Source Parameters

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ORIGINAL ARTICLE

Source parameters and scaling relations for small

earthquakes in Kumaon Himalaya, IndiaK. Sivaram & Dinesh Kumar & S. S. Teotia &

S. S. Rai & K. S. Prakasam

Received: 19 December 2011 / Accepted: 10 October 2012 / Published online: 28 October 2012# Springer Science+Business Media Dordrecht 2012

Abstract We investigate the scaling relationships

among earthquake source parameters using more than

300 good quality broad band seismograms from 30

small earthquakes in the Kumaon Himalaya from the

spectral analysis of P and S waves. The average ratio

of P/S wave corner frequency is found to be 1.13,

which is suggestive of shift in the corner frequency.

The estimated seismic moment range from 1.61013

5.81015 Nm, while the stress drop varies from 0.6 to

16 bars with 80 % of the events below 10 bars. An

analysis of stress drop and apparent stress drop indi-cates the partial stress drop mechanism in the region.

The source radii are between 0.17 and 0.88 km. The

total seismic energy varies from 1.79108 to 7.30

1011 J. We also observe the variation in seismic energy

for a given seismic moment. The scaling relation be-

tween the seismic moment and stress drop suggests the

breakdown of constant stress drop scaling for the

range of seismic moments obtained here for the re-

gion. This shows the anomalous behavior of small

earthquakes in the region. The study indicates that

the stress drop is the dominant scaling factor for themoments studied here.

Keywords Source parameters . Kumaon Himalaya.

Small earthquakes . Scaling relations

1 Introduction

The Kumaon Himalaya region of the Himalayas is one

of the youngest orogenic belts of the world, which has

resulted by continuous tectonic collision of Indian

plate with Eurasian plate since early Eocene. The

arcuate Himalayan formation extends from the north-east to the northwest over a distance of about

2,500 km. The study region, in the state of Uttarak-

hand, India, falls in the central seismic gap between

rupture zones of 1905 and 1934 great earthquakes

(Khattri and Tyagi 1983; Khattri 1987). In addition,

Bilham et al. (1997, 2001) suggest significant seismic

potential for the Himalayan region between the west-

ern Nepal and Western Himalaya. For the proper eval-

uation of the seismic hazard potential in a region,

determination of earthquake source parameters such

as the seismic moment, stress drop, radiated seismicenergy, corner frequency, and rupture dimension pro-

vides the basic building blocks. The ambient stress

conditions and ranges of stress drop may vary for

different regions. Therefore, the regional scaling rela-

tions, instead of available global relations, are appro-

priate to estimate the values of stress drop and fault

dimensions. The developed scaling relations provide

the information whether the stress drop is constant or

not for the given range of seismic moments. A number

J Seismol (2013) 17:579592

DOI 10.1007/s10950-012-9339-y

K. Sivaram (*) : S. S. Rai : K. S. PrakasamCSIR-National Geophysical Research Institute,

Hyderabad, India

e-mail: [email protected]

D. Kumar: S. S. TeotiaDepartment of Geophysics, Kurukshetra University,

Kurukshetra, India


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of studies have been done to investigate the region-

specific scaling of earthquakes, especially at lower

magnitudes. (e.g., Abercrombie 1995; Prejean and

Ellsworth 2001). In the Himalayan regions, Sharma

and Wason (1994) have investigated the scaling rela-

tions using 18 low magnitude, local events recorded

by five vertical-component and two three-componentstations for Lower Himalayan regions. Using the 2

source model, Sriram et al. (2005) have provided

insights of earthquakes in some parts of Himachal

Himalaya, whereas Kumar et al. (2006) have provided

source parameter estimation for the 1999 chamoli

earthquakes and nine of its aftershocks in Uttarakhand

Himalaya using band-limited accelerograms. Kumar et

al. (2008) suggested the self similar nature of Himala-

yan earthquake sources with seismic moments in the

range 1.4 10161.71019Nm. Their analysis is based

on the 80 band-limited accelerograms of 12 earth-quakes in the Himalayan region.

The study by Dysart et al. 1988 found different

scaling relations for the small and large earthquakes

in the same region. The purpose of this study is to

determine the source parameters and investigate the

possible sel f-similarity of small earthquakes for

Kumaon Himalaya region using spectral analysis of

the digital broadband waveforms of 30 earthquakes

recorded over a seismograph network operated by

the CSIR-National Geophysical Research Institute,

from April 2005 to June 2008. The 2

scaling model(Aki 1967; Brune 1970, 1971; Houston and Kanamori

1986; Boore 1986) has been used for this purpose in

the present study. In the following sections, we first

describe the geological framework and seismotecton-

ics of the study region, followed by dataset preparation

and methodology of spectral analysis, the source

par amete rs and scaling rel ati ons, and final ly the

conclusions.

