2nd workshop on earthquake engineering for nuclear facilities:...

H4.SMR/1645-9

"2nd Workshop on Earthquake Engineering for NuclearFacilities: Uncertainties in Seismic Hazard"

14 - 25 February 2005

Analysis of Earthquake Catalogs

A. Peresan

Department of Earth SciencesUniversity of Trieste

SeismologicalSeismological database:database:Historical seismicityHistorical seismicity & & earthquake cataloguesearthquake catalogues

Analysis of Earthquake Analysis of Earthquake CatalogsCatalogsA. A. PeresanPeresan & G.F. & G.F. Panza Panza

2nd Workshop on Earthquake Engineering for Nuclear Facilities Uncertainties in Seismic Hazard Assessment

Trieste - Italy, 14 - 25 February 2005

.

Department of Earth SciencesUniversity of Trieste

OutlineOutline

Earthquakes and earthquakes catalogsEarthquakes and earthquakes catalogsMeasuring the size of an earthquakeMeasuring the size of an earthquakeHeterogeneity of earthquake catalogsHeterogeneity of earthquake catalogsUncertainties and catalog errorsUncertainties and catalog errorsExamples of catalogs analysisExamples of catalogs analysisDetection of long lasting changes in reported magnitudesDetection of long lasting changes in reported magnitudesEffects of random errors in magnitude on intermediateEffects of random errors in magnitude on intermediate--term middleterm middle--range earthquake predictions range earthquake predictions The GutenbergThe Gutenberg--Richter lawRichter law

What are earthquakes?What are earthquakes?

Earthquakes are generally due to sudden Earthquakes are generally due to sudden fractures in the outermost fragile part of the fractures in the outermost fragile part of the EarthEarth’’s lithosphere, the crust, that cause s lithosphere, the crust, that cause permanent deformations and radiate seismic permanent deformations and radiate seismic waves.waves.Seismic waves propagate from the source Seismic waves propagate from the source through the Earth in any direction, eventually through the Earth in any direction, eventually causing detectable ground shaking at the causing detectable ground shaking at the surface. surface. Although historical records on earthquakes are Although historical records on earthquakes are known from 2100 B.C., most of them before known from 2100 B.C., most of them before the middle of the 18the middle of the 18thth century are generally century are generally lacking description or are not reliable.lacking description or are not reliable.

Most of the earthquakes happen under water which makes their Most of the earthquakes happen under water which makes their detection and measurement even more difficult. detection and measurement even more difficult.

Some earthquakes produce tsunamis.Some earthquakes produce tsunamis.

Earthquakes with magnitude M>6 (USGS-NEIC data, 1900-2004)

Measuring the size of an earthquakeMeasuring the size of an earthquake

The information about the size of historical The information about the size of historical earthquakes is generally provided in terms of earthquakes is generally provided in terms of earthquake intensityearthquake intensity, i.e. a quantitative , i.e. a quantitative estimation based on the observed damage.estimation based on the observed damage.

It was only in the 1930's that It was only in the 1930's that Charles F. RichterCharles F. Richter, , a California seismologist, introduced the concept a California seismologist, introduced the concept of of earthquake magnitudeearthquake magnitude. .

Intensity scalesIntensity scales

The The MercalliMercalli scale was put forward by scale was put forward by MercalliMercalli in in 1902. An elaboration of the 1902. An elaboration of the MercalliMercalli scale, was scale, was published by published by SiebergSieberg in 1923. in 1923. This form was in turn used as the basis for the This form was in turn used as the basis for the Modified Modified MercalliMercalli (MM) (MM) Scale of 1931 by Wood and Scale of 1931 by Wood and Neumann. Neumann. Subsequently other intensity scales have been Subsequently other intensity scales have been introduced by introduced by MercalliMercalli, , CancaniCancani and and SiebergSieberg (MCS) (MCS) and by and by MedvedevMedvedev, , SponeuerSponeuer and and KarnikKarnik (MSK)(MSK). . More More recently the EMSrecently the EMS--1992 1992 macroseismicmacroseismic scale has been scale has been proposeproposed.d.


The existence of many The existence of many different scales is a different scales is a demonstration of the demonstration of the complexity of the problem complexity of the problem of describing earthquake of describing earthquake effects. The multiplicity of effects. The multiplicity of scales generates some scales generates some problems in practical problems in practical applications, that must applications, that must therefore rely upon very therefore rely upon very conservative assumptions.conservative assumptions.

Comparison of seismic intensity scales:MM – Modified MercalliRF – Rossi-ForelJMA – Japanese Meteorological AgencyMCS – Mercalli-Cancani-SiebergMSK – Medvedev-Sponheuer-Karnik


Intensity providesIntensity provides a qualitative a qualitative description description of of the the earthquake sizeearthquake size, , based based on the on the observation observation of the of the related damagerelated damage. . HenceHence, , for a given for a given earthquake, the intensity earthquake, the intensity I I can be different in can be different in different placesdifferent places. .

Intensity values Intensity values are discrete; are discrete; undue accuracy undue accuracy in in related computations related computations can can be misleadingbe misleading..

Horizontal Peak Ground Acceleration seismic hazard map representing stiff site conditions for an exceedance or occurrence rate of 10% within 50 years for the Mediterranean region.

The GSHAP probabilistic map at 475 years

VII VIII IX X XI

Comparison between GSHAP scale used in the Mediterrnean, and MCS Intensity scale

DGA(IDGA(I--1)/DGA(I)=21)/DGA(I)=2

PGV(IPGV(I--1)/PGV(I)=21)/PGV(I)=2

PGD(IPGD(I--1)/PGD(I)=21)/PGD(I)=2

The log-linear regression between maximum observed macroseismic intensity, I (MCS), and peak values of ground motion has a slope close to0.3 (see Panza et al., 1999; Shteinberg et al., 1993 and references therein). Hence one degree of intensity corresponds to a factor two in the values of ground motion:

Magnitude scalesMagnitude scales

Richter's original magnitude scale (Richter's original magnitude scale (MML L ) held only for ) held only for California earthquakes occurring within 600 km of a California earthquakes occurring within 600 km of a particular type of seismograph (i.e., the particular type of seismograph (i.e., the WoodsWoods--AndersonAnderson torsion instrument). Then it was extended torsion instrument). Then it was extended to observations of earthquakes of any distance and to observations of earthquakes of any distance and of focal depths ranging between 0 and 700 km.of focal depths ranging between 0 and 700 km.Because earthquakes excite both body waves, which Because earthquakes excite both body waves, which travel into and through the Earth, and surface travel into and through the Earth, and surface waves, which are constrained to follow the Earth's waves, which are constrained to follow the Earth's uppermost layers, two other magnitude scales uppermost layers, two other magnitude scales evolved evolved -- the the mmbb and and MMSS

What is an earthquake catalog?What is an earthquake catalog?

An earthquake catalog is a collection of information An earthquake catalog is a collection of information about a set of seismic events, basically including:about a set of seismic events, basically including:

-- Origin timeOrigin time-- LocationLocation-- Size of the earthquakesSize of the earthquakes

Additional information can be provided, ranging from Additional information can be provided, ranging from related damage to seismic source parameters.related damage to seismic source parameters.

A catalog may include several magnitude estimations, A catalog may include several magnitude estimations, generally with a precision of one digit, even if values generally with a precision of one digit, even if values provided by different agencies may differ more than provided by different agencies may differ more than one unit.one unit.

What is an earthquake catalog?What is an earthquake catalog?

Catalogs are compiled for different purposes and by Catalogs are compiled for different purposes and by different agencies. Therefore they differ in:different agencies. Therefore they differ in:

-- geographical coveragegeographical coverage-- time span time span -- level of detectionlevel of detection-- criteria of compilationcriteria of compilation-- type and quality of earthquake datatype and quality of earthquake data

Consequence: no unique catalog for a given territoryConsequence: no unique catalog for a given territory……but usually an heterogeneous set of catalogs (historical, but usually an heterogeneous set of catalogs (historical, instrumental, local, global, etc.), not always comparable, instrumental, local, global, etc.), not always comparable, which may require different tools of analysis.which may require different tools of analysis.

A positive step forward: compilation of global catalogs A positive step forward: compilation of global catalogs (e.g. USGS(e.g. USGS--NEIC and ISC)NEIC and ISC)

Global Number of Earthquakes vs. TimeGlobal Number of Earthquakes vs. Time

0.1

1

10

100

1000

10000

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

4.04.55.05.56.06.57.07.58.08.5

The USGS/NEIC Global Hypocenter Data BaseThe USGS/NEIC Global Hypocenter Data Base

The ISC Global Data BaseThe ISC Global Data Base

Bulletin of the International Seismological Centre

Regional Catalogue of earthquakes

Felt and Damaging earthquakes

What can we learn from a catalog of earthquakes?What can we learn from a catalog of earthquakes?

There are two extreme opinions on the subject:There are two extreme opinions on the subject:

PessimisticPessimistic: : “…“… in the case of seismic data, most of the in the case of seismic data, most of the observed variations are, in fact, related to changes in the observed variations are, in fact, related to changes in the system for detecting and reporting earthquakes and not to system for detecting and reporting earthquakes and not to actual changes in the Earth.actual changes in the Earth.””OptimisticOptimistic: Among existing data seismic catalogs remain the : Among existing data seismic catalogs remain the most reliable record on distribution of earthquakes in space andmost reliable record on distribution of earthquakes in space andtime.time.

All catalogs have errors, which may render invalid conclusions All catalogs have errors, which may render invalid conclusions derived in a study based on a catalog of earthquakes. derived in a study based on a catalog of earthquakes. Two ways to avoid the errors:Two ways to avoid the errors:-- Postpone the analysis until the data are refined;Postpone the analysis until the data are refined;-- Use robust methods within the limits of their applicability. Use robust methods within the limits of their applicability. When different catalogs are available, a When different catalogs are available, a comparative analysiscomparative analysismay allow to detect errors.may allow to detect errors.

