1. science
2. geology
3. seismology
4. earthquakes

ISET GOLDEN JUBILEE SYMPOSIUM
Indian Society of Earthquake Technology
Department of Earthquake Engineering Building
IIT Roorkee, Roorkee
October 20-21, 2012
Paper No. A008
PSHA USING DIFFERENT ATTENUATION RELATIONSHIPS
FOR DIFFERENT SEISMIC SOURCES
1
1
I.D. Gupta and 2Lalitha Pattanur
Director, Central Water and Power Research Station, Pune, India, idgrh4@yahoo.com
2Senior Research Officer, Central Water and Power Research Station, Pune, India, lrpattanur@yahoo.co.in
ABSTRACT
The Probabilistic Seismic Hazard Analysis (PSHA) is commonly carried out using the same ground
motion attenuation relation for all the seismic sources. However, different attenuation relations may
characterize the seismic sources involved in many cases. For example, this may be the case when
plate boundary as well as intraplate sources, or shallow crustal and deep subduction types of sources
are involved together. This paper describes the application of PSHA methodology with different
seismic sources described by different attenuation relationships. The major issues involved in this
task are the interpolation of the regression coefficients to have all the attenuation relations at the
same natural frequencies and to carry out summations on different sets of governing parameters for
different attenuation relations by defining the input seismicity for respective seismic source in terms
of the various governing parameters.
Keywords: Probabilistic Seismic Hazard, Seismic Sources, Shallow Crustal Earthquakes, Subduction
Zone Earthquakes, and Attenuation Relations.
1. INTRODUCTION
In most of the PSHA applications, a single attenuation relationship is used for all the seismic sources.
This may not lead to realistic estimate of the hazard, because there may be a combination of seismic
sources with fundamentally different characteristics, warranting the use of different attenuation
relations for different sets of sources. Use of multiple attenuation relations as is done to consider the
epistemic uncertainties will not be able to solve this type of problem. This paper presents an example
of the PSHA with simultaneous use of different attenuation relations for different seismic sources.
The example region considered encompasses northeast Indian and part of western Burma, which are
seismically active regions of South East Asia. There are two tectonically distinct types of seismic
sources in this region, viz., shallow crustal earthquakes and the deep earthquakes within the Indian
plate subducting below the Burmese plate. Based on the knowledge of major tectonic features and the
association of past seismicity with them, ten seismic source zones have been delineated in the entire
region, of which two define the subduction zone and the remaining as shallow crustal seismicity. For
the subduction zones also, the shallow crustal events have been treated separately. The seismic hazard
has been computed using different attenuation relations for the subduction zones and the shallow
crustal sources. Some of the shallow crustal sources are taken as dipping fault plane sources, whereas
most of them are taken as area sources of diffused seismicity. The subduction sources are associated
mainly with the intra-slab earthquakes and are defined by dipping plane of the subducting Indian plate.
It has been shown that the seismic hazard may be substantially underestimated if all the seismic
sources were described by the attenuation relation for shallow crustal earthquakes. The paper thus
describes the methodology and highlights the importance of using different attenuation relations for
the seismic sources with different seismotectonic characteristics.
2. SEISMOTECTONICS AND SEISMIC SOURCES OF REGION
The major seismotectonic features example region of northeast India and western Burma are shown in
Fig. 1. The tectonic features are compiled from the GSI (2000) Atlas and the seismotectonic map due
to Thein (2009). This region is seismically one of the most active regions of the world, having
experienced several earthquakes of magnitude greater than 7.5.
28°
Putao
Dudhnoi Fault
27°
25°
ce
Eo
H
ne
24°
un
Jam
aF
au
lt
Latitude, N
26°
i ng
eZ
Myithyina
e
on
l
au
tF
he
l
Sy
t
Katha
Bhamo
23°
Shwebo
22°
90°
91°
92°
93°
94°
95°
96°
97°
98°
Longitude, E
Lineaments
Faults
Sub-surface fault
Gravity fault
Thrust
Fig. 1: Major tectonic features in region selected for computing the example results.