2 Geological framework and seismotectonicsof the study region

The Kumaon Himalayan region (latitude, 29 N

31 N; longitude, 78 E81 E) forms a part of the

Himalayas, which has resulted from a long geolog-

ical evolution, after the closure of the Tethys Ocean

and the underthrusting of the Indian with the Eur-

asian continental plate. Figure 1 shows the surface

trace of major tectonic features of the region that

includes the Southern Tibetan Detachment (STD),

the Main Central Thrust (MCT), the Main Bound-

ary Thrust (MBT), and the Main Frontal Thrust

( M FT ) . T h e L ow e r H i ma l ay a i s s tr u ct u ra ll y

bounded by MBT and MCT, consists mainly of

Precambrian clastic sediments. The greater Hima-

laya is bounded by MCT and STD and comprisesof early Cambrian metasedimentary rocks. Over the

past 200 years, nearly half of the Himalayan belt

has ruptured in at least six great earthquakes that

occurred in 1803, 1833, 1897, 1905, 1934, and

1950. Various seismo-tectonic models have been

proposed for explaining the evolution and seismic-

ity of the Himalayas (Seeber and Armbuster 1981;

Ni and Barazangi 1984; Molnar and Chen, 1982;

Yin and Harrison 2000). It is a well-accepted fact

that most of the earthquakes recorded here tend to

be shallow and restricted to a seismogenic zonewithin the upper ~25 km of the crust. Whereas

the study region is experiencing low to moderate

seismicity, a few recent moderate earthquakes being

the Uttarkashi (M6.6, 1991), Chamoli (M6.3, 1999)

earthquakes, the adjoining Himalayan regions have

experienced bigger earthquakes (Kashmir, M7.6,

2005, and Wenchuan, M8.0, 2008). Due to the

varying ambient stress conditions and absence of a

large magnitude seismic event in the region for a

long time, the seismic risk potential is enhanced

across Kumaon Himalaya region.

3 Data set

The study is based on the broad band seismograms

recorded during April 2005June 2008 at a broadband

seismograph network operated in Kumaon Himalaya re-

gion by the CSIR- National Geophysical Research Insti-

tute, under a project grant by Department of Science and

Technology, New Delhi, India (Ashish et al 2009;

Mahesh et al. 2013). Figure 1 shows the seismic networkof the study stations along with the major tectonic features

and the epicenters of the earthquakes. Table 1 shows the

details of the earthquakes considered in this study. The

seismograph stations were equipped with Guralp CMG-

3T triaxial broadband seismometer [with a flat velocity

response in the frequency range of 0.0083 Hz (120 s

period) to 50 Hz] coupled to 24-bit Reftek RT-130/1

digital data acquisition system and synchronized by glob-

al positioning system (GPS). The stations used in the

580 J Seismol (2013) 17:579592


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study were located on rock profiles and observed to have

minimum noise interference. The data have been

recorded at a sampling rate of 50 samples/s, and all the

stations were synchronized to operate in a continuous

mode. The earthquakes with focal depth


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spreading, 0 is long period spectral level, Q is

quality factor, fc is corner frequency, and R is

source receiver distance. GS(R)0R1 for RRy

and GS(R)0(RRy)0.5

for R>Ry. Ry may be takenas twice the thickness of crust (Herrmann and

Kijko 1983). In this study Ry has been taken as

100 km corresponding to a crustal thickness of

50 km (Singh et al. 2002; Rai et al. 2009) for

the Himalaya. Our frequency analysis lies in the

wider frequency band 0.220 Hz, as the maximum

cut-off frequency for the seismometer is 50 Hz.

We recognize here that we are neglecting the high

frequency decay parameter in Eq. (1), for which,

the spectra have been fitted in the frequency band

of 0.210 Hz. Another reason for this choice, as

discussed below, is that the constant Q model has

been preferred in the present analysis.The term exp (ft/Q) represents the attenua-

tion of seismic waves (Dainty 1981; Fletcher

1995). A constant Q model, considered as path

averaged Q, has been adopted for the relatively

narrow frequency band of 0.210 Hz. The model

has been found to be satisfactory in many studies

(e.g., Kjartansson 1979; Masuda and Suzuki 1982;

Archuleta 1982; Archuleta and Hartzell 1981;

Anderson and Hough (1984); De Natale et al.