Uncertainties and errorsUncertainties and errors

Uncertainty in magnitude determinationsUncertainty in magnitude determinationsEpicenter distance vs. Station magnitude Epicenter distance vs. Station magnitude for the 108 determinations for the 08 for the 108 determinations for the 08 September 2002 earthquake NEAR September 2002 earthquake NEAR NORTH COAST OF NEW GUINEANORTH COAST OF NEW GUINEA

10.0

10.5

11.0

11.5

12.0

12.5

13.0

42.5 43.0 43.5 44.0 44.5 45.0 45.5

Uncertainty in preliminary Uncertainty in preliminary epicentralepicentraldeterminationsdeterminationsFast determinations of the epicenter Fast determinations of the epicenter for the 14 September 2003 for the 14 September 2003 earthquake in Northern Italy by earthquake in Northern Italy by different seismological agencies to different seismological agencies to EuropeanEuropean--Mediterranean Mediterranean Seismological Centre (EMSC)Seismological Centre (EMSC)

The distribution of the difference between average magnitudes inThe distribution of the difference between average magnitudes inepicenter and antipodal hemispheresepicenter and antipodal hemispheres

MCHEDR 1990MCHEDR 1990--2000, all events that have three or more station magnitudes in e2000, all events that have three or more station magnitudes in each ach hemispherehemisphere

MS (4560 differences Average = -0.147, s = 0.198)

mb (8175 differences Average = 0.074, s = 0.274)

Herak, M. and Herak. D. (1993). Bull. Seism. Soc. Am., 83, 6, 1881-1892.

Historical and instrumentalHistorical and instrumental ccatalogsatalogs::the the exampleexample of of Spain Spain

TThe he catalogcatalog of of seismicityseismicity for the Iberian peninsulafor the Iberian peninsula (SSIS)(SSIS)

CatalogoCatalogo sismicosismico de la Peninsula de la Peninsula IbericaIberica (880 a.C.(880 a.C.--1900)1900)Martinez Solares and Mezcua Rodriguez (2002)

7160

39

29

1 6 1512

3 3

15,0 5,5 6,0 6,5 7,0 7,5 8,0 8,5 9,0 9,5 10,0

Intensity

1

3

5

79

20

40

60

80100

N of objects

1

474401 391

131

68

31

15

4

1 2 3 4 5 6 7 8 9 10Intensity (<=I)

5

50

500

N of objects 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900

Year

1

10

100

Ncu

m

Intensity>IAll123456789

SSIS catalog

Cumulative number of events vs. time and intensity

1 2 3


1000 1050 1100 1150 1200 1250 1300 1350 1400

Year

0

2

4

6

8

10

Inte

nsity

IntensityNo estimated intensity

SSIS catalog

Before 1400 the completeness threshold cannot be clearly identified. The catalogue is not complete for I>8 up to 1360

Time interval: 1000-1400

1300 1400 1500 1600 1700 1800 1900

Year

0

20

40

60

80

100

N(I=

0)%

SSIS catalogPercentage of events with I=0

High percentage of events without any intensity estimation in the SSIS catalogue, with some sensible reduction only since 1500


The catalogue appears complete for I>8 during the period 1400-1750


1400 1450 1500 1550 1600 1650 1700 1750

Year

1

10

Ncu

m


SSIS catalog

0 1 2 3 4 5 6 7 8 9 10

Intensity

1

10

100

1000

N o

f eve

nts

SSIS1400 - 1750

DiscreteCumulative


The catalogue appears complete for I>6 during the whole period 1750-1900and for I>5 (and eventually for I>4) since 1986.


1760 1780 1800 1820 1840 1860 1880 1900

Year

1

10

100

1000

Ncu

m


SSIS catalog

0 1 2 3 4 5 6 7 8 9 10

Intensity

1

10

100

1000

10000

N o

f eve

nts

SSIS1750 - 1900

DiscreteCumulative


The frequency-intensity distributions, obtained for the SSIS catalog over three different time intervals, are comparable only in the intensity range 7.0-8.5.

The cumulative distribution for the whole time interval 1400 – 1900 appears preferable for I>7.

The frequency of the events with I>9 appears much larger during the period 1750-1900 than for 1400-1750.

The catalog seems to be quite complete and homogeneous for intensities I>6 after 1750; nevertheless the time interval 1750-1900 alone is not enoughto characterise the frequency of thelarge events.

0 1 2 3 4 5 6 7 8 9 10

Intensity

0.001

0.01

0.1

1

10

Freq

uenc

y(N

cum/y

ear)

SSIS(main, in land events)

1400 - 19001400 - 17501750 - 1900


The overall increase in the number of earthquakes seems not due to an increased “detection” level, that should not affect the largest intensities, but would rather imply a progressive increase of the number of small events.We argue that the intensities reported in the two catalogs SSIS and IGN are not homogeneous and, if used all together, do not provide a consistent picture of seismicity.

Cumulative number of events vs. time for the SSIS catalog (1750 –1900) and for the IGN catalog (1900 – 2000). For the events reported without any intensity in the IGN catalogue, the intensity recalculated fromIGN magnitude mb (e.g. Lopez-Casado et al.,

2000) is considered.

1760 1780 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000

Year

1

10

100

1000

10000

Ncu

m


SSIS - IGN

Comparing low magnitude local cComparing low magnitude local catalogsatalogs::seismicityseismicity at Mt. at Mt. Vesuvius Vesuvius

Data used:Data used: catalog of volcanic earthquakes catalog of volcanic earthquakes recorded at the station OVO (recorded at the station OVO (OsservatorioOsservatorioVesuvianoVesuviano –– INGV, Naples) INGV, Naples)

Time periodTime period: 1972: 1972--20042004

The OVOThe OVO earthquake catalogearthquake catalog

OVOOVO

Time sequence of the events Time sequence of the events M(t) and yearly number of M(t) and yearly number of earthquakes with Mearthquakes with M≥≥MMCC=1.8 =1.8 reported in the OVO reported in the OVO catalogcatalog

1975 1980 1985 1990 1995 2000 2005Year

2.0

2.5

3.0

3.5

4.0

Mag

nitu

de

0

50

100

150

YearlyN

umber of events

Magnitude grouping:Magnitude grouping: The analysis The analysis evidences whether there are evidences whether there are dominating values of dominating values of magnitudes. It permits to magnitudes. It permits to choose the appropriate choose the appropriate intervals of magnitude intervals of magnitude grouping grouping ∆∆MM to be considered to be considered for the frequencyfor the frequency--magnitude magnitude distribution.distribution.

Catalog completeness: Catalog completeness: The The completeness of the catalog is completeness of the catalog is determined from the determined from the frequencyfrequency--magnitude magnitude distribution distribution λλ(M), where (M), where λ λ is is the number of earthquakes the number of earthquakes within each magnitude within each magnitude grouping interval grouping interval ∆∆M, M, normalized to the spacenormalized to the space--timetime--magnitude volume unit magnitude volume unit V=[1000 km2 x 1 year x 1 M]. V=[1000 km2 x 1 year x 1 M]. MMcompletenesscompleteness=M=MCC=1.8=1.8

The OVOThe OVO earthquake catalogearthquake catalog

TheThe time variations of the btime variations of the b--value in the Gutenbergvalue in the Gutenberg--Richter Richter (GR) law, (GR) law, are are analysed analysed and and show that it decreases show that it decreases progressively from 1.8, before progressively from 1.8, before 1986, to about 1.0 1986, to about 1.0 in in 1996. 1996.

N=100 events Mmin=1.8

1972 1976 1980 1984 1988 1992 1996 2000 2004Year

0.75

1

1.25

1.5

1.75

2

b-va

lue

(Maximum likelihood estimation by Wiemer & Zuniga, ZMAP software)

Time Time changes changes in in seismic activityseismic activity: : analysisanalysis of the OVO of the OVO catalocatalogg

The seismic energy release is studied considering the quantity The seismic energy release is studied considering the quantity E*E*,, energy energy normalised to normalised to the minimum the minimum magnitude eventmagnitude event,, computed from magnitude computed from magnitude according to the formula:according to the formula:

d d = const= const)( min10* MMdE −=

The The time variations of the btime variations of the b--value and seismic energy release, observed for value and seismic energy release, observed for the OVO the OVO catalogcatalog, are checked , are checked performing performing a a similar analysissimilar analysis withwith a a different different catalogcatalog of of Vesuvian earthquakesVesuvian earthquakes, , as compiled fromas compiled from the the recordsrecords at the BKE at the BKE station station duringduring the the periodperiod 19921992--2003.2003.

Time Time changes changes in in seismic activityseismic activity: : comparisoncomparison withwith the BKE the BKE catalogcatalog

t0

200

400

600

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

BKEOVO

E m*(

t)

3.1

Em*=Σmonth101.5(M-Mmin)

3.0(3.0)

3.53.1

(3.6)(3.1)

3.4(3.3)

3.4

3.1(3.1)

(3.2)

(2.7)

The The analysis performed analysis performed using the using the catalogcatalogcompiled for the BKE compiled for the BKE stations confirms the stations confirms the bb--value decrement value decrement and and the the identification of the identification of the periods of quiescence periods of quiescence and activity, since and activity, since 1994.1994.

t0

200

400

600

800

1000

1200

1400

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

BKEOVO

E y*(

t)

Ey*=Σyear101.5(M-Mmin)

L(30%)3.1

3.0(3.0)

(2.7)

3.53.1

(3.6)(3.1)

3.4

3.1(3.1)

(3.2)

3.4(3.3)

a1 a2 a3

Time Time changes changes in in seismic activityseismic activity: : comparisoncomparison withwith the the BKE BKE catalogcatalog

N=100 events Mmin=1.8

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004Year

0.75

1

1.25

1.5

1.75

2

b-va

lue

OVOBKE

The differences observed during the period 1992-1994 are well explained by a certain overestimation of BKE durations during such period of time, as shown by the comparison of OVO and BKE durations for the common events

0 20 40 60 80 100 120 140 160DBKE

0

20

40

60

80

100

120

140

160

DO

VO

1992-1993Fit Least squares

N=357Least squares: Y = 0.65 X + 0.67

0 20 40 60 80 100 120 140 160DBKE

0

20

40

60

80

100

120

140

160

DO

VO


N=546Least squares: Y = 0.94 X - 3.75

0 20 40 60 80 100 120 140 160DBKE

0

20

40

60

80

100

120

140

160

DO

VO


N=926Least squares: Y = 0.94 X - 5.19

Time Time changes changes in in seismic activityseismic activity: : comparisoncomparison withwith the BKE the BKE catalogcatalog

Problem: identification of the common events in catalogs characterised by low magnitude and highly clustered events

Analysis of Earthquake Analysis of Earthquake CatalogsCatalogsfor Earthquake Prediction purposes: for Earthquake Prediction purposes:

the Case of Italythe Case of Italy

Algorithms fully formalized and globally tested for prediction are:

CN algorithm (Gabrielov et al., 1986; Rotwain and Novikova, 1999)

M8 algorithm (Keilis-Borok and Kossobokov, 1987; Kossobokov et al., 1999)

They allow to identify the TIPs(Times of Increased Probability) for the

occurrence of a strong earthquake within a delimited region

Algorithms for Algorithms for mmiddleiddle--range range iintermediatentermediate--term term ppredictionrediction

The algorithms are based on a set of empirical functions to allow for a quantitative analysis of the premonitory

patterns which can be detected in the seismic flow:

These methods make use of detectable inverse cascade of seismic process, at different space and time ranges, to

reduce consecutively space and time limits where a disastrous earthquake has to be expected.

