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International Journal of Civil, Structural,
Environmental and Infrastructure Engineering
Research and Development (IJCSEIERD)
ISSN 2249-6866
Vol. 3, Issue 1, Mar 2013, 41-52
© TJPRC Pvt. Ltd.
EARTHQUAKE SOURCE PARAMETERS REVIEW IN INDIAN CONTEXT
ARJUN KUMAR, ASHWANI KUMAR & HIMANSHU MITTAL
Department of Earthquake Engineering, Indian Institute of Technology, Roorkee, India
ABSTRACT
Earthquakes cause loss of life and property. In order to cop up hazard made by earthquakes it is essential to study
their nature. Scientists over the world are in progress to study various aspects of earthquakes. This paper presents a brief
overview regarding some of the specific studies related to the developments of earthquake source models and scaling laws
that laid a strong foundation to study earthquake source parameters from observational data around the world. Different
methods in the time domain, frequency domain, including empirical green functionare used to estimate source parameters.
Some typical studies of earthquake source parameters based on observational data and development of scaling laws in
Indian region along with the salient results are presented.
KEYWORDS:
Earthquake Source Models, Brune Model, Source parameters, f
max,
Himalaya
INTRODUCTION
Since the dawn of seismology attempts have been made to study the attributes of earthquake source. As the
earthquakes were perceived as the sudden shaking of the ground, early efforts were made to locate the source of the
shaking and to look for the causes that produced the shaking. The term Bericenter was given to represent the center of the
isoseismal of highest shaking from which the marcoseismic field radiates. After the advent of seismograph, efforts were
made to locate earthquakes from the arival times of seismic waves using primarily graphical methods. However, after the
advent of computers that allowed fast computing, several computer programs have been developed after 1960’s to estimate
the hypocenter parameters of an earthquake (e.g., Lienert et al., 1986).
Richter (1935) gave the magnitude parameter to quantify the size of an earthquake from the measurements of
amplitudes of local earthquakes recorded using a network of short period Wood Anderson seismographs in the southern
California. This was a major break though in seismology that allowed the ranking of earthquakes according to their size.
This local magnitude scale was extended to surface wave magnitude (Ms) and body wave magnitude (m
b
) to allow
computing the size of the teleseismic earthquakes. However, it was not very clear as to how the amplitudes of the seismic
waves vary with magnitude over a whole range of frequency band. Although, some work in this direction was carried out
by Berkmhemer (1962) who showed an increase in predominent period of an earthquake with increasing magnitude. Aki
(1967) developed scaling law of seismic spectrum and this marked the beginning of an important field to understand the
variation of spectrum with the size of an earthquake. Brune (1970) derived an earthquake model by considering the
effective stress available to accelerate the two sides of the fault. This model successfully explained the observed near- and
far-field spectra of earthquakes and many researchers have been adopting this model for the last more than three decades to
compute the earthquake source parameters.
DEVELOPMENTS OF EARTHQUAKE SOURCE MODELS
Several field evidences suggested that the earthquakes are caused by faulting (e.g., Richter, 1958). On account of
this, dislocation models were developed to model an earthquake as a slip on the fault. Brief description of some of the early
models is mentioned below:
42
Arjun Kumar, Ashwani Kumar & Himanshu Mittal
Burridge and Knopof (1964) derived expression for the body force to be applied
to represent a dislocation and
produces radiation pattern identical
to that of the dislocation. This equivalent body force depends only
upon the source and
the elastic properties of the medium in
the vicinity of the source. The study demonstrated that a displacement discontinuity
is represented as an equivalent double
couple body force. At the same time Haskell (1964) proposed a rectangular fault
model to represent a propagating displacement discontinuity. This model considered a uniform displacement discontinuity
moving at a constant rupture velocity along a thin fault of length ‘L’and width ‘W’. At wavelengths much longer than the
size of the fault, this model is a reasonable approximation of a simple seismic rupture propagating along a strike slip fault.
Haskell’s model has been extensively used to invert for seismic source parameters in the near and far-field using seismic
and geodetic data. Madariaga (1978) computed the seismic radiation of Haskell’s model and showed that due to the stress
singularities around the edges, this model fails at high frequencies. All dislocation models with constant slip suffer from
this problem and Sato and Hirasawa (1973) proposed tapering the slip discontinuity near the edges of the fault to reduce
this problem.
