ed that the residuals ob-tained are within 0.5 s of those computed for atypical path from South Sandwich Islands to

northern Eurasia, using an acoustic 2D ¢nite dif-ference algorithm [34].

Mean synthetic residuals are presented in Fig.3b. As pointed out in earlier studies [18^20], it isdi¤cult to produce synthetic residuals larger thanabout 1 s with any existing tomographic model.For comparison, we also plotted the predictionsfor a standard 3.5% constant inner core anisotro-py model that has been proposed to ¢t AB3DFdata [6]. As expected, this model reproduces thevariations with h well, slightly overpredictingthem (a model with 2.75% constant anisotropywould provide the best ¢t). We tried the combi-nation of both the mantle and the inner coremodel (not shown), but the ¢t is actually slightlydegraded.

Because they represent a smoothed image ofheterogeneity in the mantle, tomographic modelsusually underpredict the trends associated withdata which sample regions where strong or smallscale heterogeneity may be present. This has beendemonstrated, in particular, using S-SKS traveltime residuals sampling DQ in the central Paci¢cand Africa [29^31]. These studies showed, how-ever, that it was possible to perturb the existingmodels locally, in order to obtain good ¢ts toS-SKS, SKKS-SKS or S-ScS travel time ob-servations [29^31]. The required perturbations,although non-unique in their details, could beachieved e¡ectively by keeping the shape of theboundaries between fast and slow anomalies ¢xed,and increasing the amplitudes of £uctuations,mostly in DQ (the bottom 300 km of the mantle),by a factor of 2^3. While there is some trade-o¡between the amplitude increase and the depthrange a¡ected, the modi¢cation of the startingtomographic model has been shown to be neces-sary only in the deepest mantle, where the pathsof the two phases in the di¡erential pair di¡er themost. In the light of these studies, we haveadopted a similar approach to try to better modelour AB3DF observations.

The geometry of the pair AB/DF is quite sim-ilar to that of S/SKS: SKS and PKP(DF) dive atsteep angles into the core, while S and PKP(AB)graze the CMB at large distances, di¡ract over afew degrees, and can accumulate large residuals inthe strongly heterogeneous DQ. As found from

Fig. 3. (a) Number of AB3DF residuals as a function of an-gle h of the path in the inner core with respect to the Earth'srotation axis. (b) Plotted as a function of h, mean AB3DFresiduals observed (solid gray line), and predicted by Creag-er's [5] inner core constant (3.5%) anisotropy model (dashedline), and by a combination of the original tomographicmodel as well as ULVZs (solid black line). The combined ef-fect of ULVZs and heterogeneity predicted by the tomo-graphic model is not su¤cient to explain the averageAB3DF variations. (c) Same as (b) with observed residuals(gray line) compared to predictions by our MMM model.Mean residuals were obtained by averaging observed anoma-lies over 5³ in h. The root mean square di¡erences betweenaverage observations and predictions are 0.32 s for the tomo-graphic model, 0.19 s for the inner core model, 0.24 s for amodel combining the tomographic and inner core models,and 0.14 s for our modi¢ed mantle model, and the scatter ofthe mean residuals is estimated at 1.8 s.

global tomographic studies, the lowermost mantlepresents two major very slow, large scale anom-alous domains: one beneath the Central Paci¢c,and one beneath Africa (e.g. [24^34]). We haveassumed, as in [29^31], that slow velocity anoma-lies were strongly underpredicted under the Paci¢cand Africa, and we have increased their amplitudein the very bottom of the mantle, while notchanging their shape. All anomalies slower than0.3% for depths greater than 2500 km only weresaturated to 2% P-velocity reduction. Note thatthe thickness of the layer over which the modelis modi¢ed trades o¡ with the assigned P-velocityreduction.

In addition, in the computation of synthetic ABand DF residuals, we have included the e¡ect ofultra low velocity zones (ULVZs) in places wherethey have been reliably documented [35]. ULVZsare particularly important to consider becausethey represent a very large average P-velocity re-duction, and may signi¢cantly slow downPKP(AB) at the largest distances. We assignedvalues of 10% for the P-wave velocity reductionand 10 km for the thickness of the ULVZ. Thesevalues are conservative since some regions of DQhave been shown to experience P-velocity reduc-tions of more than 10% over a few tens of kilo-meters (e.g. [35,36]). There are also trade-o¡sbetween thickness of ULVZs and velocity re-ductions, which will not a¡ect the resulting ¢tssigni¢cantly, in terms of our conclusions. Inwhat follows, we will describe the prediction ofthe modi¢ed mantle model, ¢rst looking atspeci¢c source regions.

