2009_acta geophysica Himalaya 2009.pdf

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Acta Geophysicavol. 57, no. 2, pp. 387-399

DOI: 10.2478/s11600-008-0068-0

________________________________________________

2009 Institute of Geophysics, Polish Academy of Sciences

Statistical Analysis on Yearly Seismic MomentRelease Data to Demarcate the Source Zonefor an Impending Earthquake in the Himalaya

Basab MUKHOPADHYAY, Anshuman ACHARYYA,

and Sujit DASGUPTA

Geological Survey of India, Central Headquarters, Kolkata, India

e-mails: [email protected] (corresponding author),

[email protected], [email protected]

A b s t r a c t

Tectonism in the Himalayan fold-thrust belt had generated great

earthquakes in the past and will spawn more in the future. Sequential

cumulative moment release data of macroearthquakes (Mb 4.5) over

the years 1964-2006 in four zones of the Himalaya was analysed by non-

parametric RUD method. The Zvalues of RUD analysis had neither re-

jected nor supported the null hypothesis of randomness. However, the

Hurst analysis and plot, a statistical procedure to identify clustering of

low and high values in a time series, brought out a pattern for earthquakeprognostication. The pattern was a negative sloping segment representing

a sluggish moment release over years, followed by a positive sloping

segment indicating a sudden high moment release with occurrence of

medium/large size earthquake(s). In recent past, such a negative sloping

has been found in Zones B (1992-2006) and D (1998-2006), indicating

an impending moderate/mega earthquake event in near future.

Key words: Himalaya, seismic moment, time series, Hurst plot.

1. INTRODUCTIONHimalayan fold-thrust belt has been revisited by large to medium size earth-

quakes over decades. The ongoing tectonic movement is likely to cause

many future quakes as a result of differential convergence rate from west to


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B. MUKHOPADHYAY et al.388

east between Indian and Eurasian Plates. Variable shortening of crust along

the strike length of the Himalayan arc manifests such a convergence. The

shortening rate measured by systematic GPS studies from western to easternHimalaya varies considerably, from 13.4 to 19 mm/yr (cf., Banerjee and

Burgmann 2002, Chen et al. 2004, Bettinelli et al. 2006, Feldl and Bilham

2006, Jade et al. 2007). This shortening of crust in the Himalaya is absorbing

a large fraction of variable plate motion, 32 to 36.4 mm/yr from western to

eastern part of Indian subcontinent, between India and Eurasia (Bettinelli et

al. 2006). Differential shortening rates across the Himalayan arc result into

locking of the basement thrust (Main Himalayan Thrust, MHT) (Zhao et al.

1993, Nelson et al. 1996, Hauck et al. 1998, Bettinelli et al. 2006). This

locking generates elastic strain and resultant earthquake in foreland part of

the Himalaya. However, the average geodetic convergence rate of 18 mm/yr

is lower than the average geological slip of 21.51.5 mm/yr measured over

the Holocene period in the central Nepal Himalaya (Lave and Avouac 2000).

From the slip deficit, moment release pattern, seismic gap, and GPS cam-

paign data on either side of active tectonic zones, various workers have

prognosticated future large earthquakes in different parts of the Himalayan

arc. From the accumulated slip deficit, Bilham and Ambraseys (2005) and

Bilham and Wallace (2005) have predicted four 8.6 magnitude earthquakesin entire length of the Himalaya. Similarly, Bollingeret al. (2004) has fore-

casted a major earthquake along the seismic gap between Kathmandu, Nepal

and Dehra Dun, India. Again, from the seismic gap area between the rupture

zones of Kangra earthquake of 1905 and Bihar Nepal earthquake of 1934,

aided by GPS data, Bettinelli et al. (2006) has guessed two M> 8 or even

larger events west of Kathmandu in the Nepal Himalaya. Feldl and Bilham

(2006) have speculated Mw > 8.6 earthquakes with rupture length of ap-

proximately 400 km in the western and central Himalaya, and eastern Nepal

seismic gaps. The slip deficit generated over decades coupled with differen-tial shortening rate may likely cause one larger-to-great earthquake, some-

times soon or not too far in time. But where, when and how large the size of

the hazard is anybodys guess.