Table 1 The earthquakes and

the number of recording stations

used in the present study

Event number Latitude

( N)

Longitude

( E)

Depth

(km)

mb

(USGS)

Number of recording

stations used for analysis

1 31.56 79.57 12.6 3.5 9

2 30.44 79.25 13.4 4.6 8

3 30.38 79.31 20.0 3.8 9

4 30.53 81.40 11.0 3.9 75 30.3 80.95 4.6 4.9 13

6 30.32 80.96 4.6 3.8 14

7 30.45 79.23 19.3 5.3 12

8 30.47 79.23 14.4 3.7 13

9 30.36 80.13 11.6 4.9 16

10 30.41 80.15 17.6 4.5 16

11 30.37 80.10 13.8 3.6 17

12 31.74 77.20 4.5 3.9 18

13 29.44 76.54 25.3 4.3 17

14 32.31 77.78 18.5 4.2 18

15 31.49 78.50 17.9 4.0 19

16 31.48 78.46 6.0 3.5 19

17 31.52 78.43 3.2 3.5 15

18 30.02 80.52 20.5 3.8 19

19 27.77 76.39 14.0 3.8 19

20 31.13 80.21 14.6 3.9 21

21 31.84 78.87 3.3 4.7 20

22 31.24 77.80 9.5 4.1 17

23 29.59 81.27 7.6 4.6 19

24 30.93 78.28 4.4 3.9 20

25 32.1 76.93 1.4 4.3 19

26 30.33 80.31 3.6 3.9 12

27 30.83 78.41 8.4 5.1 9

28 30.94 78.26 3.1 3.8 10

29 28.76 77.37 8.0 4.7 21

30 31.38 77.35 8.9 3.4 18

582 J Seismol (2013) 17:579592


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1987; M en ke e t a l. 1995; Abercrombie 1995;

Prejean and Ellsworth 2001; Kumar et al. 2006;

Tomic et al. 2009). Anderson and Hough (1984)

h av e s ho wn t ha t t he m od el o f a f re qu en cy -

independent Q for the shallow crust is consistent

with a 2 Brune source model. The fitting of the

Brunes model to the observed spectra, as dis-

cussed below, shows adequacy of constant Q

model in the frequency range of 0.210 Hz for

the region.

Three parameters0, Q, and fcare required to

define the source spectrum described by Eq. (1). The

simultaneous estimation of these three parameters may

lead to biasness because of tradeoff between Q and fcas well as between 0 and Q. Therefore, the corner

frequency has been estimated separately, in the wider

frequency band, and other two parameters0 and Q

have been determined using the grid search method.

Many methods have been proposed to estimate the

critical parameter fc (Brune 1970; Andrews 1986;

Snoke 1987; Margaris and Boore 1998; Shi et al.

1998). The Snokes method (Snoke 1987) requires

two parameters: long period spectral level 0 and the

energy flux J (integral of square of the ground

velocity). The value of 0 may be estimated either

from the known seismic moment of the earthquake

or by the visual inspection of the displacement

spectrum. The Andrewss approach (Andrews

1986) requires two spectral parametersJ a n d K (integral of square of ground displacement)to

determine the corner frequency. Garca et al.

(2004) have found that both approaches provide

similar values. In order to avoid the possible error

due to visual inspection of 0, the corner frequen-

cy in the present study has been determined using

Andrews (1986) approach. This approach helps

significantly minimizing the error associated with

the visual estimation of corner frequency, fc, given

by:

fc

ffiffiffiffiffiffiffiffiffiffiffiffiS

V2

SD2

r2p

2

where SV2 and SD2 are evaluated using the follow-

ing integrals:

SV2

Z10

V2fdf 3

And

SD2

Z10

D2fdf 4

where V(f) and D(f) are the velocity and displacement

spectra, respectively, and V0(f) and D0(f) are the cor-rected velocity and displacement spectra, respectively,

as described below. The corner frequency has been

estimated using the wider frequency band (0.220 Hz)

of the spectra.

A two-step search procedure for determining the

optimum values of the parameters 0 and Q has been

applied while adopting the corner frequency obtained

as noted above (Kumar et al. 2006). In the first step,

the values of the parameters 0 and Q are allowed to

vary over the search space. Ten trial values per decade

were chosen for0 and Q was allowed to vary from100 to 2,000. In the next step, a search was conducted

for 0 around the value obtained in the previous

search while keeping the value of Q obtained in the

first step. The updated value of0 thus obtained was

used for further analysis. A least square error function,

Eis defined between the fitted Brune spectra, D(f) and

the observed spectra, D0(f):

E 1

n

XlogDf logD0f

2 5

where n is the number of spectral values of the dis-placement spectra.