Savage (1966) proposed an elliptical fault model and studied the effects on the spectra of body and surface waves.
The spectra of the pulses from Savage’s model exhibited two band-limitated components which may be associated with
two intervals in the time domain; the first is associated with the time interval preceding the first stoping phase, and the
interval over which the first and final stopping phase occur. The second is associated with the time interval between the
stopping phases. The pulse can be approximated by the convolution of two boxcar functions having these intervals (τ
1
,τ
2
).
The amplitude spectrum of the pulse is the the product of two sinc functions for which the first zeros occur at frequencies
that are inversly proportional to the time intervals. Thus the spectrum have a ω
-1
roll-off at a frequency of 1/τ
1
hz, and a ω
-2
roll-off at a frequency 1/τ
2
hz.
Aki (1967) developed scaling law that depicted the dependence of the amplitude spectrum of seismic waves with
magnitude. Two source models of an earthquake were considered in the study---ω
3
(ω–cube) model after Haskell and the
other ω
2
(ω–square) model obtained by fitting an exponentially decaying function to the autocorelation function of
dislocation velocity. The theoretical curves were calibrated with observations by comparing the ratios of the theoretical
spectra with the observed spectra of seismic waves from earthquakes having same propagation path. The theory was also
checked with the empirical relations between different magnitude scales and spectra were calibrated with surface wave
magnitude (Ms). The study concluded that the ω
2
(ω–square) model is in aggrement with observations on the assumption
of similarity. Three years later, Brune (1970, 1971) modelled an earthquake dislocation as a tengential stress pulse applied
to the interior of a dislocation surface. The stress pulse sends a shear-stress wave perpendicular to the dislocation surface.
This model describes near- and far-field displacement time functions and spectra and takes into accounts the effects of
fractional stress drop. The model successfully explained the near- and far-field spectra observed for earthquakes and has
been extensively used to compute source parameters from observational data.
Boatwright (1980) developed a spectral theory for circular seismic sources and derived expressions to estimate
source dimension, dynamic stress drop, and radiated seismic energy. Far-field body wave radiation from this model as a
function of takeoff angle, rupture velocity, and stopping behavior was investigated and the variation of spectral shape,
pulse shape, and energy flux over the focal sphere was quantified. The study provided two new methods for estimating the
source dimension, the first through the inversion of a characteristic frequency, and the second using the rise time of the
displacement pulse shape. The model also allowed a direct estimate of the dynamic stress drop from the shape of velocity
pulse. A new spectral parameter viz., the integral of the square of the ground velocity was given to calculate total radiated
energy. The proposed theory includes directivity and found this valid for a range of subsonic rupture velocities.
Earthquake Source Parameters Review in Indian Context
43
Using these models, a large number of studies have been carried out to estimate earthquake source parameters and
to develop scaling laws from observational data collected from various parts of the world.
METHODS TO COMPUTE EARTHQUAKE SOURCE PARAMETERS
The methods to compute earthquake source parameters can be broadly classified into two categories; the time
domain methods and frequency domain methods. These methods are described in the following sections.
Time Domain Methods
O’Neel and Healy (1973) gave a simple method to estimate source dimensions and stress drops of small
earthquakes. This method is based on the measurement of time from the first break to the first zero crossing on short-
period seismograms. This time is related to rise-time as a function of ‘Q’ and instrument response and simple expressions
were given to estimate the source parameters. The method was applied on data collected from Rangely, Colorado and
Hollister, California and gave reasonable results. The need to develop this method aroused because the short period
seismographs used to record local earthquakes have limited dynamic range both in amplitude and frequency, and clipping
of records occurred when the seismographs were operated at high gain to detect events upto zero magnitude. Further, the
limited high frequency response obscured the corner frequencies of the events that can be recorded within the dynamic
range of the recording system. It was argued that the ideal data for computing source parameters should be recorded on
instruments having a wide dynamic range and broad-band frequency response. However, earlier such instruments were
expensive and were not usually operated for microearthquake studies (Tucker and Brune, 1973).