Variations in the seismic activity Seismic quiescenceSpace-time clustering of events

Algorithms for Algorithms for mmiddleiddle--range range iintermediatentermediate--term term ppredictionrediction

TIPTime of Increased

ProbabilityInterval of time when the

probability for the occurrence of a strong earthquake, within a

delimited region, increases with respect to

the normal conditionsSeismic flow

Time sequence of the earthquakes occurred within a delimited region

•DST:2) Quiescence:The sign + indicates that the sum includes only the positive terms; therefore only the time intervals (t-s,t) where the number of earthquakes is less than the average are considered.

The dotted horizontal line indicates the average number of events expected in the time interval of length s. The grey areascorrespond to the periods of quiescence.

The larger is the value assumed by the function, the more marked and prolonged is the quiescence.

•DST:2) Quiescence:The sign + indicates that the sum includes only the positive terms; therefore only the time intervals (t-s,t) where the number of earthquakes is less than the average are considered.

The dotted horizontal line indicates the average number of events expected in the time interval of length s. The grey areascorrespond to the periods of quiescence.

The larger is the value assumed by the function, the more marked and prolonged is the quiescence.

Functions of the Functions of the seismic flowseismic flow

i=1,...,n u=ns

It is a measure of the cumulative

changes in time of the earthquake number

V t M,s,u( )= i N ti M,s( )− N ti −1 M,s( )∑

Variation of seismic activity

V t M,s,u( )

DST:


Is the sum of the differences between the numbers of earthquakes in two consecutive time intervals.

It corresponds to the sum of the differences between the numbers of earthquakes in two consecutive time intervals,with fixed length s. The moments belong to the time interval (t−u,t), where u is multiple of s. Usually s is equal to one year.

DST:


Is the sum of the differences between the numbers of earthquakes in two consecutive time intervals.

It corresponds to the sum of the differences between the numbers of earthquakes in two consecutive time intervals,with fixed length s. The moments belong to the time interval (t−u,t), where u is multiple of s. Usually s is equal to one year.

CN algorithm and long lasting changes CN algorithm and long lasting changes in reported magnitudesin reported magnitudes

Keilis-Borok, , Kutznetsov, Panza, Rotwain & Costa (1990)

Costa, Stanishkova, Panza& Rotwain (1996)

Peresan, Costa & Panza (1996)

1960 1970 1980 1990 2000

0

4

-100

100.00.51.0

01020

0480240

1020

04080

02040

N2

K

G

Sigma

Smax

Zmax

N3

q

BmaxTime diagrams of the standard CN functions obtained for the Central region(Peresan et al., 1999)

Functions Sigma, Smaxand Zmax and are evaluated for 4.2≤M≤4.6, functions K, G, N3, q for M≥4.5 and functions N2 for M ≥5.0


Catalogues Catalogues comparisoncomparison

Common events:∆T≤1min

∆Lat, ∆Lon≤1°(Storchak, Bird and Adams, 1998)

ING

LDGML

PDE(NEIC)

ING

PDE(NEIC)

ML, Md

1000

1985

June1997

PFG

Paperbulletins

ING

Digital bulletins

ML, Md

ML, Md

1980

Revised

CCI1996

•DST:In order to perform the magnitude comparison, the events common to the different catalogues are identified according to the following rules: a) time difference 1 minute; b) epicentral distance: 1° for the comparison with the global catalogue (Storchak, Bird and Adams, 1998). No limitation is imposed to magnitude or depth differences.


Magnitude comparison: Magnitude comparison: Central RegionCentral Region

Yearly Average differencesNEIC-ING

Duration Magnitude

Local Magnitude

Md(NEIC)-Md(ING)Md ≥3.0

(1983-1997)∆Md=0.30±0.04

Yearly Average

ML(NEIC)-ML(ING)ML ≥3.0

(1980-1986)∆ML=0.13±0.05

(1988-1997)∆ML=0.64±0.04

Yearly Average

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

Year

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

∆ML

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

Year

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

∆Md

Md≥3.0

ML≥3.0



Magnitude comparison: Magnitude comparison: Central RegionCentral Region

Local MagnitudeDifferences

...

..

Num

of o

bs

0

10

20

30

40

50

60

70

-2,0 -1,6 -1,2 -0,8 -0,4 0,0 0,4 0,8 1,2 1,6 2,0

ML(NEIC)<3.0

∆ML

...

..

Num

of o

bs

0

20

40

60

80

100

-2,0 -1,6 -1,2 -0,8 -0,4 0,0 0,4 0,8 1,2 1,6 2,0

∆ML

3.0≤ML(NEIC)<4.2

...

..

Num

of o

bs

0

5

10

15

20

25

30

35

-2,0 -1,6 -1,2 -0,8 -0,4 0,0 0,4 0,8 1,2 1,6 2,0

∆ML

ML(NEIC)≥4.2

Central Region

(ING)M(NEIC)MM LLL −=∆



Time diagrams of the standard CN functions obtained for the Central region(Peresan et al., 1999) :

M=ML(ING)+0.5

CN algorithm and CN algorithm and long lasting changes long lasting changes in reported magnitudesin reported magnitudes

1960 1970 1980 1990 2000

0

4

-100

100.00.51.0

010200480240

1020

040800

2040

N2

K

G

Sigma

Smax

Zmax

N3

q

Bmax

Central Italy

ML(ING)+0.5 since 1987

N o r th e r n R e g io n - D M L y e a r ly a v e r a g eD M L= M L ( N E I C ) - ML ( I N G )

8 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 8 9 9 0 9 1 9 2 9 3 9 4 9 5 9 6 9 7- 0 , 8

- 0 , 4

0 , 0

0 , 4

0 , 8

1 , 2

1 , 6

Magnitude comparison: Magnitude comparison: Northern RegionNorthern Region

Yearly Average differencesNEIC-ING

Local Magnitude

∆ML=ML(NEIC)- ML(ING)

0.3(NEIC)ML ≥

Average difference:

(1980-1986) LM∆ =0.16±0.10

(1988-1997) LM∆ =0.64±0.04



Magnitude comparison: Magnitude comparison: Italian territoryItalian territory

Events used for Md analysis

Yearly number of common events used for the comparison between ING and NEIC catalogues

Events used for ML analysis1980 1982 1984 1986 1988 1990 1992 1994 1996

Year

1

10

100

1000

Num

of o

bs

ML: Common events >4.0 >3.0All

1980 1982 1984 1986 1988 1990 1992 1994 1996

Year

0

1

10

100

1000

Num

of o

bs

Md: Common events >4.0 >3.0All

a)

b)

MLML

Md

Md



Frequency scatter-plots of ∆Md and ∆ML versus the corresponding NEIC magnitude


1 case2-35 cases36-70 cases71-104 cases105-139 cases140-173 cases>173 cases

...

..

.-3

-2

-1

0

1

2

3

4

0,5 1,5 2,5 3,5 4,5 5,5 6,5 7,5

∆ML=ML(NEIC)-ML(ING)

ML(NEIC)

∆ML


...

..

.

-2,5

-1,5

-0,5

0,5

1,5

2,5

3,5

0,5 1,5 2,5 3,5 4,5 5,5 6,5

∆Md=Md(NEIC)-Md(ING)

Md(NEIC)

∆Md


Before 1987

MLNEIC

DM

L

-3

-2

-1

0

1

2

3

4

1 2 3 4 5 6 7ML(NEIC)

∆ ML


After 1987

MLNEIC

DM

L

-3

-2

-1

0

1

2

3

4

1 2 3 4 5 6 7

∆ML

ML(NEIC)

∆Md

∆ML




∆∆MMLL

∆∆MMdd




∆∆MMLL=0=0AllAll




Duration MagnitudeNEIC - ING

a)

b)1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

Year

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

Year

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

∆ML

∆Md

LocalMagnitudeNEIC - ING

MD(NEIC)-MD(ING)MD ≥3.0

(1983-1986)∆MD=0.30±0.02

YearlyAverage

YearlyAverage

ML(NEIC)-ML(ING)ML (NEIC)≥3.0

(1980-1986)∆ML=0.08±0.05

(1988-1993)∆ML=0.30±0.04

(1995-1997)∆ML=0.77±0.06




Local Magnitude:Yearly Average differences

ML(LDG)-ML(ING)ML ≥3.0

(1980-1986)∆ML=0.18±0.08

(1988-1996)∆ML=0.44±0.04

YearlyAverage

ML(NEIC)-ML(LDG)ML ≥3.0

(1980-1986)∆ML=0.03±0.06

(1988-1996)∆ML=0.08±0.03

Yearly Average

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

Year

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

∆ML

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998

Year

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

∆ML

LDG - ING

NEIC - LDG

ML≥3.0

ML≥3.0



The analysis of CN functions in Central Italy allowed us to detect a relevant long lasting change in the reported magnitudes.

The comparison of individual magnitudes, reported by ING and NEIC, indicates, since 1987, an average underestimation of about 0.5 in the Local Magnitude provided by ING.


•DST:The analysis of CN functions in Central Italy allowed us to detect a relevant long lasting change in the reported magnitudes.The comparison of individual magnitudes, and , reported by ING and NEIC catalogues indicates, since 1987, an average

underestimation of about 0.5 in the provided by ING. The hypothesis of general local magnitude underestimation in the Italian ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the use of ING bulletins for CN algorithm application and makes

necessary to use global data like NEIC.

•DST:The analysis of CN functions in Central Italy allowed us to detect a relevant long lasting change in the reported magnitudes.The comparison of individual magnitudes, and , reported by ING and NEIC catalogues indicates, since 1987, an average

underestimation of about 0.5 in the provided by ING. The hypothesis of general local magnitude underestimation in the Italian ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the use of ING bulletins for CN algorithm application and makes

necessary to use global data like NEIC.

The presence of a general local magnitude underestimation in the Italian ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.

(Peresan, Panza & Costa, GJI 2000)

(Gasperini, Vannucci & Orlanducci: “Rivalutazione della magnitudo per i terremoti italiani nel periodo post 1980”. In: “Catalogo strumentale dei terremoti Italiani dal 1981 al 1996” – 2001)

CN algorithm and long lasting CN algorithm and long lasting changes changes

in reported magnitudesin reported magnitudes

•DST:The analysis of CN functions in Central Italy allowed us to detect a relevant long

lasting change in the reported magnitudes.