The values of fc and 0 obtained from the best-

fitted Brune spectra are used to estimate the source

parameters at the recording stations. The seismic mo-

ment (M0), source radius (r), stress drop (), and

moment magnitude (Mw) of an earthquake at the re-

cording stations have been obtained using the expres-

sions (Keilis-Borok 1960; Haskell 1964; Brune 1970,

1971; Hanks and Kanamori 1979):

M0p s=

4pv3

FPRf

p s=0 6

rp s= Kv

2pfp s=

c

7

p s= 7

16

Mp s=0

r3p s=

8

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Mp s=w log10 M

p s=0

1:5

10:7 9

where Mp s=0 ,

p s=0 , rp/s,f

p s=c ,

p/s, and Mp s=w are seismic

moment, long period spectral level, source radius, cor-

ner frequency, stress drop, and moment magnitude ofthe P or S waves, respectively; is the average density

(02.67 g/cm3); Pis partition of energy (01/2); Kis the

constant (2.34 for S waves and 1.92 for P waves); vis the

shear wave velocity (03.46 km/s) or P wave velocity

(06.07 km/s), Fis the free surface effect (02) and R

is the average radiation pattern (00.52 for P waves and

00.63 for shear waves). The radiated seismic energy has

been estimated from moment rate spectra using the fol-

lowing relation (Vassiliou and Kanamori 1982):

ER AZ1

0

2pfMp0 f

2df BZ

1

0

2pfMs0f 2

df

10

where A0(155)1 and B0(10

5)1. The P and S

wave radiated seismic energy have been estimated from

the first and second term of above equation.

Table 2 Earthquake source parameters obtained from the analysis of P waves

Event

number

fc(P)

(Hz)

SD Mo

(P) (Nm)

SD r(P)

(m)

SD (P) (bars)

SD Mw SD Qp SD Ep (J) SD

1 1.998 0.094 1.47E+14 0.257 1118.60 0.094 0.461 0.349 3.399 0.022 1225.08 0.054 3.45E+07 0.313

2 3.083 0.115 7.19E+14 0.319 821.34 0.122 5.675 0.653 3.856 0.025 1144.45 0.110 3.01E+09 0.487

3 3.097 0.122 4.50E+14 0.201 721.50 0.122 5.243 0.434 3.724 0.016 1096.90 0.092 1.20E+09 0.319

4 2.549 0.118 1.39E+14 0.227 876.70 0.118 0.903 0.423 3.379 0.029 1190.87 0.059 6.38E+07 0.325

5 1.493 0.161 3.41E + 14 0 .279 154.90 0.161 0 .559 0.983 3.617 0.060 927.81 0.160 7.71E + 07 0.631

6 2.021 0.099 4.84E + 14 0 .196 958.20 0.099 2 .408 0.451 3.745 0.015 601.52 0.117 3.86E + 08 0.324

7 2.682 0.097 4.90E+15 0.122 731.60 0.097 54.785 0.327 4.416 0.008 779.61 0.156 9.23E+10 0.226

8 3.511 0.140 2.87E + 14 0 .245 599.10 0.140 5 .839 0.382 3.592 0.020 706.81 0.091 7.09E + 08 0.313

9 2.407 0.105 2.46E+15 0.128 1010.00 0.109 10.430 0.424 4.216 0.009 997.99 0.236 1.68E+10 0.276

10 2.781 0.092 1.07E+15 0.294 826.20 0.092 8.282 0.519 3.972 0.021 808.57 0.183 4.89E+09 0.407

11 3.112 0.112 2.23E+14 0.342 749.20 0.112 2.322 0.571 3.515 0.030 1112.42 0.152 2.99E+08 0.45612 4.582 0.084 4.72E+13 0.326 560.60 0.084 1.173 0.299 3.067 0.030 1274.54 0.045 4.27E+07 0.313