The decadal convergence along the Himalayan arc has accumulated elas-

tic strain that is bound to release by seismic or as aseismic slip between

earthquakes (Bilham and Ambraseys 2005). In this article, the yearly cumu-

lative moment release data from 1964 to 2006 by known macroearthquakes

(Mb

4.5) in different zones of the Himalaya has been subjected to RUD(Runs Up and Down) analysis and Hurst analysis in an attempt to identify a

characteristic pattern on moment release. The identified pattern was then

used to locate source zone(s) for a next impending major shock in the Hima-

laya. It is known that Hurst statistics and plots provide means to determine


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YEARLY SEISMIC MOMENT RELEASE DATA 389

the degree of clustering between low and high values in a time series. This

rescaled range analysis (Feder 1988) has been applied in sedimentological

studies (Chen and Hiscott 1999, Mukhopadhyay et al. 2003), several envi-ronmental quantities such as wind power variations (Haslett and Raftery

1989), hydrologic studies (Hurst 1951, 1956, Wallis and Matalas 1970, 1971)

and climatic changes (Evans 1996, Koutsoyiannis 2003) to quantify cluster-

ing in datasets. But this methodology has never been used for pattern recog-

nition on yearly earthquake moment release data, which will be demon-

strated in the following sections.

2. DATAThe earthquake data (Mb 4.5) from ISC (1964-2003) and NEIC catalogues

(2004 June 2006) from Main Frontal Thrust (MFT) in the south, followed

Fig. 1. Plot of earthquake data (Mb 4.5) in the Himalaya for 1964-2006. Noteboundaries of zones A, B, C and D in gray, where further analysis is carried out.Zone A Western Himalaya, B Western Nepal Himalaya, C Eastern NepalHimalaya, and D ortheast Himalaya. Note also the active tectonic surfaces in theHimalaya: MFT Main Frontal Thrust, MBT Main Boundary Thrust, MCT

Main Central Thrust, ITS IndusTsangpo Suture. The faults from Peninsular Indiain interaction with the Himalayan Thrusts: RF Ropar Fault, MDF Mahendra-garhDehradun Fault, GBF Great Boundary Fault, WPF West-Patna Fault,EPF East-Patna Fault, MSRMF Munger Saharsha Ridge Marginal Fault, andMKF Malda-Kishanganj Fault. Jam Jammu, Si Simla, Le Leh, Dd DehraDun, Nd New Delhi, Jai Jaipur, All Allahabad, Sh Shillong.


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successively in the north by Main Boundary Thrust (MBT) and Main Central

Thrust (MCT) to IndusTsangpo Suture (ITS) has been utilized for the

study. Earthquake events are plotted on a generalized tectonic map of thearea (Fig. 1). To account for the spatial variation of seismicity and corres-

ponding seismotectonic parameters of the Himalaya, the area is subdivided

into four zones, A, B, C and D, respectively, from west to east, within the

MFT and ITS bounded seismic zone. The earthquake events within these

four zones have been separated out into four sub-catalogues for further ana-

lyses. Zone A is named the Western Himalaya, B the Western Nepal Hi-

malaya, C the Eastern Nepal Himalaya, and finally D the Northeast

Himalaya (Fig. 1).

Seismic moment is a second rank tensor with a scalar value M0 and the

two directions define the slip and fault orientations (Scholz 2002). The latter

geometrical information is called focal mechanism or fault plane solu-

tion. Seismic moment is related to properties of the earths crust and that of

the faulting process by

0,A u= (1)

where is the shear rigidity (31011

dyne/cm2) of the crust, A is the area of

the entire ruptured surface, and u is the rupture displacement averaged overthe ruptured surface (Scholz 2002, McGuire 2004). The moment M0 (in

Fig. 2. Plot of log-cumulative moment release for successive years (1964-2006) for

four zones, A to D. Note the number of earthquakes with Mb 4.5 as labels. Zero

value in cumulative moment release data indicates absence of earthquake (Mb 4.5)

in that particular year.


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dynecm) for individual earthquake event with magnitude m is given by the

equation

0log c m d= + , (2)

where c = 1.5 and d= 16.05 (Hanks and Kanamori 1979, McGuire 2004).