Chung and Kanamori (1980) estimated the source dimensions, modes of rupture propagation, seismic moments,
and stress drops from body wave pulse-widths of 17 intermediate and deep focus earthquakes that occurred in the Tonga-
Kermadec region. These source parameters were interpreted to investigate variations in source properties and the state of
stress within the descending slab.
Frankel and Kanamori (1983) using the time between the P-wave onset and the first zero crossing on
seismograms and determined the rupture duration and stress drop of earthquakes between magnitudes 3.5 and 4.0
from a local seismic networks. This technique was applied to ten main shocks in southern California to investigate
regional variations in stress drop. The measured pulse widths (τ
1/2
) of 65 foreshocks or aftershocks showed that τ
1/2
for
small earthquakes below about magnitude 2.2 remain constant with decreasing magnitude in four sequences.
It was found the relative pulse width of a main shock at a given station can be correlated with the relative
pulse width of its aftershocks recorded at that station. From these observations it was interpreted that the waveforms of
small events (M ~ 2.2) are essentially the impulse response of the path between the source and receiver. To allow path
correction τ
1/2
of small foreshocks and aftershocks were subtracted from the pulse widths of main shocks. The corrected
pulse widths were used to estimate rupture duration and stress drop. The study brought out significant variations in rupture
durations and stress drops of the main shocks.
O'Neill (1984) estimated source dimensions and stress drops of 30 small Parkfield, California, earthquakes (1.2≤
M
D
≤3.9) from the measurements of the times from the initial P-onset to the first zero crossing. These times, corrected for
attenuation and instrument response, were interpreted adopting a circular source model in which rupture expands radially
outward from the center point until it stops abruptly. The seismic moments, were estimated from the empirical relation
between duration magnitude and seismic moment. Using the values of source radii and seismic moments, static stress
drops were estimated.
44
Arjun Kumar, Ashwani Kumar & Himanshu Mittal
Pearce and Stewart
(1989) studied earthquake source models, in which a rupture propagates along a fault plane,
and observed directivity effect in the duration of radiated signal and suggested the use of spectral corner frequencies to
estimate the parameters of an extended source. However, the authors emphasized that in time domain, the measurements of
pulse durations of teleseismic body waves recorded on broad-band seismograms have certain advantages (e.g., easier
estimation of confidence limits and treatment of interfering arrivals). A method is given to test the compatibility of
observed pulse durations with possible source geometries derived from a propagating rupture model. The study showed the
possibility to discriminate between source directivity and anelastic attenuation, and between the fault and auxiliary planes.
Further, an accurate measurement of durations is neither realistic nor essential: a confidence of ± 30% in pulse duration is
typical, but better measurements are possible if the instrument phase response is removed from the observed seismogram.
Empirical Green’s Function Method
Empirical green function method, initially given by Hartzell (1978), has been used in many studies to compute the
source parameters of earthquakes (e.g., Frankel and Kanamori, 1983; Mueller, 1985; Frankel et al., 1986; Li and Thurber,
1988; Hutchings and Wu, 1990; Hough, 1997; Domanski and Gibowics, 2008). In this method the wave- forms of smaller
earthquakes are approximated by point sources in time and space and represent the impulse response of the path between
the source and the receiver. The smaller event is assumed to have a corner frequency that is higher than the frequency band
of interest, so that there is little source contribution to the frequency spectrum, and its wave-form can be considered as an
impulse response of the path, site and the instrument. Radulian and Popa (1996) among others used the empirical green
function (EGF) technique to estimate the source parameters of small earthquakes (10
21
<Mo<10
23
dyne-cm) from the
measurements of first P-wave pulse widths on velocity record. A constant level of pulse width for magnitudes M
L
< M
min
and an increase in pulse width with increasing magnitude beyond M
min
was observed. In view of this the seismograms of
events less than M
min
were considered as an impulsive response whose pulse width is due to path and instrument response.
This impulse response is deconvolved from the wave-form of larger earthquake. In this way one can remove the
contribution of attenuation, scattering, and site response and other effects. In a sense, the EGF method provides a more
accurate account of path effects than the attenuation correction. This method is effective if larger event and smaller event
have same location as well as focal mechanism. In principle, this method can be applied in the time domain (e.g., Mori et
al., 2003) or in the frequency domain (Ide et al., 2003; Prieto et al., 2004; Abercrombie and Rice, 2005).