The comparison of individual magnitudes, and , reported by ING and NEIC catalogues indicates, since 1987, an average underestimation of about 0.5 in the provided by ING. The hypothesis of general local magnitude underestimation in the Italian ING

bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the use of ING bulletins

for CN algorithm application and makes necessary to use global data like NEIC.

•DST:The analysis of CN functions in Central Italy allowed us to detect a relevant long

lasting change in the reported magnitudes.


bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the use of ING bulletins

for CN algorithm application and makes necessary to use global data like NEIC.

Compilation of a Compilation of a homogeneous updated homogeneous updated catalogue for CN monitoring catalogue for CN monitoring in Italyin Italy

Databases available to us:

CCI1996: PFG revised+ING bulletins (Italian catalogue, available up to July 1997)Priority: ML, Md, MI

NEIC: PDE Preliminary Determinations of Epicentersfrom NEIC (global catalogue).Priority: to be defined (available M: mb, MS, M1, M2)

ALPOR: Catalogo delle Alpi Orientali (local catalogue for eastern Alps)Priority: ML, MI

•DST:The analysis of CN functions in Central Italy allowed us to detect a

relevant long lasting change in the reported magnitudes.

The comparison of individual magnitudes, and , reported by ING and NEIC catalogues indicates, since 1987, an average underestimation of about 0.5 in the provided by ING. The hypothesis of general local magnitude underestimation in the Italian

ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the use of

ING bulletins for CN algorithm application and makes necessary to use global data like NEIC.

•DST:The analysis of CN functions in Central Italy allowed us to detect a

relevant long lasting change in the reported magnitudes.

The comparison of individual magnitudes, and , reported by ING and NEIC catalogues indicates, since 1987, an average underestimation of about 0.5 in the provided by ING. The hypothesis of general local magnitude underestimation in the Italian

ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the use of

ING bulletins for CN algorithm application and makes necessary to use global data like NEIC.

Compilation of a homogeneous Compilation of a homogeneous updated catalogue for CN updated catalogue for CN monitoring in Italymonitoring in Italy

Procedure:

•Study of the completeness of PDE catalogue;

•Study of the relations between different kind of magnitudes reported in the CCI1996 and PDE catalogues;

•Formulation of a rule for the choice of magnitude priority in PDE, similar to the priority used for CCI1996;

•Construction of the Updated catalogue, integrating CCI1996, ALPOR and NEIC data (compatibly with the completeness of NEIC).

•DST:The analysis of CN functions in Central Italy allowed us to detect a relevant

long lasting change in the reported magnitudes.


bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the use of ING

bulletins for CN algorithm application and makes necessary to use global data like NEIC.






Operating Operating magnitmagnitudeudeselectionselection

M(CCI1996) – mb(PDE) M(CCI1996) – M1(PDE)

0 1 2 3 4 5 6 7 8mb(pde)

0

1

2

3

4

5

6

7

8

ML(

cci)

0 1 2 3 4 5 6 7 8mb(pde)

0

1

2

3

4

5

6

7

8

Mi(c

ci)

0 1 2 3 4 5 6 7 8mb(pde)

0

1

2

3

4

5

6

7

8

Md(

cci)

b=0.81a=0.60N=64sd=0.27P=6.25%

b=2.72a=-7.94N=118sd=0.29P=3.39%

b=1.19a=-1.07N=313sd=0.31P=6.07%

0 1 2 3 4 5 6 7 8M1(pde)

0

1

2

3

4

5

6

7

8

ML(

cci)

0 1 2 3 4 5 6 7 8M1(pde)

0

1

2

3

4

5

6

7

8

Mi(c

ci)

0 1 2 3 4 5 6 7 8M1(pde)

0

1

2

3

4

5

6

7

8

Md(

cci)

b=0.82a=0.51N=223sd=0.22P=5.38%

b=1.12a=-0.62N=17sd=0.33P=5.88%

b=0.91a=0.18N=452sd=0.24P=5.75

•DST:The analysis of CN functions in Central Italy allowed us to detect a relevant long lasting

change in the reported magnitudes.

The comparison of individual magnitudes, and , reported by ING and NEIC catalogues indicates, since 1987, an average underestimation of about 0.5 in the provided by ING. The hypothesis of general local magnitude underestimation in the Italian ING bulletins

is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the use of ING bulletins for

CN algorithm application and makes necessary to use global data like NEIC.







0 1 2 3 4 5 6 7 8MS(pde)

0

1

2

3

4

5

6

7

8

Ml(c

ci)

0 1 2 3 4 5 6 7 8MS(pde)

0

1

2

3

4

5

6

7

8

Mi(c

ci)

0 1 2 3 4 5 6 7 8MS(pde)

0

1

2

3

4

5

6

7

8

Md(

cci)

b=0.63a=1.77N=3sd=0.06P=0%

b=0.74a=1.59N=2sd=0.002P=0%

b=0.64a=1.72N=9sd=0.25P=0%

0 1 2 3 4 5 6 7 8M2(pde)

0

1

2

3

4

5

6

7

8

ML(

cci)

0 1 2 3 4 5 6 7 8M2(pde)

0

1

2

3

4

5

6

7

8

Mi(c

ci)

0 1 2 3 4 5 6 7 8M2(pde)

0

1

2

3

4

5

6

7

8

Md(

cci)

b=0.86a=0.49N=91sd=0.20P=4.40%

b=1.07a=-0.45N=31sd=0.34P=3.23%

b=0.98a=0.05N=122sd=0.26P=4.10%

M(CCI1996) – MS(PDE) M(CCI1996) – M2(PDE)












(PD E)M S

(PDE)1M

(PDE)2M

(P D E )m b

(CCI)Md

(CCI)M L

Poor statisticNot representative of any of CCI magnitudes

)M,M,(MM IdLCCI )M,1M,2(MMPDE S

•DST:The analysis of CN functions in Central Italy allowed us to detect a relevant long lasting change in the reported magnitudes.The comparison of individual magnitudes, and , reported by INGand NEIC catalogues indicates, since 1987, an average underestimation of about 0.5 in the provided by ING. The hypothesis of general local magnitude underestimation in the Italian ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the useof ING bulletins for CN algorithm application and makes necessary to use global data like NEIC.

•DST:The analysis of CN functions in Central Italy allowed us to detect a relevant long lasting change in the reported magnitudes.The comparison of individual magnitudes, and , reported by INGand NEIC catalogues indicates, since 1987, an average underestimation of about 0.5 in the provided by ING. The hypothesis of general local magnitude underestimation in the Italian ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the useof ING bulletins for CN algorithm application and makes necessary to use global data like NEIC.


0 1 2 3 4 5 6 7 8M

0

0

1

10

100

1000

10000

Ncu

m/y

ear

CCI Time: 1900-1985PDE Time: 1986-1997

CCI(ML,Md,Mi)

PDE(M2,M1,MS) recalculated

PDE(M2,M1,MS) not recalculated

Mc

0 1 2 3 4 5 6 7 8M

0

1

10

100

1000

Lat:37-42 Lon:12-18

NEIC: 1992-1993

1994-1995

1996-1997

0 1 2 3 4 5 6 7 8 9M

1

10

100

1000

Lat:37-42 Lon:12-18

1986-1987

1988-1989

1990-1991

NEIC:

NEIC:

NEIC:

NEIC:

NEIC:

a)

b)

Southern Italy

Central Italy

•DST:The analysis of CN functions in Central Italy allowed us to detect a relevant long lasting change in the reported magnitudes.

The comparison of individual magnitudes, and , reported by ING and NEIC catalogues indicates, since 1987, an average underestimation of about 0.5 in the provided by ING. The hypothesis of general local magnitude underestimation in the Italian ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the use of ING bulletins for CN algorithm application and makes necessary to use global data like NEIC.

•DST:The analysis of CN functions in Central Italy allowed us to detect a relevant long lasting change in the reported magnitudes.

The comparison of individual magnitudes, and , reported by ING and NEIC catalogues indicates, since 1987, an average underestimation of about 0.5 in the provided by ING. The hypothesis of general local magnitude underestimation in the Italian ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced magnitude change prevents the use of ING bulletins for CN algorithm application and makes necessary to use global data like NEIC.

The The Updated Updated Catalogue Catalogue of of ItalyItaly

UCI2001UCI2001

1000

1980

1986

2002

CCI ALPOR NEIC

ML(PFG)MI (PFG/CFT)

MS(NEIC)mb(NEIC)

ML(contrib)

UCI

MI (PFG/CFT/Alpor)

ML(PFG/Alpor/NEIC)

ML(INGV)Md(INGV)

NEIC(PDE)

ML(Alpor)MI(Alpor)

MS(NEIC)mb(NEIC)

M1(contrib)M2(contrib)

ML(INGV/NEIC)Md(INGV)MS(NEIC)mb(NEIC)

MS(NEIC)mb(NEIC)

MS(NEIC)mb(NEIC)

M1(contrib)M2(contrib)

The The Updated Updated Catalogue Catalogue of of ItalyItaly

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000Year

1

10

100

1000

10000

Ncu

m

Mmax>MAll1.02.03.04.05.06.07.0

UCI catalog

Stability of intermediateStability of intermediate--term earthquake term earthquake predictions with respect to random errors predictions with respect to random errors

in magnitude: the case of Central Italyin magnitude: the case of Central Italy

CN is essentially based on the information contained in the earthquake catalogues.

It analyses the seismic flow using: origin time, epicentralcoordinates and magnitudes of earthquakes.

All catalogues are inevitably affected by errors. Magnitudes are characterised by the most significant errors,

conditioning both aftershocks removal and seismic flow.

Systematic Errors Random Errors

How random errors on reported magnitudesaffect CN prediction results?

DICR MMMM ∆+∆+=

Randomised Magnitude

Mc : operating magnitude∆MI : measurement error ∆MD : error of discretisation

Measurement random errors

P(∆MI) = FTR(∆MI) Truncated normal probability distribution with:

FTR(∆MI) = F(∆MI)/[2F(∆Mmax)-1]Mmax = maximum assumed error on magnitudes

3maxM=σ

maxI MM ∆≤∆

Errors of magnitude discretisation

P(∆MD) = Uniform probability distributionInterval: [-d/2; d/2)

d=discretization step=0.1

•DST:The analysis of CN functions in

Central Italy allowed us to detect a relevant long lasting change in the reported magnitudes.

The comparison of individual magnitudes, and , reported by ING and NEIC catalogues indicates, since 1987, an average underestimation of about 0.5 in the provided by ING. The hypothesis of general local

magnitude underestimation in the Italian ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced

magnitude change prevents the use of ING bulletins for CN algorithm application and makes necessary to use global data like NEIC.

•DST:The analysis of CN functions in

Central Italy allowed us to detect a relevant long lasting change in the reported magnitudes.