In the northern part of the region, the major structural elements are the Main Central Thrust (MCT),
the Main Boundary Thrust (MBT) and the intermittently exposed Main Foothill Thrust (MFT) along
with some subsidiary thrusts and transverse fault. The important structural features in the northeast are
the NW-SE trending Lohit thrust, the Tidding Suture and the Mishmi thrust. The Mishmi thrust acts as
a buttress resisting the motion of Indian plate.
Towards the west is the Indo-Burmese Arc, a very important tectonic feature. The important structural
elements in this part of the region are the high angle reverse faults parallel to the regional north-south
folds in the eastern part of the outer arc ridge within the Eastern Boundary Thrust (EBT) zone or
Kabaw fault and the north westerly trending transverse Mat fault. The Burmese arc is an outcome of
eastward underthrusting of the Indian Lithosphere below the Burma plate. The Burmese arc defines a
Benioff zone with a dip of 45° and the depth of about 200 km (Guzman-Speziale and Ni, 1996). To the
west of Burmese arc are the Naga-Disang and Tripura fold belts. The Naga-Disang thrust system
forms a complex pattern with eight separate over-thrust sheets, known as the Belt of Schuppen.
An important tectonic feature in the easternmost part of region is the Shan Shagaing fault, a
continental transform fault between the Indian and Sunda plates. The Shagaing fault, which is more
than 1000 km long, is an active right lateral strike slip fault crossing from north to south through
Myanmar. The fault extends from north of Lake Indawgyi southward along the Irrawaddy River north
of Mandalay, and along the eastern margin of the Bago Yoma to the Andaman Sea. Further north, this
fault connects with the Mishmi Thrust, the western termination of the Himalayan Main Central Thrust.
The Shagaing fault crosscuts series of complex structures that affect both the edge of the Shan Plateau
and the central Myanmar basins. The Shagaing fault has been seismically active in the past 200 years,
with several destructive earthquakes along the fault, such as the 1839 Ava (Innwa), May 1930 Pegu
(Bago), December 1930 Pyu, and 1956 Shagaing earthquakes (Chhibber, 1934; Le Dain et al., 1984).
East of the Shagaing fault, the Shan Plateau belonging to the Asian plate is also seismically active and
intraplate deformation in this region is distributed over several left-lateral faults (Haines and Holt,
1993). In the region between the eastern Himalaya and the Burmese Plate boundaries, the major
tectonic features are associated with the Shillong Massif and its surrounding area. All of these features
are seismically very active.
Fig. 2 illustrates the correlation of available past earthquake data with the major tectonic features.
Though the epicenters are seen to follow broadly the trend of the surface traces of various tectonic
features, they are scattered very widely. This may be due to inaccuracies in the epicentral location as
well as the dipping nature of the tectonic features. The Burmese subduction zone is characterized by
very high level of seismicity, which decreases towards the north of about 25° N. The Shagaing fault is
also seen to be associated with considerable seismicity. The seismicity in the region is seen to be
clustered at several preferred locations, mainly along the faults and lineaments.
28°
27°
Latitude, N
26°
25°
24°
23°
22°
90°
91°
92°
93°
94°
95°
96°
97°
98°
Longitude, E
4.0 <_ M < 4.8
4.8 <_ M < 5.6
Lineaments
Faults
5.6 <_ M < 6.4
6.4 <_ M < 7.2
Sub-surface fault
Gravity fault
M _> 7.2
Thrust
Fig. 2: Correlation of past earthquakes with the tectonic features in the example region.
Considering the highly complex spatial distribution and correlation of seismic activity with the
tectonic features in the region, following eleven broad seismic sources have been identified in the
region:
Source-1 defines the southern part of the Indo-Burmese subduction zone to the east of Arakan
Yoma ranges.
Source-2 covers the region of shallow crustal earthquakes mainly due to the Shan Shagaing fault.
Source-3 is related to the Arakan-Yoma ranges to the west of source-1 and is characterized by
lower level of seismicity and shallower focal depths.
Source-4 is related to northern part of the Indo-Burmese subduction zone above latitude 25° N,
where the seismicity is lesser than source zone-1 with focal depths also not that deep.
Source-5 lies to the west of source-3 where the seismicity due to subduction reduces and also the
focal depths are relatively shallower.