Frequency Domain Method
Any physical phenomenon that fluctuates in time and/or space, it is important to know its rate of fluctuation (i.e.,
the frequency or the wave-number). This is achieved by transforming the time domain signal to frequency domain called
the spectrum of the signal. The frequency domain representation in many respects is more attractive than the time domain
because many Geophysical phenomena are theoretically represented in frequency domain. Further mathematical operations
(e.g., filtering, attenuation, instrument corrections) are easy to apply in the frequency domain than the time domain because
convolved signals in time domain are multiplied signals in frequency domain. Another advantage of spectral analysis is
that the whole signal shape is used in analysis, whereas, normally the time domain measurements on seismograms are point
measurements (e.g., the arrival time of the first onset of seismic waves and the direction of first arrival, and the maximum
amplitude of the seismic wave). Analysis of the whole wave-form obviously provides more information than point
measurements in time domain.
In the frequency domain, normally the independent parameter is frequency and this parameter permits
comparisons of different earthquake records as they can be referred to the same value of this parameter. The frequency
Earthquake Source Parameters Review in Indian Context
45
domain methods are based on computing the spectra of different types of waves (e.g., P-waves, S-waves, surface waves
and coda waves). Earlier studies were mainly based on computing the spectra of long period waves and the equalization
techniques were adopted to isolate source and path effects. This method involves estimating source parameters by
converting the time history to frequency domain. Path, site and instrument corrections all are applied in frequency domain.
EARTHQUAKE SOURCE PARAMETERS: INDIAN CONTEXT
Early efforts to estimate the source parameters of Indian earthquakes are attributed to Tandon and Srivastava
(1974) who estimated the stress drop and average dislocation of six earthquakes (5.0≤M≤8.5) occurred in the Indian sub-
continent. A relationship between aftershock area and the magnitude of the main shock were developed and used to
estimate seismic moment and stress drop. The study brought out that the stress drop associated with Great Assam
earthquake of 1950 occurred near the continent-continent boundary of the Indian-Eurasian plates of the order of the 140
bars and average dislocation was about 2 m. For other earthquakes (5.0≤M≤6.7), the stress drops varied between 0.14 to
4.5 bars. Singh and Gupta (1980) estimated the source parameters of two major earthquakes of the Indian sub-continent
namely, the Bihar-Nepal earthquake of 1934 (M 8.4), and Quetta earthquake of 1935 (M 7.6). These earthquakes occurred
in the Lesser Himalaya near the Main Boundary Thrust. The data used in the study involved P-wave first motions, S-wave
polarization angles and surface wave spectra. Adopting Rayleigh to Love wave spectral ratios fault lengths and rupture
velocities were estimated from the differential phase and directivity method using teleseismic data. The estimated fault
lengths, and stress drops, for the Bihar-Nepal and Quetta earthquakes were 129 km, 106 km and 275 bars and 567 bars
respectively. On the basis of high stress drop and apparent stress (138 bars and 283 bars) associated with these earthquakes
it was suggested that high tectonic stresses are prevalent in these regions.
In India, studies of earthquake source parameters using local earthquake data started in 1990s when a local digital
telemetered array was deployed in the Garhwal Lesser Himalaya to study the local seismicity of the region. Since then
several studies have been carried out in the parts of the Garhwal and Kumaon Himalaya, Himachal Himalaya, Northeast
Himalaya and in the Shield regions of India from the digital data of local earthquakes and strong motion data of moderate
earthquakes. Efforts have also been made to develop scaling laws (Kumar et al., 2008; Kumar, 2011). Results from some
of the studies carried out using local earthquake data are summarized below:
The first study to estimate the source parameters was carried out by Sharma and Wason (1994). This study
involves estimating the source parameters of 18 local events (1.4≤M
L
≤4.2) from the P-wave spectra using Brune’s model.
