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PSHA carried for Iraq region
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Probabilistic Seismic Hazard Assessment for Iraq Using Complete
Earthquake Catalogue Files
A. S. AMEER,1 M. L. SHARMA,1 H. R. WASON,1 and S. A. ALSINAWI2
Abstract—Probabilistic seismic hazard analysis (PSHA) has been carried out for Iraq. The earthquake
catalogue used in the present study covers an area between latitude 29�–38.5� N and longitude 39�–50� E
containing more than a thousand events for the period 1905–2000. The entire Iraq region has been divided
into thirteen seismogenic sources based on their seismic characteristics, geological setting and tectonic
framework. The completeness of the seismicity catalogue has been checked using the method proposed by
STEPP (1972). The analysis of completeness shows that the earthquake catalogue is not complete below
Ms ¼ 4.8 for all of Iraq and seismic source zones S1, S4, S5, and S8, while it varies for the other seismic zones.
A statistical treatment of completeness of the data file was carried out in each of the magnitude classes.
The Frequency Magnitude Distributions (FMD) for the study area including all seismic source zones were
established and theminimummagnitude of complete reporting (Mc) were then estimated. For the entire Iraq
the Mc was estimated to be about Ms ¼ 4.0 while S11 shows the lowest Mc to be about Ms ¼ 3.5 and the
highest Mc of about Ms ¼ 4.2 was observed for S4. The earthquake activity parameters (activity rate k, bvalue, maximum regional magnitude mmax) as well as the mean return period (R) with a certain lower
magnitudemmin ‡ m along with their probability of occurrence have been determined for all thirteen seismic
source zones of Iraq. The maximum regional magnitude mmax was estimated as 7.87 ± 0.86 for entire Iraq.
The return period for magnitude 6.0 is largest for source zone S3 which is estimated to be 705 years while the
smallest value is estimated as 9.9 years for all of Iraq.
The large variation of the b parameter and the hazard level from zone to zone reflects crustal heterogeneity
and the high seismotectonic complexity. The seismic hazard near the source boundaries is directly and
strongly affected by the change in the delineation of these boundaries. The forces, through which the
geological structure along the plate boundary in Eastern and Northeastern Iraq are evolved, are still active
causing stress-strain accumulation, deformation and in turn producing higher probabilities of earthquake
activity. Thus, relatively large destructive earthquakes are expected in this region. The study is intended to
serve as a reference for more advanced approaches and to pave the path for the probabilistic assessment of
seismic hazard in this region.
Key words: PSHA, earthquake catalogue characteristics, b value, mmax, Iraq.
Introduction
The ultimate goal of seismic hazard assessment for a particular site or area is to
condense seismotectonic knowledge and experience into parameters used for
1 Department of Earthquake Engineering, IIT Roorkee, Roorkee, India.
E-mail: [email protected] Middle East Seismological Forum, Reston, VA, U.S.A.
Pure appl. geophys. 162 (2005) 951–9660033 – 4553/05/050951 – 16DOI 10.1007/s00024-004-2650-y
� Birkhauser Verlag, Basel, 2005
Pure and Applied Geophysics
predicting ground motion which in turn can be applied by engineers in design and
subsequent earthquake resistant construction. The seismic hazard has to be
considered for sensitive structures like dams, mines, nuclear power plants, under-
ground depositories for radioactive waste, oil platforms, etc.
The primary advantage of probabilistic seismic hazard analysis (PSHA) is that it
integrates over all seismicity: temporal and spatial along with ground motions to
calculate a combined probability of exceedence that incorporates the relative
frequencies of occurrence of different earthquakes and ground-motion characteris-
tics. In practicality in any earthquake catalogue the quality of the different parts
(periods and areas) varies significantly with respect to completeness, magnitude
reliability, homogeneity and location accuracy. In an ‘‘edgy’’ formulation one may
say that on the basis of an incomplete, inhomogeneous and inaccurate catalogue, the
science is challenged with the task of deriving parameters that confidently reflect the
seismic potential of the region.