The comparison of individual magnitudes, and , reported by ING and NEIC catalogues indicates, since 1987, an average underestimation of about 0.5 in the provided by ING. The hypothesis of general local

magnitude underestimation in the Italian ING bulletins is substantiated by the cross-comparison performed between ING, LDG and NEIC catalogues.The presence of the evidenced

magnitude change prevents the use of ING bulletins for CN algorithm application and makes necessary to use global data like NEIC.

Magnitude Magnitude randomisationrandomisation

Discretization step

0

500

1000

1500

2000

2500

3000

3500

3 3,1 3,2 3,3 3,4 3,5 3,6 3,7 3,8 3,9 4 4,1 4,2 4,3 4,4 4,5 4,6 4,7 4,8 4,9 5

Magnitude

N(M

)

1950-19991950-19801980-1999

Discretisation step: d=0.1

3.0 4.0 5.0 6.0 7.0Magnitude

0.1

1.0

10.0

100.0

1000.0

N(M

)

a)

3.0 4.0 5.0 6.0 7.0Magnitude

0.1

1.0

10.0

100.0

1000.0

N(M

)

b)

3.0=∆ maxM

5.0=∆ maxM

Distribution of the number of events versus magnitude for the original and the

randomised catalogues



Results obtained with the Results obtained with the original catalogueoriginal catalogue

TIPs obtained with the original catalogue with a different length of the “thresholds setting

period” (Learning)

26.9.1997

23.11.198021.8.1962

9.9.1998

5.86.0 6.5

5.76.0

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Year

5.7

a)

Long Learning (1954-1998)

5.86.0 6.5

5.76.0

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

Year

5.7

b)

Short Learning(1954-1986)

PredictionPrediction of the of the events with events with MM≥≥5.65.6



Results obtained with Results obtained with the the randomisedrandomised cataloguecatalogue

∆Mmax

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

a)

∆Mmax

0.0 0.1 0.2 0.3 0.4 0.5

0

20

40

60

80

100

b)Long Learning Short Learning

Original catalogueAll randomised cataloguesAverage of randomised



Results Results obtained with obtained with the the randomisedrandomisedcataloguecatalogue

∆Mmax=0.1

0 20 40 60 80 100

0

20

40

60

80

100

0 20 40 60 80 100

0

20

40

60

80

100

0 20 40 60 80 100

0

20

40

60

80

100

∆Mmax=0.2 ∆Mmax=0.3

Central ItalyLearning: 1954-1998

RandomisedOriginal

ηη=n/N =n/N : : the rate of the rate of failuresfailures--toto--predictpredict

ττ=t/T=t/T : : the rate of time the rate of time of alarmsof alarms

•N is the number of strong earthquakes occurred during the time period T covered by predictions

•The alarms cover altogether the time t and they have missed n strong events

•N is the number of strong earthquakes occurred during the time period T covered by predictions

•The alarms cover altogether the time t and they have missed n strong events

Results obtained with theResults obtained with the randomised randomised catalogue:catalogue:variation of variation of target eventstarget events



Event date M NS, % NP, %

23.11.1980 6.5 100.0 66.7

21.8.1962 6.0 100.0 93.3

26.9.1997 6.0 100.0 40.0

9.9.1998 5.7 83.3 56.0

19.9.1979 5.5 23.3 0.0

5.5.1990 5.5 12.0 0.0

7.5.1984 5.4 0.0 0.0

List of earthquakes with

Central Italy: 1950-19995.3M ≥

Results obtained with theResults obtained with therandomisedrandomised cataloguecatalogue

>∆< η



Average differences in prediction errors

OCOriginal Catalogue

RCsRandomised Catalogues

StabilityStability of of TIPs diagnosisTIPs diagnosis

Θ(t): percentage of testsfor which the time t belongs to a TIP

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

time

0

20

40

60

80

100

Θ(t)

%

Central Italy(Long threshold setting period)

3.0=∆ maxM

Ψ=|Θ−50|

Ψ

No

of o

bs

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25 30 35 40 45 50

Ψ: percentage of tests for which the recognition of the time t does not change with

respect to its average value 0≤Ψ≤50



The results of prediction remain stable for ∆Mmax<0.3.

To guarantee the stability of the results, the thresholds setting period must be long enough to include a significant sample of dangerous and non dangerous intervals of time.

The quality of predictions is mainly controlled by the percentage of failures to predict, which depends on the changes in the number of strong earthquakes.

The identification of TIPs is very stable during most of the time and the randomisation does not introduce spurious alarming patterns associated with the occasionally strong events.

Stability of CN predictions Stability of CN predictions with respect to random with respect to random

errors in magnitudeerrors in magnitude











CN algorithm (Keilis-Borok et al., 1990; Peresan et al., 2004)

M8S algorithm (Kossobokov et al, 2002)

Main features:Fully formalized algorithms and computer codes available for independent testing;Use of published & routine catalogues of earthquakes;Worldwide tests ongoing for more than 10 years permitted to assess the significance of the issued predictions.

Italy:Stability tests with respect to several free parameters of the algorithms (e.g. Costa et al., 1995; Peresan et al., GJI, 2000; Peresan et al., PEPI, 130, 2002);CN predictions are regularly updated every two months since January 1998. M8s predictions are regularly updated every six months since January 2002.

Real time prediction experiment started in July 2003Real time prediction experiment started in July 2003

IntermediateIntermediate--term middleterm middle--range earthquake prediction range earthquake prediction experiment in Italyexperiment in Italy

The experiment, launched starting on July 2003, is aimed at a real-time test of M8S and CN predictions in Italy.

Updated predictions are regularly posted at:“http://www.ictp.trieste.it/www_users/sand/prediction/prediction.htm”

A complete archive of predictions is made accessible to a number of scientists, with the goal to accumulate a collection of correct and wrong predictions, that will permit to validate the considered methodology.

Current predictions are protected by password. Although these predictions are intermediate-term and by no means imply a "red alert", there is a legitimate concern about maintaining necessary confidentiality.

IntermediateIntermediate--term middleterm middle--range earthquake prediction range earthquake prediction experiment in Italyexperiment in Italy

Predictions asPredictions as on: 1on: 1--11--2005 (2005 (subject to updatesubject to update on: 1on: 1--33--2005)2005)

CN CN algorithmalgorithm in in ItalyItaly

Northern Region, Mo=5.4

6.5 5.4 5.8 6.0

1965 1975 1985 1995 2005

5.55.65.5

Central Region, Mo=5.65.86.0 6.5

5.76.0

1955 1965 1975 1985 1995 2005

5.7

Southern Region, Mo=5.65.86.0 6.55.8

1955 1965 1975 1985 1995 2005

5.7

Algorithm CN predicted 12 out of the 13 strong earthquakesoccurred in the monitored zones of Italy, with 32% of the considered space-time volume occupied by alarms.(updated to December 31 2004)

SpaceSpace--time volume of alarm in CN application in Italytime volume of alarm in CN application in Italy

ExperimentSpace-time volume

of alarm (%)Confidence

level (%)

Retrospective*(1954 – 1963)

41 93

Retrospective(1964 – 1997)

27 >99

Forward(1998 – 2004)

47 90

All together(1954 – 2004)

32 >99

ExperimentSpace-time volume

of alarm (%) n/N

Retrospective*(1954 – 1963)

41 3/3

Retrospective(1964 – 1997)

27 5/5

Forward(1998 – 2004)

41 4/5

All together(1954 – 2004)

32 12/13

IntermediateIntermediate--term middleterm middle--range earthquake range earthquake prediction CNprediction CN

* Central and Southern regions only

M≥6.5 M≥5.5M≥6.0

Predictions asPredictions as on: 1on: 1--77--2004 (2004 (subject to updatesubject to update on: 1on: 1--11--2005)2005)

Monitored region Alerted region

M8S M8S algorithmalgorithm in in ItalyItaly

24/11/2004Mmax=5.5

Algorithm M8S predicted 62% of the events occurred in the monitored zones in Italy, i.e. 16 out of 26 events occurred within the area alerted for the corresponding magnitude range (updated to December 31 2004).

The confidence level of M5.5+ predictions since 1972 has been estimated to be about 97%; no estimation is still possible for M6.0+ and M6.5+.

Experiment M6.5+ M6.0+ M5.5+

Space-time volume, %

n/N Space-time volume, %

n/N Space-time volume, %

n/N

Retrospective(1972-2001)

36 2/2 40 1/2 39 9/14

Forward(2002-2004)

49 0/0 43 0/0 25 4/8

All together(1972-2004)

37 2/2 40 1/2 38 13/22

SpaceSpace--time volume of alarm in M8s application in Italytime volume of alarm in M8s application in Italy

The GutenbergThe Gutenberg--Richter lawRichter law

Averaged over a large territory Averaged over a large territory and time the number of and time the number of earthquakes equal or above earthquakes equal or above certain magnitude, N(M) scales certain magnitude, N(M) scales asas

loglog1010N(M) = aN(M) = a--bMbM

This general law of similarity This general law of similarity establishes the scaling of establishes the scaling of earthquake sizes in a given space earthquake sizes in a given space time volume but gives no time volume but gives no explanation to the question how explanation to the question how the number, N, changes when the number, N, changes when you zoom the analysis to a you zoom the analysis to a smaller size part of this volume. smaller size part of this volume.

0.1

1

10

100

1000

10000

4.0 5.0 6.0 7.0 8.0 9.0

The analysis of global The analysis of global seismictyseismicty shows that a single Gutenbergshows that a single Gutenberg--Richter (GR) law is not universally valid and that a Richter (GR) law is not universally valid and that a multiscalemultiscaleseismicityseismicity modelmodel ((MolchanMolchan, , KronrodKronrod & & PanzaPanza, BSSA, 1997, BSSA, 1997)) can can reconcile two apparently conflicting reconcile two apparently conflicting conceptsconcepts the Characteristic the Characteristic Earthquake (Earthquake (CECE) the Self) the Self--Organized Criticality (Organized Criticality (SOCSOC))..

The The multiscalemultiscale seismicityseismicity model, implies that only the set of model, implies that only the set of earthquakes with dimensions that are small with respect to the earthquakes with dimensions that are small with respect to the dimensions of the analysed region can be described adequately dimensions of the analysed region can be described adequately by the Gutenbergby the Gutenberg--Richter lawRichter law..

This This conditonconditon, fully satisfied in the study of global , fully satisfied in the study of global seismicityseismicitymade by Gutenberg and Richter, has been violated in many made by Gutenberg and Richter, has been violated in many subsequent investigations. subsequent investigations.

WhichWhich are the limits of are the limits of validityvalidity of the powerof the power--law scaling law scaling expressed byexpressed by the the GutenbergGutenberg--RichterRichter lawlaw? ?