3. Predictions of the modi¢ed mantle model

3.1. Residuals for earthquakes in the Fiji Islandssource region (equatorial paths)

For events in the Fiji Islands source region, theobserved AB3DF residuals as a function of azi-muth (Fig. 4a) and angle h (Fig. 4b) show system-atic long wavelength variations, as well as largelocal scatter (in excess of 2 s), which cannot beexplained by either the tomographic (Fig. 4a,b) orinner core models considered previously (Fig.

4c,d). While we note that the tomographic modelpredicts more local scatter, both the inner coreand mantle models predict very little long wave-length variation as a function of either azimuth orh. The small e¡ect of inner core anisotropy is inagreement with the fact that, for this particularsource region, only angles hs 43³ are sampled,while the e¡ect of anisotropy only starts to besigni¢cant at h6 40³.

Synthetic residuals computed using this revisedmodel (MMM, Fig. 5) now show a better agree-ment with the observations (Fig. 4e,f), eventhough we did not attempt to adjust the modelto ¢t the data on any particular path. The modi-¢ed tomographic model predicts the large scaletrends and local scatter of the observed residuals.On the other hand, we veri¢ed that combining thenonmodi¢ed mantle model with ULVZs does notsigni¢cantly improve the ¢t compared the originaltomographic model alone. Note that the ¢t of the

Fig. 4. Observed AB3DF travel time residuals (gray dia-monds) for events located in the Fiji Islands region as afunction of azimuth from the source (left) and angle h withrespect to the Earth's rotation axis (right). Predicted anoma-lies (black triangles) are (a)(b) for the tomographic model de-scribed in (c)(d) for Creager's [5] inner core anisotropy mod-el, and (e)(f) for the MMM model

Fig. 5. Projections of the raypaths (blue lines) for the Fiji Islands events (white stars) used in this study, along with the corre-sponding stations (white triangles). Also indicated are the regions where ULVZs have been documented (bright yellow), and thepoints were the AB ray enters and exits the outer core (diamonds). The background MMM P-velocity model has been modi¢edfrom Grand's S-velocity model [24].

Fig. 6. Projections of the raypaths (blue lines) associated with stations SEY (Seymchan, Russia, 62.93³N 152.37³E), NRIL (Nor-ilsk, Russia, 69.50³N 88.44³E), and YAK (Yakutsk, Russia, 62.017³N 129.72³E) (white triangles), along with the correspondingevents (white stars) in the South Sandwich Islands source region. Also indicated are the regions where ULVZs were detected(bright yellow regions), and the points were the AB and DF rays enter and exit the outer core (diamonds and triangles, respec-tively). The background P-velocity model is the same as in Fig. 5.

MMM model is not perfect, and in particular,additional forward modeling of paths at azimuthof less 60³ (and mostly h6 50³) could improve itsigni¢cantly. This could be achieved by adjustingthe lateral extent of ULVZs near the source or thereceiver. It is not the purpose of this study, how-ever, to provide a best-¢tting model, which wouldinvolve resolving many trade-o¡s which are be-yond the scope of this paper. This simple experi-ment demonstrates how it is possible to explainboth the scatter and large scale variations ob-served in the di¡erential residuals by an e¡ect oflocally strong heterogeneities in the deep mantle,primarily on AB, with a distribution as docu-mented from previous work.

After departing from the Fiji Islands region,AB and DF both travel through several hundredkilometers of slow mantle. Although heterogene-ity is large there [29,37,38], the resulting anomalydoes not exceed about 1 s, because DF and ABare similarly a¡ected. Similarly, when AB and DFlater exit the outer core and propagate into thestrong slow African anomaly before being re-corded at African stations (Fig. 5), no di¡erentialresidual larger than 2 s is produced (Fig. 4). Someweakly anomalous di¡erential residuals corre-sponding to paths sampling the very heterogene-ous African region have also been reported [39].They do not contradict the existence of a veryslow region in this part of the deep mantle, asagain, DF and AB can sense the same structure,accumulate similar residuals, and yield di¡erentialresiduals close to zero.