The moments logM0 for individual earthquake events withinthefour sub-

catalogues (A,B,CandD) arecalculatedbyeq.(2). The cumulative logM0

for the period starting from 1964 to June 2006 are calculated for sub-cata-

logues of Zones A, B, C and D and summarized graphically in Fig. 2. The

moment release data shown in the diagrams display peaks and drops, without

any visible cyclic pattern.

3. CUMULATIVE MOMENT RELEASE PATTERNOF SUCCESSIVE YEARS RANDOM OR SYSTEMATIC?

A series of continuously measured cumulative moments of successive years

can be treated mathematically as a time series. To identify the pattern in

a time series, a number of statistical calculation methods has been devised,

the RUD (Runs Up and Down) being one of them (Davis 2002, Chakraborty

et al. 2002). This test not only verifies the randomness in the data but also

identifies the presence and absence of a local trend (either increase ordecrease on moment release pattern in successive years). In RUD, the dataset

is coded by +1, 0 or 1 by comparing the cumulative moment release of one

year with the successive year. If the cumulative moment is higher than the

previous one, then +1 is noted. Alternately, if the cumulative moment

is lower, then 1 is recorded. If both cumulative moments are equal, then 0

is registered. Runs U are defined as uninterrupted sequence of same state

(+1 or 1). In a dataset, the number of positive runs (+1) is n1 and the num-

ber of negative runs (1) is n2 , so the expected mean number of runs in a

randomly generated sequence is (Davis 2002):

1 2

1 2

21

n n

n n = +

+(3)

and the expected variance in the mean number of runs is

2 1 2 1 2 1 2

2

1 2 1 2

2 (2 ).

( ) ( 1)

n n n n n n

n n n n

=

+ + (4)

A cumulative moment sequence of successive years may yield either an

increasing moment release pattern or a decreasing moment release pattern in

successive years for which a two-tailed test is appropriate with a null hypo-

thesis that presumes a random distribution of cumulative moments. Alter-

nately, failure of the hypothesis yields the presence of asymmetric cycles.

For testing, theZstatistic has been employed,


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( ) / ,Z U = (5)

where Uis the total number of runs. Z is normally distributed with mean 0and standard deviation 1 and lies between +1.96 and 1.96 (for = 0.05) for

random sequence following the null hypothesis; any other value ofZsup-

ports the alternate hypothesis.

The RUD test has been applied to the four sub-catalogues containing log-

cumulative values of moments. The total number of data in each case is 43

and the results of the analysis are summarized in Table 1. It is interesting to

note that in the western Himalaya and western Nepal the number of runs is

less than the mean run, and theZvalues are negative. The situation is reverse

in eastern Nepal and northeast Himalaya, where theZvalue is positive. TheZvalues lie between the critical values of +1.96 and 1.96 (for=0.05); it can

be concluded that the number of runs Udoes not suggest the sequences to be

systematic. Failure ofnull hypothesis does not always indicate an absence of

deterministic systematic patterns in the cumulative moment release data. It

has been found earlier that the sequential bed thickness data of turbidite sec-

tions in Andaman Island that fails to give hints about the systematic pattern

by RUD analysis (Chakraborty et al. 2002), gives facies clustering of thick

and thin beds by Hurst plot (Mukhopadhyay et al. 2003). Thus, a search for

systematic pattern is attempted by the Hurst plot in the following section.

Table 1

Comparative results of RUD analysis on successive cumulative moment releases

of successive years 1964-2006 from west to east in the Himalaya (Zones A to D).

Parameters , andZare calculated from eqs. (3), (4), and (5).

Zone A Zone B Zone C Zone D

Number of data 43 43 43 43

Positive transition, n1 19 20 21 20

Negative transition, n2 23 22 21 22

Mean run, 21.8095 21.952 22 21.9523

Parameter, 3.1708 3.1931 3.20 3.1931

Number of runs, U 19 16 24 26

Parameter,Z 0.8860 1.8640 +0.6248 +1.2676

4. PATTERN RECOGNITION BY HURST PLOT AND INFERENCESHurst (1951, 1956) proposed Hurst statistics while working on the long-term