The counts in sets of cascading The counts in sets of cascading squares, squares, ““telescopestelescopes””, estimate the , estimate the natural scaling of the spatial natural scaling of the spatial distribution of earthquake epicenters distribution of earthquake epicenters and provide evidence for rewriting the and provide evidence for rewriting the GutenbergGutenberg--Richter recurrence law the Richter recurrence law the generalisedgeneralised form: form:

The scheme for boxThe scheme for box--countingcounting

loglog1010N = A + BN = A + B··(5 (5 -- M) + CM) + C··loglog1010LL

where N = N(M, L) is the expected where N = N(M, L) is the expected annual number of earthquakes with annual number of earthquakes with magnitude M in an area of linear magnitude M in an area of linear dimension L.dimension L.

The first resultsThe first results

The method was tested successfully on artificial catalogs and apThe method was tested successfully on artificial catalogs and applied in a plied in a dozen of selected seismic regions from the hemispheres of the Eadozen of selected seismic regions from the hemispheres of the Earth to a rth to a certain intersection of faults.certain intersection of faults.

((KossobokovKossobokov and and MazhkenovMazhkenov, 1988, 1988))

MultiscaleMultiscale seismicityseismicity modelmodel

UCI2001 catalogue1900-2002

1.6 2 2.4 2.8 3.2

Log(L)

0.1

1

10

100

1000

10000

100000

Num

ber o

f eve

nts

Magnitude33.544.555.566.5

0 1 2 3 4 5 6 7 8Magnitude

0.1

1

10

100

1000

10000

100000

Num

ber o

f eve

nts

AreaLL/2L/4L/8L/16

Physics of the Earth and Planetary Interiors 130 (2002) 117–127

Stability of intermediate-term earthquake predictions with respectto random errors in magnitude: the case of central Italy

A. Peresana,∗, I. Rotwainb, I. Zaliapinb, G.F. Panzaa,ca Department of Earth Sciences, University of Trieste, via E. Weiss 1, 34127 Trieste, Italy

b International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences,Warshavskoe sh.79, kor.2, Moscow 113556, Russia

c The Abdus Salam International Centre for Theoretical Physics, SAND Group ICTP, 34100 Trieste, Miramare, Italy

Received 22 December 2000; received in revised form 26 November 2001; accepted 3 December 2001

Abstract

The influence of random magnitude errors on the results of intermediate-term earthquake predictions is analyzed in thisstudy. The particular case of predictions performed using the algorithm CN in central Italy is considered. The magnitudes ofall events reported in the original catalog (OC) are randomly perturbed within the range of the expected errors, thus generatinga set of randomized catalogs. The results of predictions for the original and the randomized catalogs, performed followingthe standard CN rules, are then compared. The average prediction quality of the algorithm CN appear stable with respect tomagnitude errors up to±0.3 units. Such a stable prediction is assured if the threshold setting period corresponds to a timeinterval sufficiently long and representative of the seismic activity within the region, while if the threshold setting period istoo short, the average quality of CN decreases linearly for increasing maximum error in magnitude. © 2002 Elsevier ScienceB.V. All rights reserved.

Keywords: Earthquake prediction; Algorithm CN; Magnitude error; Randomization; Italy

1. Introduction

A generation of intermediate-term earthquake pre-diction algorithms was developed and exhaustivelytested during the past two decades (Gabrielov et al.,1986; Keilis-Borok, 1990; Minster and Williams,1992; Keilis-Borok and Shebalin, 1999; Kossobokovet al., 1999; Rotwain and Novikova, 1999; Vorobieva,1999). The empirical nature of these algorithms, how-ever, makes it difficult to evaluate their efficiency andstrength in a formal way, due to the long time requiredfor the tests in real predictions and to the possible

∗ Corresponding author. Tel.:+39-40-6762-129;fax: +39-40-6762-111.E-mail address: [email protected] (A. Peresan).

over-fitting in retrospective studies. This stimulatedthe development of different specific methods forthe evaluation of algorithms quality (Habermann andCreamer, 1994; Minster and Williams, 1992; Keilis-Borok and Shebalin, 1999). One relevant questionthat still needs to be answered is: to what extentare predictions influenced by the unavoidable errorsaffecting the input data?

Earthquake catalogs represent the most widely avai-lable geophysical data, containing systematicallycollected information about seismicity. This is whymost of the studies concerning precursory phenom-ena, and therefore earthquake predictions, are basedon the analysis of earthquake catalogs. The catalogscontain errors which can be distinguished into sys-tematic and random ones (this is comprehensively

0031-9201/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S0031-9201(01)00311-9

118 A. Peresan et al. / Physics of the Earth and Planetary Interiors 130 (2002) 117–127

discussed by Kossobokov, 1995). Systematic errorscan be associated to changes in the data acquisitionsystem or in the methods for the determination ofearthquake parameters. Random errors correspondgenerally to the uncertainty of determination and topossible mistakes made during the data input pro-cess. The presence of a systematic error in magni-tude may hamper prediction results and is generallyquite difficult to detect (Habermann, 1991; Haber-mann and Creamer, 1994; Kossobokov and Shebalin,1995); some aspects of this problem for the Ital-ian catalog have been considered by Peresan et al.(2000).

The goal of this work is to study the influence onthe results of intermediate-term earthquake predictionof random errors in magnitude determination. We ana-lyze here the particular case of earthquake predictionsperformed by CN algorithm (Keilis-Borok and Rot-wain, 1990). The algorithm uses origin time, hypocen-tral coordinates and magnitude of earthquakes. Amongthese parameters, magnitude is the most significantsource of errors in the results of predictions, becauseit enters in the determination of the values of the func-tions describing the seismic sequence as well as inthe definition of the strong earthquakes (Rotwain andNovikova, 1999).

Our analysis is based on the predictions per-formed for central Italy (Peresan et al., 1999b). Toestablish the dependence of the prediction resultson possible random errors in magnitude, the algo-rithm CN is applied to several “randomized” catalogs(RC). These RC are obtained by random modifica-tion, within the range of the assumed errors, of themagnitudes of all events. The results of predictionsobtained for the original catalog (OC) and the RCsare compared, providing useful information aboutthe stability and the expected performances of thealgorithm.

2. General scheme of prediction with CNalgorithm

The algorithm CN has been designed for the pre-diction of strong earthquakes, which are the eventswith magnitude greater or equal to a fixed thresholdM0. The algorithm is based on the analysis of a setof empirical functions describing the earthquake flow.

These functions are normalized by thresholds in mag-nitude, which are selected on the basis of the averagereturn period of events observed during thethresh-olds setting period. The functions are discretized intosmall, medium and large values, accordingly to thelevel of seismic activity in the considered region, andthe thresholds for discretization are selected by the ret-rospective analysis of seismicity within the thresholdssetting period. The discretization of functions causessome loss of information, but makes the algorithmmore robust with respect to fluctuations in the data.The thresholds setting period must correspond to aninterval of time long enough to provide a representa-tive sample of the seismic activity within the consid-ered region, including periods of quiescence as wellas periods of high activity (Keilis-Borok and Rotwain,1990).

The algorithm CN identifies the times of increasedprobability (TIPs) for the occurrence of strong earth-quakes. When a strong event occurs during a TIP, thenit is indicated as asuccessful prediction, otherwise it isreferred asfailure to predict. If no strong earthquakeoccurs during a declared TIP, then the TIP is called afalse alarm.

According to Molchan (1990), the results of a pre-diction can be characterized by two types of errors.The first one is the percentageη of failures to pre-dict: η = F /N, whereF is the number of failures topredict andN the number of events to be predicted.The second one is the percentageτ of the total dura-tion of alarms:τ = A/T, whereA is the total durationof alarms andT the length of the whole time intervalconsidered. The strength of a prediction is estimatedby the analysis of theerror diagram, collecting infor-mation on both types of errors. According to Molchan(1990, 1996), in order to characterize the quality ofpredictions in terms of the errorsη andτ , it is possibleto consider any convex functionΩ = f (η, τ ). Amongthe several possible functions, the sum of errors ap-pears to be the most straightforward and suitable forthe evaluation of the outcomes, as recommended byMolchan (1996). Hence, in the present analysis thequality of predictions will be quantified by the sumof errors:Ω = η + τ . Since the random predictiongives Ω = 1 (Molchan, 1990), one can roughly es-timate the quality of prediction by the deviation ofΩ from unity (or from the corresponding percentageΩ = 100%).

A. Peresan et al. / Physics of the Earth and Planetary Interiors 130 (2002) 117–127 119

3. Magnitude randomization procedure

The procedure of magnitude randomization simu-lates possible random magnitude errors in the analyzedcatalog. In the present study, we concentrate on twotypes of random errors: the error ofmeasurement andthe errors of magnitudediscretization.

The value of magnitude reported in the catalog isusually the result of estimations made from severalstations recording the occurrence of an earthquake.The error of measurement represents the several fac-tors (radiation pattern, local effects, etc.) that mayinfluence the records of an event at different stationsand consequently affect the magnitude estimation.We use here a rough assumption that the final mea-surement errorMM is normally distributed. Sincethe observed magnitude is finite, we use forMMthe truncated normal distributionFTR(x), that isdefined on the intervalx ∈ [−Mmax, ∆Mmax]as

F TR(x) = F(x) − F(Mmax)

F (Mmax) − F(−Mmax)

= F(x) − F(Mmax)

2F(Mmax) − 1(1)

whereF(x) denotes the cumulative normal distributionwith 0 mean and S.D. = ∆Mmax/3. The measurementerrorMM thus becomes normally distributed on theinterval [−Mmax, Mmax] while the values outsidethis interval are disallowed.

The values of magnitudes are calculated as realnumbers with several digits, but their precision hardlyexceeds the first decimal digit (e.g. the magnitudes cal-culated from intensity, which is a discrete scale, exhibita discrete distribution); for this reason the measuredvalues are usually rounded, i.e. they are discretized tofit some predefined lattice. LetMC be the operatingmagnitude selected from the catalog andk the step ofthe discretization lattice, when discretizing (i.e. round-ing) the magnitude, an error as large as±k/2 can beintroduced. Since the measured magnitude may cor-respond to any of the values in the magnitude interval[MC − (k/2), MC + (k/2)), then we assume that theerror of magnitude discretizationMK has a uniformdistribution within the interval [−k/2, k/2].

Considering the quantitiesMC, MM, andMK defined earlier, we introduce the randomized

magnitudeMR

MR = MC + MM + MK (2)

where the measurement errorMM and the error ofdiscretizationMK are independent.