Specifically, the estimation of the maximum regional magnitude mmax and its
occurrence in space and time is the most difficult of the seismic hazard parameters to
assess. Mostly the methods employed in estimating mmax, are dependent on the
extrapolation of the classical, log-linear, frequency-magnitude Gutenberg-Richter
relationship. To avoid confusion mmax, is defined here as the upper limit of
magnitude for a given region. Also, synonymous with the upper limit of earthquake
magnitude, is the magnitude of the largest possible earthquake. The estimation of
mmax is necessarily required for engineering applications and seismic hazard analyses
(see KIJKO, 2002). In addition to reviewing newly available data for inclusion in
updated probabilistic analyses, the primary aim of the present study is to consider the
potentially damaging earthquakes throughout Iraq and to consider new models of
FMD (Frequency Magnitude Distributions) for Iraq. PSHA is conducted for Iraq
taking into account the newly compiled data set and the new models of FMD, and an
endeavor is made to interpret the results with respect to the various seismogenic
sources present in Iraq.
Geology and Tectonic Setting of Iraq
The study area comprises entire Iraq, which falls in the eastern Arabian Plate.
The Arabian subcontinent plate is one of the Earth’s largest blocks that has held
together and moved many kilometers as a unit since the late Cretaceous, experiencing
relative transitional motion with respect to the Eurasian, African, Somalian, Iranian,
Anatolian, and Aegean plates. The Arabian platform comprises Paleozoic intracr-
atonic basins overlying crystalline basement. The Mesozoic basins were formed as a
result of the late Permian and early Triassic opening of the adjacent Neo-Tethysides
ocean and the development of its passive margins. Tectonic setting of the Arabian
plate indicates that it is almost surrounded by active plate boundaries. The western
952 A. S. Ameer et al. Pure appl. geophys.,
boundary is marked by the left-lateral Dead Sea fault system which extends from the
Gulf of Aqaba in the south to the northern Triple Junction of Cyprus subduction
zone, Bitlis zone and the Dead Sea Transform (BEYDOUN, 1991; ALSINAWI and AL
DILAIMI, 1993).
The Arabian Subcontinent plate is subducted under the Anatolian and Iranian
plates compressing the Tethyesides geosyncline belt as part of the Alpine movement,
which reached its climax in the Tertiary and continued until the Oligocene and early
Pliocene, where the Tethys Sea was completely closed in the region. The Zagros
mountains which are part of the Alpine-Himalayan orogenic system can be divided
into three structural zones: an inner crystalline zone of overthrusting, an imbricate
belt, and a zone of folding often referred to as the simply folded belt (the north and
northeastern parts of the study area). The Taurus belt took an E-W trend in the
north of the study area. These two plate boundaries have complicated patterns and
their seismicity is diffused without sharp borders, and is believed that the forces that
have formed these plate boundaries are still active (Fig. 1) (GHALIB and ALSINAWI,
1974; ALSINAWI, 1988).
The tectonic framework of Iraq (Fig. 1) has a NE-SW classification starting with
(i) the stable shelf restricted by a set of deep faults of AbuJir, Euphrates and Palmyra
fault zones and characterized by a reduced thickness of sedimentary cover. (ii) The
Mesopotamian zone. (iii) The simply folded zone which lies to the northeast of the
Mesopotamian zone, most foldings are buckle folds, e.g., Hatra-Bekhme fault,
Fatha-Houran fault and Diyala faults. (iv) The thrust zone which comprises the
Alpine Euogeosynclinal rocks is characterized by complex thrust structures and
subjected to orogenic movements in late Triassic, upper Cretaceous, Miocene and
Pliocene. Ophiolite facies and flysch sediments ascertained the latest movements. (v)
The Central Iranian zone which is characterized by a chain of Mesozoic and
Cenozoic volcanic.
The region was folded and faulted during the Alpine movement in the Tertiary.
More comprehensive analyses are given by AL NAQIB (1967), BUDAY and JASSIM
(1987), and ALSINAWI (2002).
Database and Seismogenic Sources
The seismicity catalogue has been prepared for the study from various sources
(PDE, Baghdad Seismological Observatory, FAHMI and AL-ABBASI, 1989). The
data have been acquired from PDE’s (Preliminary Determination of Epicenters),
which are routinely updated at the National Earthquake Information Center.