The seismic moments, source radii and stress drops of the events ranged from 7×10
18
dyne-cm to 6.23×10
21
dyne-cm, 347
to 545 m and 0.04 to 38 bars respectively. The occurrence of low stress drop events at shallow depths was interpreted to
indicate that the crust has low strength to accumulate strain energy. Kumar et al. (1994) estimated the source parameters of
thirteen local events (1.35≤M
L
≤4.85; focal depth<20 km) that have occurred in the Garhwal Himalaya. Both P-wave and S-
wave spectra were used to estimate the source parameters using Brune’s model. Using S-wave spectra the values of
seismic moment, source radii and stress drop ranged between 1.4×10
19
and 2.99×10
22
dyne-cm, 152 and 840 m and 1and
233 bars respectively. An event with high stress drop of 233 bars occurred close to the epicenter of Uttarkashi earthquake
of 1991.
Wason and Sharma (2000) computed the source parameters of 15 local earthquakes (2.44≤M
L
≤3.32) occurred in
the Garhwal Himalaya from September 1997 to December 1997. The seismic moments and stress drops of events
computed using Brune's model ranged from 2.89x10
18
to 3.90x10
20
dyne-cm and 2.97 bars to 83.42 bars respectively. The
stress drops showed increasing trend with the magnitudes of the earthquakes.
46
Arjun Kumar, Ashwani Kumar & Himanshu Mittal
Kumar et al. (2006) estimated source parameters of 81 local events (-1.5≤M
L
≤3.8) recorded employing a local
network operated in the western part of the Arunachal Lesser Himalaya. The source parameters were estimated from S-
wave displacement spectra employing Brune’s model. It was found that in the Arunachal Lesser Himalaya, maximum
stress drop varied from 16 bars at shallow depth around 2 km to 36 bars at a depth of about 11 km.
Paul et al. (2007) observed low stress drop values between 1 bar and 10 bars for regional earthquakes recorded by
a ten station VSAT network installed in the Garhwal Himalaya. The maximum stress drop is found to be 41 bars for an
earthquake of magnitude 4.9 with focal depth of 15km. Paul and Kumar (2010) estimated the source parameters using P-
wave spectra and Brune’s model for Kharsali earthquake (M 4.9) of the July 2007 and its 17 aftershocks (1.2≤M
L
≤2.4).
The earthquake occurred close to the Main Central Thrust (MCT) and was recorded on eleven stations of the local network.
The seismic moment and stress drop of the main shock are 4.16x10
16
Nm and 41.5 bars whereas, for aftershocks these
parameters ranged from 7.5x10
13
to 2.3x10
14
Nm and 1 bar to 29.7 bars respectably. It has been inferred from the analysis
of time series that the Kharsali earthquake occurred due to a northerly dipping low angle thrust fault at a depth of 14 km.
From the strong motion records of the Uttarkashi earthquake of 1991, Sriram and Khatri (1997) estimated source
spectrum and noticed two corner frequencies. The high frequency portion of the spectrum was interpreted due to the
roughness of faulting with a stress drop of 40 bars, whereas, intermediate to low frequency portion of the spectrum
represented the overall slip over the fault plane with a stress drop of 31 bars. Using the same strong motion data set of
Uttarkashi earthquake, Kumar et al. (2005) estimated stress drop of 53 bars whereas, Joshi (2006) from the strong motion
data estimated stress drops of the Uttarkashi earthquake and Chamoli earthquake as 77 and 29 bars respectively.
Scaling and self-similarity, from the source spectra of twelve small, moderate and large earthquakes that occurred
in northwest and central Himalaya, have been studied by Kumar et al. (2008). The study showed a self-similar scaling
relationship M
0
f
c
3
=1.7×10
16
N-m/sec
3
between the seismic moment and corner frequency for the Himalaya earthquakes
with the stress drop in the range of 50-60 bars. Raj et al. (2009) used finite fault modeling to estimate the source
parameters of the earthquakes occurred in the Sikkim and the Garhwal Himalayas and adopted Brune’s model to calculate
source parameters using far field displacement amplitude spectra. They argued that source parameters obtained from this
procedure have higher resolution.
The Dharamsala earthquake of 1986 (m
b
5.5) occurred in the Himachal Lesser Himalaya. From the strong motion
records, Sriram et al. (2005) estimated the source parameters of this earthquake as seismic moment (2.1×10
24
dyne-cm),
stress drop (36 bars), source radius (2.8 km) and moment magnitude (Mw 5.4). The spectra displayed a rapid decay for
frequencies higher than 10 Hz at all the stations. The authors argued that this frequency is related probably to the
characteristics of the source radiation, beyond which the source radiation drops off.