4. Data analysis

4.1. Numerical parameters for randomization

The randomization procedure, introduced in Section3, depends on two parameters:k andMmax. The pa-rameterk is uniquely determined by the used catalog,which is fully described by Peresan et al. (1999a).

The catalog is composed by the CCI1996 (Peresanet al., 1997) for the period 1900–1985, and is updatedusing the NEIC preliminary determinations of epicen-tres (PDE) since 1986. The operating magnitude inthe catalog CCI1996 is selected according to the fol-lowing priority order: ML, Md, MI (Molchan et al.,1997), whereML is the local magnitude,Md the du-ration magnitude andMI the magnitude from intensi-ties. A corresponding priority choice has been definedfor the magnitudes in the PDE catalogue as follows:M2, M1, Ms. The magnitude from the surface wavesestimated by NEIC is given byMs, while M1 andM2correspond to magnitudes of different kind, suppliedby different agencies, mainly corresponding to localand duration magnitudes (Peresan et al., 1999a andreferences therein).

The number of earthquakes in different magni-tude intervals and for three time periods (1950–1980,1980–1999 and for the entire interval 1950–1999) isgiven in Fig. 1. It is possible to observe that since1950 the magnitudes are determined to the first deci-mal digit, hence the discretization step isk = 0.1.

The second parameter of randomization,Mmax, isa variable one. According to Båth (1973), from empir-ical observations we can expect errors as large as±0.3units in reported magnitudes; such a value is confirmedby theoretical arguments (Panza and Calcagnile, 1974;Herak et al., 2001). Hence, in the present study wewill assumeMmax = 0.3 as an upper bound for re-alistic errors in magnitude. Larger values forMmaxare considered in order to evaluate the dependence onMmaxof the quality of the results. The randomizationprocedure is applied to the OC, varying the parameter


Fig. 1. Number of earthquakes with 3≤ M ≤ 5 reported in the OC (Peresan et al., 1999a) for three different periods of time: 1950–1980,1980–1999 and 1950–1999.

Mmax, and a set of 110 RCs is generated: 30 cata-logs forMmax = 0.1, 0.2 and 0.3, plus 10 catalogsfor Mmax = 0.4 and 0.5.

It is necessary to check that the randomization pro-cedure does not affect the basic features of the earth-quake sequence, the magnitude–frequency relationbeing the most important. The magnitude–frequencyrelations for the OC and for the RCs withMmax =0.3 andMmax = 0.5 are shown in Fig. 2. The dis-tributions are quite similar and the differences withrespect to the OC become relevant only at the largestmagnitudes, due to the small number of events. Thelinearity of the frequency–magnitude relation is pre-served even forMmax as large as 0.5 and theb-valuedoes not change significantly, since it is mainlycontrolled by the small and intermediate magnitudeevents.

4.2. Predictions based on the original catalog

The application of CN algorithm for the inter-mediate-term earthquake prediction in central Italy(Fig. 3) is described in detail by Peresan et al.(1999b). Six strong events withM ≥ M0 = 5.6 oc-curred during the considered time interval. In two

cases (21 August 1962 and 26 September 1997) twostrong earthquakes occurred in the same day andvery close in space. Such “coupled” events cannot bedistinguished at the time scale characteristic of thealgorithm, since CN predictions are performed with atime step of 2 months. These earthquakes will be as-sociated to the same TIP, hence they must be countedjust as a single event (i.e. instead of six strong earth-quakes, there are just four events to be predicted).

The results of predictions obtained for two differ-ent thresholds setting periods are shown in Fig. 4. Inthe first case the thresholds setting period, referred aslong period, lasts from 1 January 1954 to 31 Decem-ber 1998. In the second case, it lasts from 1 January1954 to 31 December 1985, and it is referred asshortperiod. The results of predictions are summarized inthe following paragraphs.

For the long thresholds setting period (Fig. 4a),three out of the four strong events are predicted, withthe percentage of the total alarm durationτ ≈ 21%.The coupled event (M = 5.7 and 6.0), occurred on 26September 1997, is a failure to predict; henceη = 25%andΩ ≈ 46%. For the short thresholds setting period(Fig. 4b), TIPs occupy about 22% of the total time andprecede all the four strong events, henceη = 0, τ ≈


Fig. 2. Distribution of the number of events versus magnitude for the RCs with (a)Mmax = 0.3 and (b)Mmax = 0.5. For eachmagnitude interval the average number of events (filled dots) and its S.D. (vertical bars) are given for the RCs, together with the numberof events in the OC (open squares).


Fig. 3. Region used for the routine application of the algorithmCN in central Italy (Peresan et al., 1999b). The epicentres of thestrong events are given together with their occurrence time. Notethat the events occurred on 21 August 1962 and 26 September1997, are “coupled” events (i.e. two strong earthquakes occurredin the same day and close in space).

22% andΩ ≈ 22%. Therefore, predictions associatedwith the short thresholds setting period seem to pro-vide a better score, despite of the reduced informationconsidered. However, the analysis of the stability ofthese two results, described in Section 4.3, will showthat the long thresholds setting period supplies morestable results.

Fig. 4. TIPs obtained with the OC for (a) the long thresholdssetting period and (b) the short thresholds setting period. Blackboxes indicate the TIPs (periods of alarm). Arrows with a numberabove indicate the time of occurrence of strong earthquakes andtheir magnitude; failures to predict are given in gray.

4.3. Predictions based on the randomized catalogs

The algorithm CN is applied to each of the RCs in-dependently, following the standard rules. The thresh-old M0 for the selection of the events to be predictedis kept equal to 5.6, the same as for the OC, in order tocheck the stability of the set of events to be predictedwith respect to this threshold.

The results of predictions obtained for 50 RCs—10 for eachMmax from 0.1 to 0.5—are syntheticallydescribed by means of the sum of errorsΩ = η + τ .The values ofΩ versusMmax are shown in Fig. 5.

With the long thresholds setting period (Fig. 5a),individual results can be comparable or even betterthan the original one forMmax up to 0.4; the valuesof 〈Ω〉, averaged for eachMmax, are approximatelyequal to the original value (Ω = 46%) forMmax ≤0.2. The exact values of the average errors of predic-tion, 〈τ 〉, 〈η〉 and〈η+τ 〉 (together with its S.D.σ ) forthe differentMmax, are given in Table 1. The orig-inal result obtained with the long thresholds settingperiod appears quite stable with respect to magnitudeerrors up to±0.2.

For the short thresholds setting period (Fig. 5b), onecan observe an increasing trend of〈Ω〉, showing thatthe quality of predictions decreases almost linearlywith Mmax. In particular, the average values〈Ω〉 aresignificantly larger than theΩ = 22.1% correspond-ing to the OC and all the results obtained using the RCsappear worse than the original one. Hence, this resultappears very sensitive to possible magnitude errors. Itsgood quality, obtained at the price of stability, seemsto indicate some over-fitting to the original data, andcasts some doubts about the real predictive capabilityof CN, when using the short thresholds setting period.

The analysis described earlier allows us to singleout the instability of the prediction results related tothe insufficient length of the thresholds setting period.In fact, due to the small number of strong events oc-curred during the short thresholds setting period (onlytwo events), the information provided to the algorithmabout the seismic activity preceding the strong eventsis limited, and hence it strongly depends on the fewgiven cases.

Henceforth, we consider only the long thresholdssetting period. ForMmax = 0.4 and 0.5, 10 testspermit already to evidence the instability of results;therefore it seems not necessary to investigate further


Fig. 5. Diagram showing the dependence of prediction errorsΩ = η + τ on Mmax for (a) the long thresholds setting periodand (b) the short thresholds setting period. The circles indicatethe η + τ values for the 10 RCs used for eachMmax; stars showtheir average values. The horizontal dashed line and the full dotindicate theη + τ value for the OC. The quantitiesη and τ aredefined in the text.

Table 1Average errors of prediction for differentMmax

Mmax 〈τ 〉 (%) 〈η〉 (%) 〈η + τ 〉 ± σ (%)

0.1 22.8 22.5 42.7± 19.10.2 24.1 28.8 46.7± 19.60.3 26.5 40.6 62.8± 20.90.4 27.1 30.3 57.4± 17.00.5 28.6 41.2 69.8± 12.7

the effects of such large errors. For smaller errors, in-stead, additional tests are needed, in order to prop-erly evaluate the stability of the results, as well asto improve the significance of the analysis. A com-prehensive analysis is then performed for 90 RCs, 30each forMmax = 0.1, 0.2 and 0.3, respectively. Infact, Mmax = 0.3 is a realistic estimate of the up-per bound for the error which can affect magnitudes(Båth, 1973; Panza and Calcagnile, 1974; Herak et al.,2001) and it corresponds to the value ofMmax forwhich predictions begin to be unstable (Fig. 5a).

The stability of the results is evaluated by meansof the error diagrams (Molchan et al., 1990), com-piled for the results obtained with the OC and the RCs(Fig. 6). Each point in the (η, τ ) plane corresponds tothe prediction obtained for a given catalog; the diag-onal line defined by the equationΩ = η + τ = 100%corresponds to the results of a random guess. Theclustering of points indicates the stability of predic-tions, while the increasing distance from the diagonalline indicates the increasing quality of the predictions.Fig. 6 shows that, forMmax ≤ 0.2, the results arequite well clustered around the one obtained with theOC, while forMmax ≤ 0.3 they appear much morescattered. The errorτ , indicating the percentage oftime occupied by alarms, does not vary significantlywith respect to the original predictions. Therefore, thechanges in the quality of the results are mainly due toa larger percentage of failures to predictη, which isstrictly related to the changes in the number of eventsto be predicted. This aspect emerges quite clearly fromTable 2, showing the average difference between theCN results obtained using the OC and those obtainedusing the RCs:〈τ 〉 = 〈τ 〉−τO and〈∆η〉 = 〈η〉−ηO,whereτO andηO are the prediction errors for the OC(Fig. 6). The average variation of the number of strongeventsNSE has been evaluated by means of the re-lation: 〈NSE〉 = 〈|NR − NO|/NO〉, whereNO and


Fig. 6. Error diagrams for the results of TIPs diagnosis using theOC (bold cross) and the RCs (circles) with long thresholds settingperiod. The diagonal line corresponds to the results of a randomguess. Thirty tests have been performed for eachMmax.

NR are the numbers of events to be predicted (withM ≥ 5.6) in the OC and in the RCs, respectively; forMmax = 0.3 both〈NSE〉 and〈η〉 increase signif-icantly.