storage on reservoirs along the river Nile and deduced a relationshipR/S~Nh,

where R is the maximum range of cumulative departure from mean annual

river discharge, Nis the year of observations, Sis the standard deviation of


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the river discharge. Hurst approximated the coefficient h by K, where K is

equal to log(R/S)/log(N/2). The logarithm of cumulative moment calculated

for the earthquake events of successive years in an earthquake catalogue mayexhibit a pronounced alternate clustering of high and low values. To deter-

mine this pattern a rescaled scaled plot (Hurst plot) is used. The rescaling

process is done against the mean value in the time series. The cumulative

moment values of successive years for an individual zone (Zone A of Fig. 2)

are taken. Mean M and standard deviation S of data are calculated. From

each data, the meanMis subtracted and then cumulative difference from the

mean is computed by adding the values. The moment release pattern can be

graphically seen from the Hurst plot of cumulative difference from the mean

moment against years. It contains both positive and negative sloping seg-

ments. The negative sloping segment suggests a slow release of moment (or

temporal slackening of elastic strain release) compared to the average (mean)

rate and may indicate a precursor for large impending event. Alternately, a

positive sloping segment suggests a rapid release of moment in quick suc-

cession compared to the whole catalogue and indicates occurrence of me-

dium to large earthquake events. Hurst plots corresponding to the four zones

in Fig. 3 have been prepared and subject to detail analysis.

Fig. 3. Hurst plots of years against cumulative difference from mean log-cumulative

moment release data of earthquakes in four zones (A-D). Note the IDs of Table 2 are

plotted as numbers.

The plot of Zone A (western Himalaya) indicates a prolong negative

sloping segment from 1964 to 2004 with two small positive perturbations in-

dicating high moment release by two medium-sized earthquakes, one in

1972 and the other in 1981 (IDs 1,2 of Table 2, Fig. 3a). This extremely


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Table 2

Important medium- to large-sized events in A to D zones in the Lesser Himalaya.

Note the IDs that are plotted in Fig. 3.

Zone ID Date Time Lat Long Mbh

[km]Name of the

earthquake

A

1 1972 Sep 03 16h48m29.00s 35.94 73.33 6.2 45

2 1981 Sep 12 07 15 54.00 35.68 73.60 6.1 30

3 2005 Oct 08 03 50 41.00 34.54 73.59 7.7 26 Kashmir

B

4 1966 Mar 06 02 15 57.00 31.49 80.50 6.0 50

5 1966 Jun 27 10 41 08.10 29.62 80.83 6.0 33

6 1966 Jun 27 10 59 18.10 29.71 80.89 6.0 367 1975 Jan 19 08 01 57.70 32.39 78.50 6.2 1

8 1975 Jan 19 08 12 09.80 31.94 78.52 5.8 49

9 1980 Jul 29 14 58 41.60 29.63 81.09 6.1 23

10 1991 Oct 19 21 23 15.00 30.77 78.79 6.4 15 Uttarkashi

11 1999 Mar 28 19 05 12.30 30.51 79.42 6.3 20 Chamoli

12 2004 Oct 26 02 11 33.00 31.02 81.15 6.0 10

C

13 1965 Jan 12 13 32 24.10 27.40 87.84 5.9 23

14 1974 Sep 27 05 26 33.60 28.59 85.51 5.5 20

15 1980 Nov 19 19 00 45.00 27.40 88.80 6.0 47 Gangtok16 1986 Jan 10 03 46 30.90 28.65 86.56 5.5 53

17 1987 Aug 09 21 15 02.70 29.47 83.74 5.5 74

18 1988 Aug 20 23 09 10.10 26.72 86.63 6.4 65 Bihar-Nepal

19 1990 Jan 09 02 29 21.80 28.15 88.11 5.7 41

20 1993 Mar 20 14 51 59.70 29.03 87.33 5.7 15

21 1998 Sep 03 18 15 52.10 27.86 86.95 5.6 14

22 2003 Mar 25 18 51 26.00 27.26 89.33 5.5 47

D

23 1964 Sep 01 13 22 37.30 27.12 92.26 5.6 33

24 1964 Oct 21 23 09 19.00 28.04 93.75 6.0 3725 1967 Mar 14 06 58 04.40 28.41 94.29 5.7 20