Source-6 encompasses the area related to the seismically active Shillong massif and nearby
features.
Source-7 defines the part of the Tripura Fold Belt and the Bengal Basin to the south of Shillong
plateau.
Source-8 covers the widely spread events near the Nan-Ting fault in Burma.
Source-9 encompasses the Assam Syntaxis and the Lohit-Mishmi Thrusts.
Source-10 defines the region of the Himalayan tectonic features of MBT, MCT and MFT.
Source-11 defines the area of Brhamputra Valley between the seismically active Himalayan
thrusts and the Shillong Massif areas.
28°
Source zone-9
Source zone-10
27°
Source zone-11
26°
Latitude, N
Source zone-6
1
25°
2
3
Source zone-8
24°
23°
22°
90°
Source zone-7
91°
92°
93°
94°
95°
96°
97°
98°
Longitude, E
4.0 M 4.8
4.8 M 5.6
5.6 M 6.4
6.4 M 7.2
M 7.2
Locations analysed
Fig. 3: Possible seismic sources identified in the example region along with the epicenters of past
earthquakes.
All the eleven seismic sources are depicted in Fig. 3 along with the epicenters of past earthquakes. It
may be noted that the deep subduction sources-1 and 4 are also characterized by shallow crustal
earthquakes. Thus, the seismic activity within about 50 km depth in these sources is defined by two
gently dipping shallow crustal sources.
3. PROBABILISTIC SEISMIC HAZARD ANALYSIS
The probabilistic seismic hazard analysis (PSHA) approach is used to consider the random and
uncertain nature of seismicity as well as the ground motion attenuation. This approach considers the
effect of total expected seismicity with suitable spatial distribution to evaluate the response spectrum
at a site of interest with a desired confidence level during a specified exposure period. The
probabilistic MCE level of ground motion is commonly specified with a confidence level of 98 %
during 50 years exposure time (FEMA, 2004). When same attenuation relation is used for all the
seismic sources, the PSHA approach is normally based on the following form of composite probability
distribution of the spectral amplitude SA(T) at a particular natural period T (McGuire, 1977; Anderson
and Trifunac, 1978; Gupta, 2002).
I J


P[ SA(T )]  exp  Y   q[ SA(T ) | M j , Ri ] ( M j , Ri )
 i1 j 1

(1)
In this expression,  ( M j , Ri ) is the annual occurrence rate of earthquakes within small magnitude and
distance ranges ( M j - M j , M j  M j ) and ( Ri - Ri , Ri  Ri ) in all the seismic sources and Y is
the exposure time considered. The quantity q[ SA(T ) | M j , Ri ,  ij ] is the probability of exceeding the
spectral amplitude SA(T) due to earthquake of magnitude M j at distance Ri , as estimated by the
probability distribution of the residuals around the median estimate from an empirical attenuation
relationship.
However, to consider shallow crustal as well as deep subduction types of seismic sources,
characterized by different attenuation relations defined in terms of different governing parameters, the
total probability function of eqn. (1) gets modified as:
I C JC

P[ SA(T )]  exp  Y   qC [ SA(T ) | M j , Ri ] C ( M j , Ri ) 
 i1 j 1
(2)
IS J S KS

Y    q S [ SA(T ) | M j , Ri , H k ] S ( M j , Ri , H k ) 

i 1 j 1 k 1
In this expression, subscripts C and S refer to the crustal and subduction seismic sources, respectively.
It may be noted that in addition to the closest distance to the fault rupture, the attenuation for
subduction zone sources depends explicitly on the focal depth also. The estimation of design
seismicity for these sources forms an important part of the PSHA analysis as will be described later in
the paper.