13 2.601 0.106 1.06E+14 0.107 804.00 0.106 0.891 0.360 3.306 0.009 1337.52 0.030 3.92E+07 0.234

14 2.542 0.112 4.42E+13 0.157 755.70 0.112 0.465 0.234 3.052 0.015 1254.30 0.046 6389871 0.195

15 2.566 0.169 5.92E+13 0.266 840.30 0.169 0.437 0.870 3.114 0.061 1015.14 0.108 1.18E+07 0.568

16 2.838 0.153 1.35E+14 0.434 807.60 0.153 1.123 0.733 3.366 0.040 1232.08 0.056 8.32E+07 0.583

17 2.732 0.148 1.17E+14 0.139 904.90 0.126 0.692 0.491 3.335 0.012 1122.69 0.129 5.57E+07 0.315

18 2.722 0.130 5.47E+13 0.404 913.10 0.130 0.314 0.238 3.106 0.037 1043.08 0.130 1.20E+07 0.324

19 2.094 0.164 1.41E+14 0.241 853.80 0.164 0.389 0.293 3.386 0.020 1210.83 0.060 3.62E+07 0.267

20 3.249 0.506 1.49E+14 0.242 850.40 0.155 1.061 0.505 3.403 0.021 1039.07 0.101 1.52E+08 0.373

21 2.254 0.149 1.03E+14 0.184 1092.40 0.149 0.344 0.593 3.295 0.016 1056.81 0.182 2.40E+07 0.389

22 3.367 0.091 2.11E+14 0.308 636.70 0.091 3.580 0.518 3.502 0.026 1269.15 0.065 3.39E+08 0.413

23 2.956 0.158 1.17E+14 0.385 624.90 0.158 2.089 0.390 3.323 0.040 1379.40 0.014 6.98E+07 0.387

24 3.922 0.199 8.88E+13 0.263 550.10 0.199 2.334 0.763 3.252 0.023 680.19 0.368 9.48E+07 0.513

25 3.607 0.302 1.39E+13 0.164 912.10 0.302 0.449 0.776 2.717 0.017 1127.88 0.072 672677.4 0.470

26 2.593 0.180 3.49E+13 0.311 658.60 0.182 0.535 0.468 2.978 0.034 1109.56 0.118 1.29E+07 0.390

27 3.761 0.156 7.69E+15 0.251 998.90 0.156 33.740 0.357 4.540 0.027 1210.83 0.060 8.42E+10 0.304

28 1.927 0.154 1.83E + 14 0 .45 761.60 0.152 1 .812 0.340 3.454 0.039 994.34 0.051 9.85E + 07 0.395

29 2.454 0.136 1.83E+14 0.249 829.00 0.136 1.403 0.351 3.461 0.021 1298.46 0.024 5.65E+07 0.300

30 2.042 0.191 5.04E+13 0.231 752.00 0.191 0.519 0.377 3.089 0.022 1155.42 0.043 6844693 0.305

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The average values () and standard deviations SD

(log ) of seismic moment, source radius, stress drop,

and seismic energy have been obtained using the fol-

lowing expressions (Archuleta et al. 1982):

by anti log1

Ns XNs

i1

logyi 11

SD logby 1Ns 1

XNsi1

logyi logby 2" #1

2

12

where Ns is number of stations used for analysis. The

average values have been obtained using P and S

waves separately for each of the 30 events used in

the analysis.

5 Results and discussion

Table 1 shows the details of the earthquakes consid-

ered in this study. The average values of parameters

estimated from the analysis of P and S waves are given

in Tables 2 and 3 respectively. Figure 2 shows the

Table 3 Earthquake source parameters obtained from the analysis of S waves

Event

number

fc(S)

(Hz)

SD Mo

(Nm)

SD r(S)

(m)

SD (S)(bars)

SD Mw SD Qs SD Es (J) SD

1 1.826 0.112 1.09E+14 0.130 610.2 0.113 1.369 0.238 3.190 0.012 1319.844 0.028 1.44E+08 0.239

2 2.437 0.091 6.27E+14 0.458 467.7 0.091 22.929 0.463 3.766 0.036 1023.130 0.232 1.95E+10 0.598

3 2.461 0.115 3.75E+14 0.190 476.1 0.115 12.162 0.322 3.606 0.015 1235.850 0.040 6.28E+09 0.333

4 2.637 0.032 8.99E+13 0.132 450.6 0.032 1.943 0.138 3.028 0.013 1400.000 0.000 1.42E+08 0.176

5 1.508 0.149 2.98E+14 0.327 202.6 1.416 3.785 0.585 3.557 0.026 1101.510 0.089 1.05E+09 0.593

6 2.125 0.158 3.21E+14 0.081 531.7 0.158 4.566 0.510 3.420 0.007 1156.600 0.100 1.11E+09 0.384

7 2.23 0.155 4.20E+15 0.419 534.0 0.155 100.686 0.705 4.312 0.029 1276.060 0.039 6.38E+11 0.731

8 2.881 0.085 2.53E+14 0.139 362.7 0.085 20.177 0.191 3.517 0.012 1228.910 0.066 5.42E+09 0.215

9 2.166 0.085 1.65E+15 0.282 552.3 0.123 21.856 0.486 3.903 0.021 757.540 0.170 3.37E+10 0.499

10 2.626 0.109 5.75E+14 0.236 461.0 0.109 3.699 0.378 3.232 0.021 1086.820 0.076 5.82E+08 0.399

11 2.913 0.221 1.67E+14 0.334 482.5 0.221 4.294 0.595 3.312 0.029 1022.080 0.138 1.41E+09 0.60412 3.149 0.109 6.32E+13 0.174 384.1 0.109 6.11 0.269 3.221 0.016 1274.540 0.045 9.16E+08 0.288