3.2. South Sandwich to Eurasia (polar paths)

In some other regions, however, DF may prop-agate through a normal to fast heterogeneous re-gion in the lowermost mantle, while AB experien-ces some large delays due to a consistently veryslow anomaly. We believe this is the case for thequasi-polar paths from South Sandwich Islandsevents to northern Eurasia (Fig. 6). There is ac-tually direct evidence of an average mantle con-tamination of about 4 s on PKP(AB): for SouthSandwich Islands events, station SEY (62.93³N152.37³E) reports an average AB3DF residualof 5.0 s, but an average DF residual of 31 s [6].

This type of path happens to correspond to ageometry for which AB spends most of its timein the lower mantle within the large African slowanomaly (Fig. 7), while DF misses the zone ofstrongly reduced velocity. In addition, there areseveral paths which, on the receiver side, samplethe very anomalous ULVZ region recently de-tected beneath Iceland [36]. Predictions of the in-ner core anisotropy model (Fig. 8) are unable tomatch either the short or the long wavelengthtrends and amplitudes of AB3DF travel time re-siduals, at the three stations considered, whereasthe MMM model explains the large values of theresiduals as well as their variations much better,as a function of both the longitude of the CMBentry point of AB, and of angle h.

3.3. E¡ect on the complete dataset

We now compute the predictions of the MMMmodel for the complete, global dataset. Fig. 3cshows the predictions of the modi¢ed mantlemodel, without adding inner core anisotropy, asa function of angle h. The ¢t to both the trendand variation with angle of the binned data is atleast as good as that obtained with the inner coreanisotropy model in Fig. 3b. Fig. 2c,d shows theAB3DF residuals corrected for model MMM asa function of distance and h. While MMM hasnot been adjusted to provide a best ¢t for indi-vidual paths, and therefore some dispersion re-mains, a surprising result is that the trend of in-creasing residuals with decreasing h (Fig. 2b) haspractically disappeared (Fig. 2d). However, sev-eral unexplained anomalies are still present at an-gles close to 25³. These correspond to paths fromSouth Sandwich Islands to stations COLA andBILL (Fig. 1b). These paths have previouslybeen identi¢ed, on the basis of PKP(BC3DF)travel time measurements, as particularly anoma-lous, and correspond to very strong small scalelateral variations [40]. Comparing individualmeasurements at COL and neighboring stationINK (Fig. 1b), we ¢nd travel time residuals for(AB3DF) of 5 s and 2.6 s respectively, indicatingthat a highly complex zone is sampled somewherealong these paths, requiring strong heterogeneity.DF and AB station legs for COL and INK are

separated by about 400 km at the CMB. While avery complex anisotropic pattern could be presentin the inner core, these strong local variationscould also result from heterogeneity in DQ givenwhat we independently know about the deepmantle. For example DF at COL could be sam-pling a fast region on the border of an ULVZ, ashas been documented to exist in the Central Pa-ci¢c [29], while both DF and AB would be travel-ing through the ULVZ at INK. The e¡ect of sub-ducted slabs along the raypaths could alsocontribute to the di¡erential travel times [41].

4. Discussion

Observations of PKP(AB3DF) travel time re-

siduals exceeding 5^6 s are generally interpretedas evidence for the presence of a 3.5% averagecylindrical anisotropy in the bulk of the innercore. Because of the uneven distribution of sour-ces and receivers, these residuals happen to be, fora large part, associated with raypaths between theSouth Sandwich Islands region and northernEuropean, North American and Russian stations,which sample the edge of the African plume, atthe base of the mantle. AB3DF di¡erential resid-uals are extremely sensitive to P-velocity varia-tions at the base of the mantle [18^20], and wehave shown that it is possible to explain theirtrends, and even their sometimes large values, us-ing a simple modi¢cation to an existing tomo-graphic model that takes into account the com-plexity of the DQ region, as recently documented.

Fig. 7. (a) Cross section through the original tomographic model for a path between South Sandwich Island event 93/01/10(359.42³N 325.78³E 33 km) and station NRIL (distance 151.50³). Also plotted are AB, BC, and DF raypaths. (b) Same as (a)for a path to station SEY (distance 176.37³). Also plotted are the AB and DF raypaths (BC does not exist at this distance). (cand d) Same as (a) and (b) for the modi¢ed MMM velocity model. Note that the latter model is arbitrary outside regionssampled by our paths.

4. Discussion

Our forward modeling of AB3DF travel timessuggests that these large distance residuals arelikely to be signi¢cantly a¡ected by the strongheterogeneity present in the deep mantle beneaththe Paci¢c and Africa, and that this heterogeneitymust be taken into account accurately beforemaking inferences from this type of data regard-ing the strength and characteristics of inner coreanisotropy. The latter may have been much over-estimated, and, as Fig. 3b,c shows, there arestrong trade-o¡s between both e¡ects.