Konya reservoir is located in the shield region of India and has experienced a major induced earthquake on
December 10, 1967 (M
L
6.5). Since then continuous local seismicity of small and moderate level has been observed in this
region. Gupta and Rambabu (1993) estimated source parameters namely; seismic moment, stress drop, source radius, and
fault dislocation from 25 strong motion records of nineteen earthquakes (3.2≤M
L
≤6.5) in the Konya region. The source
parameters were computed from shear-waves displacement spectra adopting Brune’s model. The seismic moment of the
December 10, 1967 (M
L
6.5) earthquake is 8.6x10
22
dyne-cm whereas, for remaining earthquakes (3.2≤M
L
≤5.2) the
seismic moment ranged from 3.3x10
21
dyne-cm to 4.44x10
22
dyne-cm. The stress-drop of events varied from 61 bars to
487 bars with majority of events having stress drop between 100 bars and 300 bars. The study concluded that an average
constant stress drop of 170 bars represents the source mechanism of the Koyna dam earthquakes.
Earthquake Source Parameters Review in Indian Context
47
Jain et al. (2004) investigated precursory changes in stress drop and corner frequency associated with five main
shocks (4.1≤M
w
≤4.7) that occurred near the Koyna and Warna reservoirs in the shield region of India. Most of the
earthquakes (M≥4.0) have been associated with foreshocks for 15–30 days and aftershocks for over a month after the main
shock. The study brought out that at the beginning of all foreshock sequences (1.5≤M
w
≤2.4), the maximum stress drops
ranged from 0.25 to 0.65 MPa; the corner frequency ranged from 7.0 to 10.0 Hz. The stress drops decreased by about 50
per cent of their maximum value during the precursory period of 4–17 days prior to main shocks and remained at that low
level for a few days after the main shocks. Following an initial increase, the corner frequency decreased by 8 to 45 per
cent. These observations have been interpreted to show an increase in fault length caused due to increased pore pressure as
a result of dilatancy.
Source parameters of the earthquake of March 2005 that occurred in the Koyna–Warna region were estimated by
Kumar et al. (2008) from the spectra of SH-waveforms. The estimated seismic moment, source radius, stress drop and
moment magnitude for this earthquake are 3.9x10
16
N-m, 975m, 19 MPa and 5.1 respectively. The near-surface attenuation
factor was found to be 0.01, and has been interpreted to represent thin low velocity sediment beneath this region. The
authors argued that the estimated stress drop of the earthquake is higher as compared to the other intraplate earthquakes in
India.
Jabalpur earthquake of 1997 (M
w
5.7) occurred in Indian Peninsular shield region and was recorded by a 10-
station broadband seismographic network. Singh et al. (1999) using this data estimated Q
Lg
for the Indian shield region as
Q = 508f
0.48
(1≤f ≤ 20 Hz). To explain high-frequency spectral level of corrected source spectrum adopting ω
2
-source
model, required a value of seismic moment, 5.4×10
24
dyne-cm, and stress parameter of 420 bars. The computed seismic
energy is 7.4×10
20
erg, which yielded an apparent stress and Brune stress drop of 62 and 270 bars, respectively.
Bodin and Horton (2004) from the spatial distribution of more than 1000 aftershocks estimated the rupture area
about 1300 km
2
of Bhuj earthquake of January 2001. The estimated static stress drop of the main shock was 16±2 MPa.
Mandal and Johnston (2006) estimated the source parameters of 213 aftershocks (2.16≤M
w
≤5.74) of Bhuj earthquake of
2001, using the spectra of SH- waveform of seismograms as well as accelerograms. The estimated seismic moment, source
radius and stress drop for aftershocks ranged from 1.95x10
12
to 4.5x10
17
N-m, 239 to 2835 m and 0.63 to 20.7 MPa,
respectively. The value of near-surface attenuation factor (0.03) suggested thick low velocity sediments beneath the
Kachchh region. The larger stress drop values (>15 MPa)) were observed in 22–26 km depth range. The study inferred that
concentration of large stress drops at depths between 10 and 36 km may be related to the large stress/strain associated with
a brittle, competent intrusive body of mafic nature.