3.1 Attenuation Relationships Used
The attenuation characteristics of strong ground motion are seen to depend significantly on the
tectonic features of the region of interest. For this purpose, the tectonic environment can be classified
into four basic types, viz. shallow-crustal active tectonic regions, shallow-crustal stable tectonic
regions, (3) intermediate-depth subducting plates, also known as Wadati-Benioff or intraslab regions,
and interslab deep subducting plates. The shallow-crustal environments can further be divided into
compressional and extensional stress regimes. The seismic activity in the example region is associated
with both the subduction of the Indian plate below the Burmese plate as well as to the shallow crustal
portions. The subduction zone earthquakes have slower attenuation than crustal earthquakes, and the
difference is more significant for very large earthquakes contributing more to the seismic hazard. This
naturally necessitates the use of two different attenuation relations for the two types of seismic
sources. In the present study, it is proposed to use the attenuation relationship of Atkinson and Boore
(2003) for the subduction sources and that of Abrahamson and Silva (1997) for the shallow crustal
earthquakes.
Abrahamson and Silva (1997) developed the following form of frequency-dependent attenuation
relation for acceleration spectral amplitudes, SA(T), using a database of 655 accelerograms from 65
shallow crustal earthquakes in tectonically active regions the world over.
ln SA(T )  f1 ( M , R )  F  f 3 ( M )  HW  f 4 ( M , R )  S  f 5 ( a max )
(3)
Here, M is the moment magnitude and R is the closest distance to the fault rupture plane. Parameter F
defines the type of faulting, HW specifies the location of site on hanging or footwall of dipping faults,
and S defines the site condition using index variables as:
1 for reverse fault

F  0.5 for reverse oblique fault
0 for strike slip fault

(4a)
1 for sites over hanging wall
HW  
0 otherwise
(4b)
0 for rock or shallow soil sites
S
1 for deep soil sites
(4c)
Functions f1, f3, f4 and f5 in eqn. (3) are expressed in terms of 12 regression coefficients, a1(T), a2(T),
……, a12(T), evaluated at 28 natural periods between 0.02 sec and 5.0 sec, using which the expression
of eqn. (3) gives the least squares median estimate of the spectral amplitudes. Abrahamson and Silva
(1997) have also evaluated the standard deviation at each period, which along with median estimate
can be used to obtain the probability of exceeding any specified spectral amplitude.
Atkinson and Boore (2003) have developed the attenuation relation for subduction zone using a very
large worldwide database. The functional form for this relation is given by
log SA(T )  C1  C2 M  C3 h  C 4 R  g log R  C5 slS C  C 6 slS D  C7 slS E
(5)
Here, R  D fault 2  2 with Dfault as the closest distance to fault surface and   0.00724 x 10 0.507 M
as a near source saturation term, h the focal depth (limited to 100 km for depths >100km), and
g  10 (0.3010.01M ) is the geometric attenuation factor for inslab events. The last three terms in eqn. (5)
accounts for the effect of local soil condition defined by NEHRP site classes based on the shear wave
velocity, VS30, in the top 30 m of ground. All these terms are taken as zero for the generic rock type of
site (NEHRP class B defined by VS30 greater than 760 m/sec), whereas only one of SC, SD and SE is
taken equal to 1 for soil classes C, D and E, respectively. Further, the scaling factor sl in these terms
accounts for the nonlinear soil behavior, which is defined as a function of peak ground acceleration on
rock. Atkinson and Boore (2003) have provided the regression coefficients at only eight natural
periods, which have been interpolated on log-log scale to get the coefficients at the same natural
periods as in the relationship of Abrahamson and Silva (1997). Atkinson and Boore (2003) have also
given the standard deviations for the median estimates to estimate the probability of exceeding
specified spectral amplitude.
3.2 Estimation of Design Seismicity
To obtain the seismicity rates for each of the seismic sources, following form of Gutenberg-Richter’s
(1944) recurrence relationship has been first defined for each of the seismic sources
log N ( M )  a  bM
(6)
In this expression, N(M) is the annual number of earthquakes with magnitude M or greater and a and b
are the constants specific to the seismic source of interest. To evaluate these constants, the past
earthquake data in the source zone has been converted into moment magnitude using empirical
conversion relations (Chung and Bernreuter, 1981). Also, the dependent events namely foreshock and
aftershocks, have been removed (Gardner and Knopoff, 1974; Uhrhammer, 1986), and the
completeness of data in different magnitude ranges has been accounted by the method of Stepp (1973).