The MMM model which we have used to cor-rect PKP(AB3DF) data is not a de¢nitive model,since, with the exception of the ULVZ regions, ithas not been designed to ¢t any speci¢c dataset. Itshould not be expected to provide particularlygood ¢t to other dataset sensitive to DQ structure;it is a composite model re£ecting recent evidenceon the strength and distribution of heterogeneityin DQ [29^31,35,36]. While the MMM model, withall its trade-o¡s, may be valid in the regions

sampled by our dataset, we make no claims thatit is valid everywhere on the globe. Our goal inde¢ning it globally was only to qualitatively illus-trate the point that current tomographic modelsunderestimate amplitudes of lateral variations inDQ. In fact, MMM only ampli¢es low velocityzones, but stronger anomalies in high velocity re-gions are also needed in some places [29]. Also,MMM should not be expected to predict absoluteresiduals better than standard tomographic mod-els. Such travel times are very sensitive to mislo-cation e¡ects, and to the structure of the wholemantle, which is not accounted for in MMM.

Because MMM is not a real model, more accu-rate inferences on whether or not any anisotropyis still required in the central part of the innercore cannot be made at this point. In particular,DF absolute residuals should also be considered.We note however that, in order to attribute theobserved trends in di¡erential travel times to DF,rather than AB, a much more complex model ofinner core anisotropy or lateral heterogeneity inthe inner core [17] would be required, as has beensuggested for the very anomalous paths from theSouth Sandwich Islands to station COL [40].While the former deserves further investigation,the latter would imply extremely strong lateralgradients of velocity within the inner core, in or-der to explain the local scatter in the data as dis-cussed above. This is physically much less plausi-ble than a DQ origin, considering that the innercore is thought to have been formed by freezingof liquid core material largely homogenizedthrough vigorous convection. The strength of aprimarily DQ interpretation lies in its ability toexplain both long and short wavelength trendsin the data.

The large distance data discussed here provideinsight only into the structure of the deepest two-thirds of the inner core. In order to make infer-ences about the shallower parts, PKP(DF) abso-lute travel times, PKP(BC3DF) travel times [41],and normal mode data [42] must be consideredalso. Recent evidence based on PKP data in theBC range suggests however that at least one hemi-sphere may be isotropic [14]. Interestingly, quasi-polar paths sampling this hemisphere also happento propagate almost exclusively in a region of the

Fig. 8. AB3DF residuals for stations SEY, NRIL, andYAK, and South Sandwich Islands earthquakes, plotted as afunction of the longitude of the point where AB enters theouter core (a) and as a function of h (b). We compare obser-vations (black diamonds, black line), to predictions forCreager's [5] inner core anisotropy model (white circles,dashed line), and our modi¢ed tomographic model (gray tri-angles, gray line). The rms residual is 0.32 s for Creager'smodel, and 0.16 s for the MMM model.

deep mantle which seems to be less heterogeneousthan Africa or the central Paci¢c: there is so farno evidence for ULVZs between longitudes of 60and 150³E (Fig. 6). Recently, we have discussedcomplex trends in BC3DF travel time data forpolar paths, which require complex structure (ani-sotropic or isotropic) either at the top of the innercore, or at the bottom of the mantle [17]. Whilethis needs to be investigated further, the possiblelack of anisotropy near the top of the inner core[15] requires a reconsideration of anomalous nor-mal mode splitting [42].

There has been a lack of consensus as to thedetails of anisotropic structure in the inner core.We believe that the contamination of inner coresensitive data by structure at the bottom of themantle may have been generally underestimated,and that future e¡orts to derive realistic models ofinner core structure will have to accurately ac-count for such e¡ects.

Acknowledgements

The authors are grateful to an anonymous re-viewer for helpful comments and Emile Okal forhis careful review, and for suggestions on how toimprove the manuscript. We thank Michael Wy-session for helpful discussions, and the IRIS,CNSN, Geoscope, GRSN, Mednet, BDSN,SCSN, and GRSN teams. Figures were madewith the General Mapping Tools (P. Wessel,W.H.F. Smith, EOS Trans. AGU 76 (1995)329). This is BSL contribution 99-09.[RV]

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the e¡ect of dq on pkp(ab3df) travel time residuals and possible implications for...

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