Kayal et al. (2009) estimated the source parameters of two local earthquakes M<3 recorded on a three-component
broadband seismograph installed at Indian School of Mines (ISM) campus that is located to the south of the MBT in the
Ganga fore deep. The study showed that these earthquakes occurred in the lower crust at a depth of 26 km by strike slip
faulting. The North-south compression and east-west tensional stresses are dominant in the area.
Khan et al. (2009) studied source parameters of 46 microearthquakes (0.5≤MW≤3.7) recorded during 2007 by a
three-component broadband digital seismograph installed in the Eastern Indian shield region. The seismic moments ranged
from 6.0x10
16
to 15.4x10
18
dyne-cm and stress drops ranged between 0.1bar and 1.9 bars. The results provided preliminary
information to understand the subsurface geological processes of the region.
Kumar et al., (2012) developed a software EQK_SRC_PARA to estimate spectral parameters namely: low
frequency displacement spectral level (Ω
0
), corner frequency above which spectrum decays with a rate of 2 (f
c
), the
48
Arjun Kumar, Ashwani Kumar & Himanshu Mittal
frequency above which the spectrum again decays (f
max
) and the rate of decay above f
max
(N). A Brune’s source model that
yield a fall-off of 2 beyond corner frequency has been considered with high frequency dimunition factor, a Butterworth
high-cut filter presented by Boore (1983) that fits well for frequencies greater than f
max
. The software has been written in
MATLAB and it uses input data in Sesame ASCII Format (SAF) format. These spectral parameters are used to estimate
source parameters, namely: seismic moment, source dimension and stress drop and to develop scaling laws for an area.
Kumar et al., (2013) estimated source parameters for a data set of 79 local events (0.7≤Mw≤3.7) occurred during
February 2003 to May 2003, collected by a temporary network deployed in Kameng region of Arunachal Lesser Himalaya.
The software EQK_SRC_PARA (Kumar et al., 2012) has been used to estimate the spectral parameters and source
parameters. Seismic moment varies from 1.42x10
17
dyne-cm to 4.23x10
21
dyne-cm; the source radii varies from 88.7 m to
931.5 m. Stress drops for majority of events (59) have been less than one bar, 19 events (Mw≥2.0) have stress drop
between one bar and 10 bars and only one event has stress drop around 21 bars. A breakdown in constant stress drop
scaling has been observed for events below magnitude 2.1. A scaling relation M
0
(dyne-cm) =2x10
22
fc
-3.34
has been derived
for earthquakes having magnitude greater than 2.1. Based on plots of both f
c
and f
max
with seismic moment having same
amount of scatter, they suggested that both these quantities, f
c
and f
max
, are related to source process and get affected by site
effects.
Kumar (2011) analyzed data collected by two networks–Indian strong motion instrumentation network (Kumar et
al., 2012) and TehriTelemetered Network (TTN) operated by Indian Institute of Technology Roorkee in Garhwal
Himalaya.Earthquakes (3.1≤Mw≤4.7) have seismic moments (Mo), ranges from 5.1×10
20
to 1.06×10
25
dyne-cm. The
source radii(r) are confined between 197 to 894 meters, the stress drop ranges between 25.9 bars to 83.4 bars. The
estimated average stress drop 59.1±19.2 bars byand large agrees with the earlier reported average stress drop of 56±36 bars
(Kumar et. al., 2008).A scaling relation, Mo (dyne-cm) = 3.0x10
23
f
c
-2.98
hasbeen derived for the Garhwal Himalaya.
CONCLUDING REMARKS
The paper begins with a brief account of some of the landmark studies related to the developments of earthquake
source models and scaling laws that laid a strong foundation to study earthquake source parameters from observational
data. The rapid passage over some common methodologies to estimate source parameters excludes many relevant studies.
Different methods in the time domain, frequency domain, including empirical green function, that are commonly adopted
to estimate source parameters are then described briefly. Some typical studies of earthquake source parameters based on
observational data and development of scaling laws in Indian region along with the salient results are discussed.
ACKNOWLEDGMENTS
The first and third authors are grateful to Prof. Ashok Kumar, Department of Earthquake Engineering for
providing all the necessary support.
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