These are eventually replaced by the pruned and final determinations of ISC from
time to time. Further, the database has been updated using the compiled ISC
events from the Baghdad Seismological Observatory. The database consists of
more than 1,000 seismic events spanning the last 95 years from 1905 to 2000. The
Vol. 162, 2005 Probabilistic Seismic Hazard Assessment 953
sizes of events have been re-evaluated in terms of surface wave magnitude ‘‘Ms’’
(either observed or converted from ‘‘mb’’), for further use. Figure 2 illustrates the
compiled data set, grouped into six classes, in the form of histograms per decade
for various magnitude ranges. Examining Figure 2 we can immediately detect the
phenomenal rise in the total number of reported events in the last five decades.
Another interesting feature in Figure 2 is the characteristic exponential behavior
of that group of magnitude classes, especially in the last three decades in the
database.
The study area is divided into various seismic sources which are identified by
using the macro-seismic locations of historic earthquakes and instrumental locations
for the last 95 years. Delineations of the source boundaries are based on neotectonic
Figure 1
Main structural zones of Iraq.
954 A. S. Ameer et al. Pure appl. geophys.,
elements and sudden variations in the homogeneity of the seismicity. In total 13-
seismic source zones (S1 to S13) have been identified. The seismic sources so selected
are shown in Figure 3 along with the seismicity plot.
To analyze the nature of the completeness of the data sample in detail, the
entire data set has been grouped in several magnitude classes and each magnitude
class was modeled as a point process in time. The method as given by STEPP
(1972) has been used to check the completeness of data for firstly, Iraq as a whole
as shown in Figure 4 and secondly, for the entire 13-seismic source zones S1 to
S13 individually. Figure 4 reveals that the data are complete for magnitudes
(3.6 < Ms > 4.1) and (4.2 < Ms < 4.7) for the last 45 years. For magnitude
Ms > 4.8 the data sets are complete for 95 years. The same procedure was
applied for all 13 seismic source zones and the result of completeness for different
magnitude ranges has been compiled in Table 1. For seismic source zones S10 and
S11 the magnitude range for 3.0 < Ms < 3.5 has also been included, which is
due to the denser networks of seismographs reporting lower magnitudes from
these sources. The analysis of completeness of the updated seismicity file shows
that the earthquake catalogue is not complete below Ms ¼ 4.8 for entire Iraq.
Based on the analysis, similar conclusions have also been drawn for seismic
source zones S1, S4, S5, and S8. The value of Mc for entire Iraq has been
estimated as Ms ¼ 4.0, which varies slightly for the 13 seismic source zones
considered in this study (AMEER et al., 2002a, b).
Figure 2
Annual distribution of earthquales for Iraq 1905–2000, grouped in six magnitude classes.
Vol. 162, 2005 Probabilistic Seismic Hazard Assessment 955
The FMDs for entire Iraq and for all 13 seismic source zones have been re-
evaluated after correcting for incomplete reporting in the data sample, i.e., by
creating an artificially complete sample of data below the magnitude which was
completely reported over the total 95 years of data. For this purpose Table 1 was
utilized and the complete mean rate of recurrence for each incomplete magnitude
class was used to ‘‘fill in’’ the lower end of FMD. For example Figures 5, 6 and 7
illustrate this treatment for entire Iraq and seismic sources zones S11 and S13
respectively, where the open circles represent the complete data below the
complete magnitude reporting over 95 years and solid circles show the incomplete
data. The regression analysis (least-squares, LS) was then applied to the
incomplete (b-LS incomplete) and complete data sets (b-LS complete) (see
Table 2) to select the minimum magnitude of complete reporting, Mc, as the value
where the FMD graph clearly departs from the straight line plot, while the largest
earthquake in the sample was usually taken to be the upper magnitude. The
better estimates in evaluation of the b-slope after the treatment for incompleteness
have been achieved in sources S7, S11 and S6, which tend to increase the b-slope
to about 27%, 25% and 17%, respectively.
Figure 3
Seismicity map of Iraq during the last 95 years (1905–2000) with Ms ‡ 3.0 (borders outlined) and the area
surrounding it. The seismic source zones used for seismic hazard estimation shown as (S#).