26 1967 Sep 15 10 32 44.20 27.42 91.86 5.8 19

27 1998 Sep 26 18 27 01.00 27.76 92.81 5.5 15

28 2005 Jun 01 20 06 41.00 28.88 94.63 6.1 25

29 2006 Feb 23 20 04 54.00 26.91 91.71 5.8 10

slow release of moment (elastic energy) is followed by a megaevent, Kash-

mir earthquake ofMb 7.7 in 2005 (ID 3 of Table 2, Fig. 3a). A positive slop-

ing segment marks this megaevent indicating a sudden rise in momentrelease. This suggests that a long negative sloping trend indicating slow

moment release pattern is bound to hit back by a megaevent. The aim of this

analysis is to find out such a pattern in the datasets of the rest of the zones

(B to D) under scrutiny, and predict a possible source zone for the next im-

pending mega event in the Himalaya.


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The Hurst plot of Zone B (Western Nepal Himalaya) indicates alternate

positive and negative sloping segments. The initial negative segment of

1964-1965 is followed by a positive sloping segment upto 1966, yieldingthree earthquakes (IDs 4, 5, 6 of Table 2 and Fig. 3b). The pattern again re-

peats; there is a negative sloping segment (1967-1974) followed by a posi-

tive sloping segment, releasing two medium-sized earthquakes in 1975

(IDs 7, 8 of Table 2 and Fig. 3b). This is followed by a nearly horizontal

segment from 1976 to 1983, a small negative sloping segment between 1984

and 1990, followed by a positive sloping segment yielding Uttarkashi earth-

quake in 1991 (ID 10 of Table 2 and Fig. 3b). The negative sloping segment

from 1992 to 1998 is followed again by Chamoli earthquake of 1999 (ID 11

of Table 2 and Fig. 3b). A low-angle negative segment between the years

2000 and 2003 is immediately followed by an earthquake in 2004 (ID 12 of

Table 2 and Fig. 3b). The pattern in this plot testifies that a negative sloping

segment always precedes a medium-sized earthquake event. It is interesting

to note that an overall negative sloping segment prevails from 1992 to 2006.

Zone B is a place where interactions of two sets of cross cutting tectonic

trends take place; the E-W trending Himalayan MFT-MBT-MCT with NE-

SW trending MDF-GBF (Fig. 1). Geologically, it is known that domains of

intersecting faults are favourable sites for stress build up and are seismicallypotential (Andrew 1989). Furthermore, this zone has already recorded some

large historical earthquakes, like the July 1720 (Mw 7.5) Uttarpradesh earth-

quake, or August 1916 (Mw 7.3) and July 1926 (Mw 6.5) Uttaranchal earth-

quakes. Considering the recent negative trend (between 1992 and 2006) in

the Hurst plot (Fig. 3b), as well as the occurrence of historical earthquakes

and zones of fault interaction, this source zone may produce a megaevent of

comparable size to the Chamoli and Uttarkashi events or even stronger, any

time in near future.

The plot of Zone C (Eastern Nepal Himalaya) indicates two positive andtwo negative sloping segments. The negative sloping segment, from 1964 to

1985, with positive perturbations generates earthquakes with IDs 13, 14, 15

of Table 2 and Fig. 3c. The following positive sloping segment, from 1986

to 1993, yields five earthquakes (IDs 16 to 20 of Table 2 and Fig. 3c) includ-

ing the Bihar-Nepal earthquake (Mb 6.4) of 1988. A negative sloping seg-

ment from 1994 to 2002 with a spike due to the occurrence of a medium-

sized earthquake (ID 21 of Table 2 and Fig. 3c) is followed by a small posi-

tive segment spawning earthquake in 2003 (ID 22 of Table 2 and Fig. 3c).

The absence of any characteristic trend in this zone makes any prediction

difficult.