The constants a and b have been then obtained using the maximum likelihood method of Weichert
(1980). In the case of seismic source 1 and 4 related to the Indo-Burmese subduction zone, the shallow
crustal earthquakes within 50 km depth and the deeper subduction earthquakes have been treated
separately. The parameters a and b thus obtained for all the sources are given in Tabule-1.
Table-1: Recurrence parameters and maximum magnitudes for various seismic sources considered.
Source
.
1a.
1b.
Description of the Source
Southern Indo-Burma Subduction Zone
Shallow Crustal Portion above Source 1a
b-value
a-value
Mmax
1.05
0.87
4.57
4.61
6.4
7.8
2.
Area of Shan Shagaing Fault
0.73
3.70
8.2
3.
Area of Arakan-Yoma Ranges
0.90
4.25
7.5
4a.
4b.
Northern Indo-Burma Subduction Zone
Shallow Crustal Portion above Source 4a
0.68
0.89
3.39
3.64
8.2
7.2
5.
0.56
2.06
5.5
6.
Low Seismicity Area Facing Source 4b
Shillong Massif and Surrounding Area
0.79
3.71
8.3
7.
Bengal Basin and Tripura Fold Belt
1.00
4.39
7.5
8.
Area of Nan-Ting Fault
0.70
2.96
6.3
9.
Lohit-Mishmi Thrust Zone
0.85
3.28
5.9
10.
Eastern Himalayan Zone
0.75
3.63
7.0
11.
Brhamputra Valley
1.05
4.87
7.0
From a knowledge of parameters a and b for a source, the relationship of eqn. (6) can be used to obtain
the total number N ( M min ) of earthquakes above a specified threshold magnitude M min , which is
taken as 5.0 in the present study. For practical applications, it is however necessary to consider an
upper bound magnitude Mmax also. The maximum magnitudes assigned to the various source zones are
given in the last column of Table-1. With both upper and lower bound magnitudes, the expression for
N(M) can be written as (Cornell and Vanmarcke, 1969)
N ( M )  N ( M min )
exp(   ( M  M min ))  exp(   ( M max  M min ))
1  exp(   ( M max  M min ))
(7)
Parameter β in this relation is related to the b value as b ln 10 . The relationship of eqn. (7) describes an
exponential decay of N(M) with increase in M up to the maximum magnitude. A typical example of
the recurrence relationship of eqn. (7) fitted to the available past earthquake data for the subduction
zone events in seismic source zone-1a is shown in Fig.4. From the recurrence relationship for a source
zone, the occurrence rate of earthquakes within a small magnitude range ( M j  M j , M j  M j )
around magnitude M j can be obtained as
n ( M j )  N ( M j  M j )  N ( M j  M j )
(8)
Fig. 4: Typical example of the exponentially decaying recurrence relationship.
In the present study, the magnitude has been discretized into ten intervals with central magnitude Mj =
5.0, 5.4, 5.8,…..., 8.6 and M j  0.2 for all the intervals. The numbers n ( M j ) for various magnitudes
are required to be distributed spatially to get the design seismicity for a source.For this purpose,
sources 1 to 5 and 10 are taken as dipping fault planes, whereas the remaining sources as areas of
diffused seismicity. Further, except sources 1 and 4, which exhibit shallow crustal as well as deep
subduction zone earthquakes, all the other sources are associated only with shallow crustal seismicity.
For the case shallow crustal as well as deep subduction zone sources with strike and dip of the rupture
plane specified, the seismicity is estimated by dividing the entire fault plane into small size elements
of 4 km along the length and 2 km along the width. The center of each element is assumed to be the
possible hypocentral location. The total number of earthquakes n M j in a source is then distributed
( )
uniformly among all the elements to obtain the seismicity rates υ (M , R ) and  n M j , Ri , H i  for the
n
j
i
crutal and the subduction sources, respectively. The distance Ri refers to the closest distance to fault
rupture, which for a given magnitude Mj and hypocentral location on the fault plane is estimated by
assuming unilateral ruptures along both length and width estimated from empirical relations due to
Wells and Coppersmith (1994) with hypocenter at the upper left corner of the rupture area. Once the
rupture reaches the boundaries of the fault plane, the other source elements are not to be considered,
because it will result in duplicating the rupture. The focal depth Hi needed for the subduction sources
is taken as the depth to the assumed hypocentral location.