13 2.107 0.077 1.86E+14 0.329 543.0 0.064 7.286 0.426 3.569 0.026 1252.560 0.053 3.11E+09 0.491

14 1.755 0.069 1.08E+14 0.320 836.0 0.069 1.293 0.718 3.443 0.027 1109.560 0.119 7.55E+08 0.675

15 2.347 0.090 8.23E+13 0.135 537.3 0.090 2.975 0.329 3.304 0.012 983.800 0.088 6.73E+08 0.302

16 2.56 0.134 1.21E+14 0.192 535.4 0.134 3.047 0.376 3.307 0.017 1133.600 0.106 8.98E+08 0.369

17 2.409 0.142 9.05E+13 0.369 560.0 0.142 1.592 0.297 3.153 0.033 845.150 0.174 2.67E+08 0.433

18 2.423 0.135 4.80E+13 0.122 658.8 0.135 0.632 0.384 3.033 0.012 1065.420 0.082 1.13E+08 0.329

19 2.087 0.106 1.05E+14 0.118 314.0 0.106 1.307 0.272 3.182 0.011 1144.720 0.080 2.03E+08 0.254

20 2.91 0.145 1.11E+14 0.199 566.6 0.145 1.769 0.621 3.199 0.018 1232.080 0.056 6.24E+08 0.533

21 1.963 0.130 1.01E+14 0.287 678.5 0.130 1.332 0.504 3.271 0.026 1062.170 0.089 3.48E+08 0.515

22 3.079 0.113 1.96E+14 0.152 388.8 0.113 13.447 0.326 3.460 0.013 1377.990 0.026 4.46E+09 0.311

23 2.56 0.114 2.00E+14 0.059 413.8 0.114 17.463 0.392 3.591 0.005 1134.430 0.141 6.28E+09 0.293

24 3.255 0.178 8.23E+13 0.164 433.9 0.178 4.056 0.487 3.190 0.013 1147.560 0.097 9.26E+08 0.423

25 2.435 0.203 1.57E+13 0.464 619.6 0.203 4.954 0.289 2.774 0.047 1244.980 0.045 2.08E+07 0.489

26 3.046 0.160 5.72E+13 0.217 487.0 0.160 3.011 0.376 3.221 0.019 1013.720 0.076 8.37E+08 0.386

27 2.066 0.123 5.78E+15 0.325 526.7 0.123 115.893 0.132 4.345 0.022 1053.540 0.101 6.19E+11 0.297

28 2.43 0.123 1.28E + 14 0.511 657.8 0.125 1.11 0.269 3.186 0.041 972.800 0.060 3.53E + 08 0.507

29 1.853 0.125 2.78E+14 0.280 540.3 0.068 11.194 0.364 3.667 0.022 849.930 0.128 4.15E+09 0.418

30 2.848 0.163 5.07E+13 0.351 340.0 0.163 3.493 0.517 3.088 0.034 1210.830 0.060 2.82E+08 0.564

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fitting of Brune displacement spectra obtained

from estimated parameters to the observed spectra

as an example. The agreement between the Brune

spectra and the observed spectra, in general, is

good for the frequencies up to about 10 Hz, be-

yond which the observed spectra show a more

rapid fall off. This represents the characteristic fall

off of source spectrum (Hanks 1981). The ob-

served spectra are higher as compared to the

Brune spectra in narrow frequency bands at some

stations. These are possibly caused by the site

amplifications. Overall, the agreement between

the observed and estimated spectra indicates that

the estimated parameters are well constrained.

0.0001

0.001

0.01

0.1

1

10

100

1000

AMPLIT

UDE

SPECTRA

0.001

0.01

0.1

1

10

100

1000

0.0001

0.001

0.01

0.1

1

10

100

1000

AMPLITUDES

PECTRA

0

0.0001

0.001

0.01

0.1

1

10

100

1000

ALI BNK

GTHHLG

FREQUENCY (Hz)

0.0001

0.001

0.01

0.1

1

10

100

1000

AMPLITUDE

SPECTRA

1 10 100 1 10 100

1 10 100 1 10 10

1 10 100 1 10 100

FREQUENCY (Hz)

0.001

0.01

0.1

1

10

100

1000KSL KTD

Fig. 2 Examples of fitting

of Brune displacement

spectra obtained from esti-

mated parameters to the ob-

served spectra

586 J Seismol (2013) 17:579592


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Figure 3 shows the comparison between the es-

timated P and S wave corner frequencies. The

estimated values of P wave corner frequency,

fc(P), are in the range of 1.494.58 Hz, while those

of S wave corner frequency, fc(S), vary from 1.51

to 3.26 Hz. The ratios of P wave corner frequency

to S wave corner frequency, fc(P)/fc(S), are withinthe range of 0.721.46 with an average of 1.13.