Table 2Average difference between the results of CN obtained using theOC and those obtained using the RCs

Mmax 〈τ 〉 (%) 〈η〉 (%) 〈(η + τ )〉 (%) 〈NSE〉 (%)

0.1 2.2 −2.5 −0.3 0.00.2 3.5 3.8 7.3 2.50.3 5.9 15.6 21.5 13.4

〈τ 〉, 〈η〉: average variation of prediction errors for the RCs;〈NSE〉 = 〈|NR − NO|/NO〉: average variation of the number ofstrong events;NO: number of events to be predicted in the OC;NR: number of events to be predicted in the RC.

A list of the earthquakes, ordered by decreasingmagnitude, withM ≥ 5.3 in the OC, occurred incentral Italy (Fig. 3) during the period 1950–1999, isprovided in Table 3. This table contains informationabout all the events whose randomized magnitude mayexceed the thresholdM0 = 5.6 for Mmax = 0.3.The percentage of times each earthquake turns out tobe a strong event,NSE, and the percentage of times itis predicted (NP) are provided as well, considering 30RCs. The table shows that the earthquakes with orig-inal magnitude less than 5.6, sporadically becomingstrong events, are never predicted. This explains thedrastic increase of the errorη for Mmax = 0.3, andat the same time indicates that the randomization doesnot introduce spurious alarming patterns, as it clearlyappears from the analysis of the stability of TIPsidentification.

To evaluate the stability of predictions we haveanalyzed also the variation of TIPs. Considering aset of predictions made for the same time interval,the quantityΘ(t) has been defined as the percentageof cases where the instantt is identified as a TIP.

Table 3List of earthquakes withM ≥ 5.3, central Italy 1950–1999

Event date M NSE (%) NP (%)

23 November 1980 6.5 100.0 66.721 August 1962a 5.8/6.0 100.0 93.326 September.1997a 5.7/6.0 100.0 40.09 September 1998 5.7 83.3 56.019 September 1979 5.5 23.3 0.05 May 1990 5.5 12.0 0.07 May 1984 5.4 0.0 0.0

a “Coupled” events, occurred in the same day and very close inspace. The magnitudes of both the strong earthquakes are provided.


Fig. 7. The percentageΘ(t) is the number of tests for which the time (t) belongs to a TIP. Black boxes represent the TIPs declared usingthe OC. Black arrows indicate the time of occurrence of strong earthquakes (M ≥ M0 = 5.6) in the OC. Grey open arrows indicateadditional strong earthquakes sporadically appearing in the RCs. The distance of the arrows from the dashed line is proportional to themagnitude reported in the OC. Thirty tests have been performed withMmax = 0.3.

Fig. 7 shows the functionΘ(t) based on the results ofpredictions for the 30 RCs withMmax = 0.3.

All the original TIPs appear to be very stable; more-over, TIP is never declared during considerable part ofthe time. This confirms the conclusion about the highstability of the results.

5. Discussion and conclusions

The stability of the intermediate-term predictionswith respect to random errors in magnitudes has beenevaluated considering as an example the CN predic-tion for central Italy. The algorithm has been applied,following the standard rules, to a set of catalogs with

magnitudes randomly modified (RCs) within the rangeof the assumed errors, and the outcomes of these pre-dictions have been compared with the results obtainedwith the OC. Our analysis shows that the results ofprediction remain stable forMmax < 0.3. The qual-ity of predictions seems to be mainly controlled bythe percentage of failures to predict, which dependson the changes in the number of strong earthquakes(M ≥ M0), almost negligible forMmax ≤ 0.2. Thestrong events generated by the randomization are neverpredicted, thus increasing the percentage of failures topredict.

The procedure used here for magnitude random-ization has been defined on the basis of quite roughand sketchy arguments. This study, however, is not


aimed to provide neither the optimal randomizationprocedure nor the best definition of random magni-tude errors and certainly, the appropriate constructionof the optimal model for such errors represents anopen problem.

Prediction algorithms have generally a set of fit-ting parameters that, in the case of CN algorithm,correspond to the thresholds for normalization and dis-cretization of functions. These parameters are fixedby the retrospective analysis of seismicity during thethresholds setting period; once they are assigned fromthe analysis of past seismicity the algorithm is ap-plied for prediction, using such fixed parameters. Therandomization procedure introduced in this paper canhelp both to evaluate the stability of the algorithm andto prevent data over-fitting. The tests performed withthe RCs show that, with a short thresholds setting pe-riod, the average quality of results decreases linearlyfor increasing magnitude error, while with a longerthresholds setting period it appears to be constant, atleast forMmax < 0.3. This indicates that, in order toguarantee a certain stability of the results, the thresh-olds setting period must be long enough to includea significant sample of dangerous and non-dangerousintervals of time, otherwise the assigned parameters ofthe algorithm will strongly depend on the few givencases. This would lead to an excessive sensibility topossible data errors and hence to worst predictionresults.

Therefore, from now onward, the application of thealgorithm CN in Italy will be performed using the pa-rameters fixed with the analysis of the OC with thelong thresholds setting period. In this case, the resultsshould be robust at least for magnitude errors lowerthan±0.3, with an expected score aroundΩ = 55%.This value ofΩ is in good agreement with the av-erage performance of CN in 22 regions of the world(Rotwain and Novikova, 1999). The results of routinepredictions for the central Italy region (Fig. 3), up-dated to 1 September 2001, indicate a TIP, lasting fromNovember 2000 up to 1 September 2002, both consid-ering the short and the long thresholds setting period.

Acknowledgements

We are grateful to M.G. Shnirman and I. Kuznetsovfor the precious suggestions and for the useful

discussions. During this study AP was supportedby MURST (Cofinanziamento and 60% funds) andby CNR (contract 98.03238.PF54), IR and IZ weresupported by a sucontacted with Cornell University,Geological Sciences, under EAR-9804859 from theUS National Science and administered by the USCivilian Research & Development Foundation forthe Independent States of the former Soviet Union(CRDF) and by the Abdus Salam International Centrefor Theoretical Physics, Trieste, Italy.

References

Båth, M., 1973. Introduction to seismology. Birkhauser, Basel, 365pp.

Gabrielov, A.M., Dmitrieva, O.E., Keilis-Borok, V.I., Kossobokov,V.G., Kutznetsov, I.V., Levishina, T.A., Mirzoev, K.M.,Molchan, G.M., Negmatullaev, S.Kh., Pisarenko, V.F., Prozorov,A.G., Rinheart, W., Rotwain, I.M., Shelbalin, P.N., Shnirman,M.G., Schreider, S.Yu., 1986. Algorithms of long termearthquakes’ prediction, International School for ResearchOriented to earthquake Prediction Algorithms. Software andData Handling. Lima, Peru.

Habermann, R.E., 1991. Seismicity rate variations and systematicchanges in magnitudes in teleseismic catalogs. Tectonophysics193, 277–289.

Habermann, R.E., Creamer, F., 1994. Catalog errors and the M8earthquake prediction algorithm. Bull. Seismol. Soc. Am. 84,1551–1559.

Herak, M., Panza, G.F., Costa, G., 2001. Theoretical and observeddepth corrections for Ms. Pure and Appl. Geophys. 158,1517–1530.

Keilis-Borok, V.I. (Ed.), 1990. Intermediate-term EarthquakePrediction: Models, Algorithms, Worldwide Tests (specialissue). Phys. Earth Planet. Int. 61.

Keilis-Borok, V.I., Rotwain, I.M., 1990. Diagnosis of time ofincreased probability of strong earthquakes in different regionsof the world: algorithm CN. Phys. Earth Planet. Int. 61, 57–72.

Keilis-Borok, V.I., Shebalin, P.N. (Eds.), 1999. Dynamics ofLithosphere and Earthquake Prediction (special issue). Phys.Earth Planet. Int. 111 179–330.

Kossobokov, V.G., 1995. Analysis of earthquake catalogs. In:Proceedings of the Third Workshop on Non-Linear Dynamicsand Earthquake Prediction. International Centre for TheoreticalPhysics, Trieste, Italy.

Kossobokov, V.G., Shebalin, P.N., 1995. Comment on CatalogErrors and the M8 Earthquake Prediction Algorithm. In:Habermann, R.E., Creamer, F (Eds.), Proceedings of the ThirdWorkshop on Non-Linear Dynamics and Earthquake Prediction.International Centre for Theoretical Physics, Trieste, Italy.

Kossobokov, V.G., Romashkova, L.L., Keilis-Borok, V.I.,Healy, J.H., 1999. Testing earthquake prediction algorithms:statistically significant real-time prediction of the largestearthquakes in the Circum-Pacific, 1992–1997. Phys. EarthPlanet. Int. 111 (3/4), 187–196.


Minster, J.B., Williams, N.P., 1992. The M8 intermediate termearthquake prediction algorithm: an independent assessment.EOS (Transactions, AGU) 73, S22B-06.

Molchan, G.M., 1990. Strategies in strong earthquake prediction.Phys. Earth Planet. Int. 61, 84–98.

Molchan, G.M., 1996. Earthquake prediction as a decision-makingproblem. PAGEOPH 147 (1), 1–15.

Molchan, G.M., Dmitrieva, O.E., Rotwain, I.M., Dewey, J., 1990.Statistical analysis of the results of earthquake prediction, basedon bursts of aftershocks. Phys. Earth Planet. Int. 61, 128-139.

Molchan, G.M., Kronrod, T.L., Panza, G.F., 1997. Multiscaleseismicity model for seismic risk. Bull. Seismol. Soc. Am.87 (5), 1220–1229.

Panza, G.F., Calcagnile, G., 1974. Some remarks about the focaleffect on the magnitude determination from Rayleigh waves. In:Proceedings of the XIIIth General Assembly of the EuropeanSeismological Commission, Tech. Econ. Stud. 10, 327–334

Peresan, A., Costa, G., Vaccari, F., 1997. CCI1996: the currentcatalog of Italy, Internal report IC/IR/97/9. International Centrefor Theoretical Physics, Trieste, Italy.

Peresan, A., Costa, G., Panza, G.F., 1999a. A proposal ofregionalization for the application of the CN earthquakeprediction algorithm to the Italian territory. Ann. Geofisica. 42,281–306.

Peresan, A., Costa, G., Panza, G.F., 1999b. Seismotectonic modeland CN earthquake prediction in Italy. PAGEOPH 154, 281–306.

Peresan, A., Panza, G.F., Costa, G., 2000. CN algorithm andlong lasting changes in reported magnitudes: the case of Italy.Geophys. J. Int. 141, 425–437.

Rotwain, I.M., Novikova, O., 1999. Performance of the earthquakeprediction algorithm CN in 22 regions of the world. Phys. EarthPlanet. Int. 111, 207–213.

Vorobieva, I.A., 1999. Prediction of a subsequent large earthquake.Phys. Earth Planet. Int. 111 (3/4), 197–206.

2nd workshop on earthquake engineering for nuclear facilities:...

Documents