956 A. S. Ameer et al. Pure appl. geophys.,
PSHA for IRAQ
Probabilistic seismic hazard analysis allows estimation of the likelihood that
the selected ground motion parameter will be exceeded at a given site, within a
reference time interval (CORNELL, 1968). It represents a powerful tool that
integrates over all earthquake occurrences (in space and time) surrounding a
specific site. In the present paper mmax and other hazard parameters have been
evaluated for earthquakes in Iraq and conterminous regions utilizing the available
maximum possible seismological information. The procedure applied in the study
utilizes solely the complete part of the seismicity database of Iraq for
approximately the last 95 years. The completeness of the data files using the
statistical analysis has been checked in this study and the Mc’s were taken for the
further seismic hazard analysis (as described in earlier sections). KIJKO and
SELLEVOLL (1989, 1992) have developed an approach using both information on
strong events contained in the macroseismic part of the catalogue as well as that
contained in the complete catalogue which contains complete data above a certain
magnitude threshold (TINTI and MULARGIA, 1985). This approach was applied to
Figure 4
Completeness analysis for the entire Iraq region for different magnitude classes.
Vol. 162, 2005 Probabilistic Seismic Hazard Assessment 957
Table 1
Variability in the Beginning of Completeness Times for Magnitude Ranges
Sources Time period (in years) for various magnitude ranges
Ms ‡6.0 5.4 – 5.9 4.8 – 5.3 4.2 – 4.7 3.6 – 4.1 3.0– 3.5
1 1905–2000 1905–2000 1905–2000 1945–2000 1950–2000 —
2 1905–2000 1905–2000 1945–2000 1955–2000 1955–2000 —
3 1905–2000 1905–2000 1930–2000 1930–2000 1985–2000 —
4 1905–2000 1905–2000 1905–2000 1935–2000 1960–2000 —
5 1905–2000 1905–2000 1905–2000 1940–2000 1955–2000 —
6 1905–2000 1905–2000 1920–2000 1955–2000 1965–2000 —
7 1905–2000 1905–2000 1925–2000 1960–2000 1980–2000 —
8 1905–2000 1905–2000 1905–2000 1925–2000 1945–2000 —
9 1905–2000 1905–2000 1915–2000 1945–2000 1955–2000 —
10 1905–2000 1905–2000 1920–2000 1925–2000 1955–2000 1960–2000
11 1905–2000 1905–2000 1925–2000 1955–2000 1960–2000 1960–2000
12 1905–2000 1905–2000 1915–2000 1945–2000 1980–2000 —
13 1905–2000 1905–2000 1920–2000 1980–2000 1980–2000 —
Ir 1905–2000 1905–2000 1905–2000 1955–2000 1955–2000 —
Figure 5
The frequency magnitude distribution for Iraq.
958 A. S. Ameer et al. Pure appl. geophys.,
estimate other hazard parameters for entire Iraq and 13 seismic source zones. A
computer program written by A. Kijko was used for the analysis. Table 3
summarizes the input data used for the estimation of mmax and seismic hazard of
Iraq and those of thirteen seismic source zones.
Results and Discussion
The evaluation of earthquake potential is very sensitive to the estimate of the
regional maximum magnitude mmax. The hazard parameters (parameter b in G-R
equation by maximum likelihood (ML), earthquake activity rate k, and mmax) are
tabulated in Table 4 which shows that the b value on a regional scale is estimated to
be relatively high (about 1.09 ± 0.14) for seismic source zone S3, which represented
the Taurus belt, thus reflecting the high seismotectonic complexity and crustal
heterogeneity of the region. Similarly for seismic source zone S4 it is estimated as
0.49 ± 0.19. The mmax estimated for the whole Iraq region is 7.87 ± 0.86 while the
maximum observed magnitude is Ms ¼ 7.2. For the other thirteen sources in Iraq the
Figure 6
The frequency magnitude distribution for seismic source zone S11.
Vol. 162, 2005 Probabilistic Seismic Hazard Assessment 959
minimum and maximum estimates for mmax are 5.66 ± 0.33 and 7.92 ± 1.55 (zones
S11 and S8), respectively.
Figure 7
The frequency magnitude distribution for seismic source zone S13.