This is lower than the ratio / expected for simple

source model. This may be due to nondouble cou-

ple source and/or specific takeoff angle of observa-

tion. For more than 80 % of events studied here,

the ratio is >1 and bounded between the lines

fc(P)0fc(S) and fc(P)0(/)fc(S) (Fig. 3). Similar

observations have been made in a number of stud-

ies and is attributed to enrichment of P waves in

high frequency compared to the S waves for the

same earthquake (e.g., Furuya, 1969; Masuda andTakagi 1978; Hanks 1981; Majer and McEvilly

1979; Fletcher 1980; Somerville et al. 1980; Prieto

et al. 2004). Based on the analysis of spectra of

earthquakes in the magnitude range of 0.54.5,

Molnar et al. (1973) observed that the corner fre-

quency for P waves is systematically larger than

that for S waves for the physically reasonable dis-

location models. Upadhyay and Duda (1980) found

that the corner frequencies for P waves are about

twice those for S waves for Himalayan earthquakes.

This phenomenon of corner frequency shift has

been reported even when attenuation is accounted

for (Hanks 1981; Fletcher and Boatwright 1991;

Abercrombie 1995; Garca et al. 2004). Hanks

(1981) concluded on the basis of spectral analysis

and time-domain modeling that the corner frequen-cy shift is the manifestation of an intrinsic prop-

erty of earthquakes, source finiteness. The average

values of source radii vary from 179 to 885 m.

The mean ratio r(P)/r(S) is found to be 1.5, sim-

ilar to those obtained by Garca et al. 2004. The

difference in the estimated values of source radii

from P and S waves may be due to corner fre-

quency shift.

The seismic moments estimated from P waves,

M0(P), range from 1.391013 to 7.691015Nm and

those from S waves, M0(S), range from 1.571013

to5.781015N m. The corresponding moment magni-

tudes range from 2.98 to 4.54 for P waves and from

2.77 to 4.35 for S waves. The average ratio M0(P)/

M0(S) is 1.04 (Fig. 4). The agreement between the

seismic moments estimated from two waves indicates

the validity of the procedure adopted in this study.

The total seismic energy, estimated for the frequen-

cy band 0.210 Hz, varies from 2.15107 to 7.30

1011J. We note here that the total seismic energy may

be underestimated here due to the limited frequency

band used. Figure 5 shows the correlation between P

1 2 3 4 5

S-wave corner frequency, fc (S), (Hz)

1

2

3

4

5

P-wave

cornerfrequency,

fc(

P),(Hz) f

c(P)/

f c(S)

=1.

7

fc(P)/f

c(S)

=1

Fig. 3 Comparison between P and S waves corner frequencies.

The solid lines represent different scaling factors

1E+013 1E+014 1E+015 1E+016

seismic moment M0 (S) N-m

1E+013

1E+014

1E+015

1E+016

seismic

momentM0(P)N-m

Fig. 4 Correlation between the seismic moments estimated

from P and S waves along with the least square fitted line

J Seismol (2013) 17:579592 587


10/14

and S wave energy with the lines of equal energy

ratios. We note that that almost all the events lies

between the energy ratio E(P)/E(S) of 0.011. Similar

results are obtained by Fletcher and Boatwright 1991;

Garca et al. 2004.

T he m ea n s tr es s d ro p v ar ie s f ro m 0 .6 t o16 bars. More than 80 % of the events analyzed

here show the average stress drop values


11/14

stress drop scaling for small earthquakes in the region.

A decrease in stress drop with decreasing seismic

moment has been found to be a scaling relation for

small earthquakes (e.g., Archuleta et al. 1982; Haar et

al. 1984; Dysart et al. 1988; Abercrombie 1995; Garca

et al. 2004; Ide et al. 2003; Mayeda et al. 2005;

Venkataraman et al. 2006). The plot of source radius with

seismic moment is shown in Fig. 8 along with the lines of

constant stress drop. We note that most of the events

(>70 %) analyzed here lie in the stress drop values

1E+013 1E+014 1E+015 1E+016

Seismic moment (N m)