For the case of shallow crustal sources with diffused seimicity, the entire source area is divided into a
large number of elements of size 0.05 lat  0.05 long with the center of each element as the possible
epicentral location for future earthquakes. The total number n M j of earthquakes is then divided
uniformly among all the elements to get the number υn M j , Ri . However, to assign the distance Ri to a
given source element as the shortest distance to the fault rupture plane, the strike and dip angles of the
fault rupture are not known. A statistical approach is therefore proposed to estimate this distance in the
present study. For this purpose, from the trend of focal depths for the past earthquakes, an average
focal depth is assigned to each central magnitude Mj in a source element. Then assuming the the
hypocenter to lie at the geometric center of the rectangular fault rupture area, distance Rrup can be
(
)
( )
estimated easily for any specified dip and strike angles. As the dip and strike values are not known, the
Rrup distance is proposed to be taken as the average of the distances obtained for all possible angles of
strike and dip. For seismic sources 6, 8, 9,and 11, the strike and dip angles could be constrained over
limited ranges based on the tectonic considerations, whereas for source 7 they are taken to be
distributed randomly over the complete ranges. For computational efficiency, the seismicity υn M j , Ri
is obtained by clubbing together the seismicity for all the source elements within same magnitude and
distance intervals.
(
)
4. RESULTS AND DISCUSSION
To illustrate the application of the foregoing PSHA method using different attenuation relations for
two different types of seismic sources, three different sites designated as sites 1, 2 and 3 in Fig. 3, are
considered to compute response spectra. These sites are selected to be located at different distances
and in azimuthal directions with respect to the subduction zone sources. Using the total expected
seismicity evaluated separately for the shallow crustal and subduction zone types of seismic sources,
the probability distribution function of eqn. (2) has been used to compute the 5 % damped horizontal
spectral amplitudes at various natural periods with a confidence level of 0.98 during a life period of 50
years, which corresponds to a recurrence period of about 2500 years. The response spectra thus
obtained are known as uniform hazard response spectrum, which forms the basis of the probabilistic
design ground motion. For the purpose of comparison, uniform hazard response spectra have been
computed by using the attenuation relation for shallow crustal earthquakes for the deep subduction
type of seismic sources also. The comparisons of the response spectra based on different attenuation
relations for deep subduction and shallow crustal sources with those based on only shallow crustal
attenuation relation for the three selected sites are shown in Fig. 5.
1.0
Site #2
0.9
Spectral acceleration, g
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
1
2
3
Period, sec
1.3
1.1
0.9
1.0
0.8
Spectral Acceleration, g
Spectral acceleration, g
1.0
Site #3
1.2
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Subduction zone and shallow crustal attenuations
Only shallow crustal attenuations
Site #1
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.1
0.0
0.0
0
1
2
Period, sec
3
0
1
2
3
Period, sec
Fig. 5: Comparison of the 5% damped uniform hazard response spectra for three typical sites in the
example region as obtained by using different attenuation relations for shallow crustal and deep
subduction zone earthquakes with those based on shallow crustal attenuation only.
The results in Fig. 5 indicates that the use of appropriate attenuation relations for subduction zone
seismic sources results in much higher seismic risk at even very large distances and the position of the
site with respect to the deep subducting plate. The site-2 is considered to lie well over the Benioff
Zone, whereas site-3 lies just outside the Benioff Zone on the hanging wall side of the subducting
Indian plate. On the other hand, site-1 lies on the footwall side far away from the Benioff Zone. It is
seen that the spectral amplitudes are the lowest for site-2 and the highest for site-3. However, the trend
of the results is seen to be similar when the shallow crustal attenuation relation is used for the deep
subduction seismic sources also. Thus, the relative difference in the spectra at three example sites may
be attributed more to the general level and spatial distribution of the seismicity and less to the
attenuation relationship. However, to get accurate absolute estimates, it is necessary to use different
attenuation relationships for the deep subduction sources. From the results in Fig.5 it is observed that
using the attenuation relation for shallow crustal earthquakes for all the sources has underestimated the
seismic hazard considerably.
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