The Hurst plot of Zone D (Northeast Himalaya) indicates two positive

and two negative sloping segments. The positive pattern between 1964 and

1969 yields earthquakes with IDs 23-26 of Table 2 and Fig. 3d. The negative


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sloping segment prevails upto 1981 and is followed by a positive sloping

segment upto 1998 yielding an earthquake ofMb 5.5 in 1998 (ID 27 of

Table 2 and Fig. 3d). The negative sloping segment from 1998 to 2004 isfollowed by a positive spike in 2005-2006, yielding earthquakes of IDs 28,

29 of Table 2 and Fig. 3d. Considering the recent negative trend (1998-2006)

in the moment release pattern, coupled with seismotectonic vulnerability of

the area in terms of spawning large earthquakes of June 1897 (Mw 8.7),

January 1941 (Mw 6.5), October 1943 (Mw 7.2), July 1947 (Mw 7.5), and

August 1950 (Mw 8.6), we can expect a medium to large-size earthquake in

near future.

5. CONCLUSIONSAny study on the earthquake parameters aims to find out a pattern to prog-

nosticate a future shock. In this study, the non-parametric statistical RUD

test and construction of Hurst plots on the cumulative moment release data

of successive years (1964-2006) on four zones (A to D) of the Himalaya

have been made for identification of such a pattern. The RUD analysis does

not suggest that the cumulative moment release pattern is systematic. How-

ever, the failure of null hypothesis does not always mean the absence of sys-

tematic patterns in the dataset. Therefore, a search for a systematic pattern to

identify clusters of low and high values in the moment release has been

carried out by Hurst analysis. The Hurst plots (Fig. 3) of four zones bring out

the inherent clustering patterns of moment release by revealing the succes-

sive series of low and high values in the dataset which corroborates well the

occurrence of large to medium-sized earthquakes. The plots also suggest

a characteristic pattern that bears the signature to prognosticate a next

impending earthquake in the Himalaya. The pattern is a long negative slop-

ing segment (indicating slow and decreasing moment release) immediatelyfollowed by a medium to large-sized earthquake with a pattern reversal to

positive sloping segment. Such a pattern exists in Zone A prior to Kashmir

(Mb 7.7) earthquake in 2005, in Zone B before Chamoli (Mb 6.3) earth-

quakes of 1999, and also in Zone C preceding Bihar-Nepal (Mb 6.4) earth-

quake of 1988.

A relook on the Hurst plot of Zone A (Fig. 3a) shows that it takes almost

21 years (1964-2004) of seismic lull period to accumulate sufficient elastic

strain to generate an earthquake of magnitude 7.7 (2005 Kashmir earth-

quake). Though within this seismic lull period two earthquakes with magni-tude greater than 6.0 at 1972 and 1981 (IDs 1, 2 of Table 2, Fig. 3a) have

occurred, these earthquakes were not sufficient to release the entire amount

of elastic strain accumulated within rock-masses so far. Hence, within a

seismic cycle, the possibility of occurrence of a megaevent (Mb 7.0) is not


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delayed by the occurrence of several moderate (Mb ~ 6.0) events prior to it.

Similarly, seismic lulls of 8 years each (1967-1974, 1992-1998) have gener-

ated earthquakes of comparable size, of 6.2 (1975) and 6.3 (1999 Chamoliearthquake) in Zone B. Therefore, as the duration of seismic lull increases,

the size of impending event increases too. A focus on Hurst plots of Zones B

and D (Figs. 3b, d) indicate that Zone B (between years 1992-2006) and

Zone D (between years 1998-2006) do exhibit negative sloping moment re-

lease pattern in recent times. Within these periods, both these zones have re-

leased some of the accumulated strain by spawning earthquakes with

Mb 6.0 (IDs 11, 12, 28 of Table 2 and Fig. 3). As these zones still maintain

the negative sloping moment release trend, two possibilities can be appre-

hended keeping in view the moment release signature of Zone A. One possi-

bility is the occurrence of an immediate moderate size earthquake with

magnitude Mb~6.0 that may reverse the moment release trend from nega-

tive to positive. Otherwise, the negative trend may continue for a couple of

years more and spawn an earthquake comparable to the size of Kashmir

earthquake of 2005 as found in Zone A. Evaluating the consequences of both

possibilities it can be logically concluded that Zones B and D are in the

verge of experiencing an earthquake of magnitude ~6.0 or >7.0 immediate-

ly or pretty soon, depending on the period of seismic lull. Thus, from theabove study we can only constrain the source zone for the next impending

event but the exact size and timing of the event cannot be deciphered.

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Received 10 April 2008

Accepted 7 August 2008

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