0

0.4

0.8

1.2

1.6

2

ZunigaParameter,

1

23

4

5

6

7

8 9

10

11

12 13

14

15

16

17

18

19

2021

22

23

24

25

26

27

28 29

30

Partial Stress drop

Frictional Overshoot

Fig. 6 Ziga parameter, ,

for the events with respect to

moment. The corresponding

event numbers are indicated

below the solid blue circles

0.1 1.0 10.0 100.0

stress drop (bars)

1E+13

1E+14

1E+15

1E+16

seis

micmoment(N-m)

Fig. 7 Relation between seismic moment and static stress drop

along with the least square fitted line

0001001

source radius (m)

1E+013

1E+014

1E+015

1E+016

seism

icmoment(Nm)

1 bar

(0.1MP

a)

10bar (

1 MPa

)

40bar (

4 MPa

)

Fig. 8 Seismic moment versus source radius along with the

lines of constant stress drop

J Seismol (2013) 17:579592 589


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between 1 and 10 bars. The source radius appears to be

uncorrelated with the moment in this analysis, and there is

a scatter in the values of source radius for the same

moment. This observation, together with the observed

increase in stress drop with seismic moment for Kumaon

Himalaya, is evidence for the breakdown of the concept of

similarity among smaller earthquakes. This breakdown ofsimilarity may be attributed to the anomalous behavior of

small earthquakes that shows the corner frequencies are

independent of moment/magnitude (e.g. Frankel 1981;

Takeo 1983; Dysart et al. 1988; Mayeda et al. 2005;

Venkataraman et al. 2006). Studies citing similar results

by Okada et al. 1981 and Takeo (1983) reported a group

of earthquakes with moments differing by up to a factor of

1,000 but with essentially identical corner frequencies.

Aki (1984) interpreted these events as examples of

barrier-type earthquakes where stable regions on the fault

plane can limit the extent of fracture but allow variableslip. However, the role of site effects needs to be investi-

gated especially, in the light of the variation of source radii

for the events of similar moments in the region.

Kumar et al. (2008) suggested the self-similar na-

ture of Himalayan earthquake sources with seismic

moments in the range of 1.410161.71019N m.

Their analysis is based on the 80 accelerograms of

12 earthquakes in the Himalayan region. The present

analysis suggests the breakdown of similarity of the

earthquakes with seismic moments in the range 1.6

1013

5.81015

Nm in the Kumaon Himalaya.Figure 9 shows the plot of the total seismic

energy versus seismic moment along with the lines

of constant apparent stress drop. This shows the

energy may vary for a given seismic moment.

Garca et al. 2004 have found the similar observa-

tion for the earthquakes in the region of Granada

Basin (Southern Spain).

6 Conclusions

Based on the source parameters estimated from the

spectral analysis of P and S wave digital broad-

band records of 30 events from Kumaon Hima-

laya, we draw the following inferences. The

agreement between the seismic moments from P

and S waves and good fitting of theoretical Brune

spectra to the observed one justifies robustness of

the methodology. One of the important findings of

present analysis is the breakdown of the constant

stress drop scaling for the earthquakes with seis-mic moments in the range of 1.610135.81015N

m in the region. The low stress drop values esti-

mated in the study can be explained by partial

stress drop mechanism in the region. A phenome-

non of corner frequency shift has been observed in

the region in consistent with the similar studies of

other active regions. The estimated source radii are

found to be uncorrelated with the seismic moments

showing the corner frequency independence of

seismic moments for the small earthquakes ana-

lyzed here. The increase in stress drop with in-creasing moment and noncorrelation of source

radius with seismic moment shows that the stress

drop is the dominant scaling factor for moments

1.0E+7 1.0E+8 1.0E+9 1.0E+10 1.0E+11 1.0E+12

Seismic Energy (J)

1.0E+11

1.0E+12

1.0E+13

1.0E+14

1.0E+15

1.0E+16

1.0E+17

1.0E+18

SeismicMom

ent(N-m)

0.5bar

10ba

r

Fig. 9 Total seismic energy

versus seismic moment

along with the lines of ap-

parent stress drop. These

lines show the range of en-

ergy variation for a given

seismic moment

590 J Seismol (2013) 17:579592


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considered here. This has important bearing on the

estimates of seismic hazard in the region as the stress

drop controls the high frequency ground motions.

Acknowledgments The above project was sanctioned from

the grants by the Department of Science & Technology, India

to CSIR-National Geophysical Research Institute (NGRI),

Hyderabad, India (Research grant: DST/MMS-2/SU/2003).The authors acknowledge the support of NGRI, Hyderabad,

and Kurukshetra University, Kurukshetra, India. The authors

are grateful to Grzegorz Kwiatek, an anonymous reviewer, and

the associate editor for their extremely constructive comments,

which helped us to improve the manuscript significantly.

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