Table 2
Values after Re-evaluation of FMD for Complete and Incomplete Data Sets
Source b-LS incomplete b-LS complete b-ML
1 0.69 ± 0.02 0.74 ± 0.02 0.72 ± 0.05
2 0.78 ± 0.04 0.81 ± 0.04 0.66 ± 0.06
3 0.79 ± 0.04 0.91 ± 0.04 1.09 ± 0.14
4 0.92 ± 0.09 0.95 ± 0.09 0.49 ± 0.19
5 0.71 ± 0.05 0.81 ± 0.05 0.74 ± 0.13
6 0.75 ± 0.04 0.90 ± 0.04 0.93 ± 0.10
7 0.52 ± 0.03 0.71 ± 0.03 0.95 ± 0.09
8 0.62 ± 0.04 0.66 ± 0.04 0.78 ± 0.10
9 0.73 ± 0.04 0.70 ± 0.02 0.86 ± 0.08
10 0.70 ± 0.03 0.74 ± 0.03 0.60 ± 0.05
11 0.73 ± 0.05 0.97 ± 0.05 0.68 ± 0.05
12 0.90 ± 0.06 1.10 ± 0.04 0.98 ± 0.07
13 0.85 ± 0.06 1.00 ± 0.06 0.77 ± 0.10
Ir 0.84 ± 0.03 0.89 ± 0.02 0.82 ± 0.03
960 A. S. Ameer et al. Pure appl. geophys.,
The return period R of the earthquakes with a magnitude equal to or larger
than a certain value, ‘‘Ms’’ is a useful parameter in seismic hazard determination
and has been used as direct input to seismic hazard evaluations. Figure 8 provides
the values of the return period for several ‘‘Ms’’ values starting from Ms ¼ 2.5. It
also illustrates the mean return period for all of Iraq and 13 seismic source zones.
For instance, the return period for Ms ¼ 6.0 is the largest for S3 as 705.3 years,
while the smallest value has been estimated for S2 as 25.3 years and for entire
Iraq as 9.9 years.
It is clear from Table 4 that the value of b is smallest equal to 1.15 ± 0.44 and
1.38 ± 0.12 in seismic source zones S4 and S10, respectively while the highest value
for b has been achieved as 2.75 ± 0.94 in S3 and consequently b-ML values also
change accordingly to 0.49 ± 0.19 and 0.60 ± 0.05 for seismic source zones S4 and
S10 while the b-ML value for S3 is 1.09 ± 0.14. It is important to point out the range
of k’s values as (1.04 ± 0.35 to 12.71±1.60) for 13 seismic source zones while for
entire Iraq as (34.03 ± 1.65).
Considering the values of return period R6.0 one may argue that seismic source S2
is the most active in the whole region. The maxima of different seismic hazard
parameters in different zones reveal the complex tectonic environment of the region
under study. For most of the engineering studies the estimated lifetime is generally 50
to 100 years, and therefore, the probability of occurrence of earthquakes in 50- and
100- years return periods has been estimated and is plotted in Figures 9 and 10 for
further use by earthquake engineers. Figures 9 and 10 provide the probability of
occurrence in 50-year and 100-year return periods, which reveal clearly that the
occurrence of earthquakes with large magnitudes is most likely in the Taurus-Zagros
thrust zones.
Table 3
Input Data for Fourteen Seismic Zones in IRAQ and Surrounding Area
Seismic zone Mc Number of events Standard deviation Max. observed
magnitude
1 3.7 237 0.56 7.30
2 4.0 137 0.57 7.30
3 4.0 58 0.44 6.00
4 4.2 31 0.42 5.70
5 3.9 43 0.49 5.80
6 3.7 89 0.45 6.20
7 3.9 110 0.51 5.80
8 3.8 63 0.58 6.80
9 3.9 122 0.55 6.50
10 3.7 143 0.63 7.30
11 3.5 364 0.49 5.60
12 3.9 189 0.42 6.10
13 3.9 76 0.47 6.00
Ir 4.0 783 0.53 7.20
Vol. 162, 2005 Probabilistic Seismic Hazard Assessment 961
Table
4
Seism
icHazard
ParametersforIraq
Seism
iczone
kb
b-M
Lm
max
RM
s¼6:0
Pr
(T=
100)M
s¼6:0
18.62±
0.72
1.70±
0.11
0.72±
0.05
7.68±
0.52
34.0
0.9471
24.65±
0.51
1.56±
0.14
0.66±
0.06
7.53±
0.42
25.3
0.9809
34.30±
0.94
2.57±
0.94
1.09±
0.14
6.53±
0.91
705.3
0.1322
41.04±
0.35
1.15±
0.44
0.49±
0.19
5.85±
0.35
——
-—
—-
51.81±
0.41
1.75±
0.31
0.74±
0.13
6.45±
0.77
232.8
0.3492
65.16±
0.88
2.17±
0.23
0.92±
0.10
6.62±
0.64
339.5
0.2551
75.75±
0.76
2.23±
0.22
0.95±
0.09
6.52±
1.10
257.0
0.3217
82.39±
0.37
1.84±
0.23
0.78±
0.10
7.92±
1.55
157.4
0.4702
95.18±
0.60
2.02±
0.19
0.86±
0.08
6.80±
0.51
125.7
0.5486
10
4.13±
0.41
1.38±
0.12
0.59±
0.05
7.51±
0.39
26.5
0.9770
11
14.22±
1.16
1.60±
0.11
0.68±
0.05
5.66±
0.33
——
——-
12
12.71±
1.60
2.31±
0.17
0.98±
0.07
6.99±
1.54
114.3
0.5830
13
3.44±
0.61
1.81±
0.23
0.77±
0.10
6.53±
0.67
127.9
0.5425
Ir34.03±
1.65
1.93±
0.07
0.82±
0.03
7.87±
0.86
9.9
1.0000
962 A. S. Ameer et al. Pure appl. geophys.,
Figure 8
Return periods using complete data for fourteen seismic source zones in Iraq.
Figure 9
Probability-magnitude diagram for the fourteen seismic source zones for 50-year return periods for Iraq.
Vol. 162, 2005 Probabilistic Seismic Hazard Assessment 963
Conclusion
In the present study the probabilistic seismic hazard analysis has been carried
out for the seismically active region of Iraq. The seismicity catalogue has been
prepared for the period 1905–2000. The whole Iraq region has been divided into
thirteen seismic source zones based on their seismic characteristics, geological
setting and tectonic framework. The analysis of completeness of the updated
seismicity file indicates that the earthquake catalogue is not complete below
Ms ¼ 4.8 for entire Iraq and seismic source zones S1, S4, S5, and S8. The Mc
estimated for entire Iraq was Ms ¼ 4.0 and varies slightly for the 13 seismic
source zones. The gradually curved FMDs (as happened for most seismic zones in
Iraq) tend to underestimate Mc, which is indicative of spatial and temporal
heterogeneity of the earthquake catalogue for these seismic zones, making it
necessary to re-evaluate FMDs.
The FMD relation re-evaluated after correcting for incompleteness of entire
Iraq and for most of the seismic source zones shows an increase in b slope. The
better estimates in evaluation of the b slope after the treatment for incompleteness
have been achieved in sources S7, S11 and S6, which tend to increase the b slope
about 27%, 25% and 17%, respectively. For all source zones the slope (b values)
of FMD varies between –0.49 ± 0.19 and –1.09 ± 0.14, with most zones having
values around –0.80, obviously depending on the size and the seismicity of the
source zone. Such type of results poses a major problem in seismic hazard
Figure 10
Probability-magnitude diagram for the fourteen seismic source zones for 50-year return periods for Iraq.
964 A. S. Ameer et al. Pure appl. geophys.,
assessment which may be attributed to a recent increase in the level of crustal
stress release, causing an increase in the lower magnitude level which perturbed
the standard b slope.
The maximum regional magnitude mmax has been estimated as 7.87 ± 0.86 for
entire Iraq. The return period for magnitude 6.0 is 705 years; the largest for source S3
years while the smallest value is estimated to be 25 years for source S2. The Zagros-
Taurus thrust zones display high seismic activity, particularly in seismic source zones
S1, S2, S9, and S10. The mmax for these sources is comparatively higher than the
other sources. The seismic hazard near the source boundaries is directly and strongly
affected by the change in the delineation of these boundaries. The forces which have
formed the geological structure along the plate boundary in eastern and northeastern
Iraq are still active, causing stress-strain accumulation, deformation and thus may
foreshadow relatively large destructive earthquakes in the future. The study is
intended to serve as a reference for more advanced approaches and to pave the path
for the probabilistic assessment of the seismic hazard in Iraq.
Acknowledgment
The authors sincerely acknowledge the valuable suggestions and comments from
the anonymous reviewers in the preparation of this paper. The computer program
provided by Dr. Andrzej Kijko is used in this study and is gratefully acknowledged.
The authors are thankful for the assistance provided by Prof. and Head, Department
of Earthquake Engineering, Indian Institute of Technology Roorkee.
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