ArticlePDF Available

# A composite source model for computing realistic synthetic strong ground motions

Authors:

## Abstract and Figures

A composite source model is presented for convolution with synthetic Green's functions, in order to synthesize strong ground motions due to a complex rupture process of a large earthquake. Subevents with a power-law distribution of sizes are located randomly on the fault. Each subevent radiates a displacement pulse with the shape of a Brune's pulse in the far field, at a time determined by a constant rupture velocity propagating from the hypocenter. Thus, all the input parameters have a physical basis. We simulate strong ground motions for event - station pairs that correspond to records obtained in Mexico by the Guerrero accelerograph network. The synthetic accelerations, velocities, and displacements have realistic amplitudes, durations, and Fourier spectra.
Content may be subject to copyright.
GEOPHYSICAL RESEARCH LETTERS, VOL. 21, NO. 8, PAGES 725-728, APRIL 15, 1994
A composite source model for computing realistic synthetic strong
ground motions
Yuehua Zeng, John G. Anderson, and Guang Yu
Seismological Laboratory and Department of Geological Sciences
Mackay School of Mines, University of Nevada, Reno
Abstract. A composite source model is presented for
convolution with synthetic Green's functions, in order to
synthesize strong ground motions due to a complex rupture
process of a large earthquake. Subevents with a power-law
distribution of sizes are located randomly on the fault. Each
subevent radiates a displacement pulse with the shape of
a Brune's pulse in the far field, at a time determined by a
constant rupture velocity propagating from the hypocenter.
Thus, all the input parameters have a physical basis. We
simulate strong ground motions for event - station pairs
that correspond to records obtained in Mexico by the
Guerrero accelerograph network. The synthetic acceler-
ations, velocities, and displacements have realistic ampli-
tudes, durations, and Fourier spectra.
Introduction
One goal of strong motion seismology is to develop a
capability to estimate strong ground motions from an
arbitrary future event, with sufficient accuracy that the
synthetic seismograms are useful for engineering appli-
cations. If realistic seismograms can be computed, then
any derived parameters of engineering interest, such as
peak acceleration or velocity, duration of shaking, or
response spectral values, can be obtained easily. Several
techniques are available to compute synthetic seismograms
for strong motion applications, but all of these have some
limitations. This paper presents a new approach that
overcomes some of the problems, and seems to effortlessly
yield synthetic strong motion records that have a very
realistic appearance. Two sample applications demon-
strate the realism of the results.
One approach for generating synthetic time series is a
stochastic simulation. Following Boore (1983), accelera-
tion time histories are generated by shaping an initially
random time series so that it has an appropriate duration,
and then filtering in the Fourier transform domain so that
it has the appropriate spectral shape. Limitations that have
not been addressed include that this approach only gen-
erates an S-wave pulse, and that it does not naturally
generate three-component seismograms with physically
expected coherency. Phases of arrivals, such as dispersed
mation about wave propagation can be included by the use
of empirical Green's functions (e.g. Hartzell, 1978;
Hutchings and Wu, 1990) in simulations. However, the
empirical Green's functions may be generated by earth-
Copyright 1994 by the American Geophysical Union.
Paper number 94GL00367
0094-8534/94/94GL-00367503.00
quakes with differing focal mechanisms from the desired
main shock, are often not available for the desired
source-station pair, and may not have a sufficient signal to
noise ratio at low frequencies. Finally, models for wave
propagation can be included by representing the ground
motion as a convolution of a slip function on the fault with
a synthetic Green's function (e.g. Aki and Richards, 1980).
Methods for computing synthetic Green's functions are
rapidly improving (see Anderson, 1991 for references). A
difficulty with this method has been to develop an appro-
priate source description. For example, in a recent
application Somerville et al. (1991) simply used an
empirical source function derived from smaller earth-
quakes. This paper proposes a synthetic composite source
model for use in these applications.
Method
Composite source time function
We hypothesize that the source slip function can be
simulated, in a kinematic sense, by randomly distributed
subevents on the fault plane. The size distribution of
subevents is based on a self-similar model proposed by
Frankel (1991). In this model, an earthquake is made up
of a hierarchical set of smaller earthquakes. The number
of circular subevents with radius R is specified by
dN -v
d(•n•)
where D is the fractal dimension, N is the number of
subevents, andp is a constant of proportionality. Frankel
predicted that if the static stress drop of the sub-events is
independent of their size, and if the sum of the areas of all
the sub-events equals the area of the main shock, the high
frequency roll-off of the displacement spectrum will be
proportional to co -(•-v/z). The condition on the area is
removed in our procedure, so this prediction may not
strictly hold. Integrating Equation (1), the number of
subevents with radii larger than R is
P -D -D (2)
m(•)-- 3(• - •m•x)
In (2), R max is the largest subevent allowed. We consider
it to be approximately the largest subevent that will fit inside
the fault plane. We use the power law distribution in
Equation (2) to define the relationship between the
number of sub-events and their radius.
After Keilis Borok (1959), the stress drop of a subevent
is related to its radius, R, and seismic moment, M o, by
Mo(R ) = ICR3Ao (3)
725
726 ZENG ET AL.: COMPOSITE SOURCE MODEL
For this application, we take A o to be independent of the
subevent radius. To define the total moment, M E of a o,
collection of subevents with a distribution given by (2), we
note that
dN (4)
n(R) pR
dR
and that R max (5)
M •= / n(R)M (R)clR
0 0
Rmln
This constraint leads to the value for the constant of
proportionality, p, of:
œ
7,•o 3-o D =• 3
p = (6a)
max- rain
p- 16AOl.(Rmax/Rmln ) (6b)
R mi n is intended to be a purely numerical parameter
defined by computational constraints, and for D • 2 it
generally does not affect the value ofp.
To realize the size distribution (2) numerically, we
generate N random real numbers, N ,, which are uniformly
distributed from 0 to N. The size of the corresponding
subevent is:
(7)
R, P max
The actual seismic moment for this realization of the
probability distribution is, from (3):
~ ] 6 ~
I=l I=l
Thus in our numerical simulations wc adjust A o as nec-
essary to achieve M = M E These adjustments arc gen-
erally less than 10%, determined by the sizes of the few
The source time function for each subevent is deter-
mined from its size. Wc assumed that the radiation from
each subevent takes the shape of the Brunc (1970) pulse.
Then:
,
•o = (2r[]•) M'oxexp(-2r[]•x)H(x )
wheref • is the corner frequency, q: is time after the subevent
is triggered, and H (•) is the Heavyside step function. The
function M o(t) is the net seismic moment at any instan-
taneous time during the rupture, and at sufficiently large
time it equals the momentM o. Its derivative is• o ( t ). We
relate the corner frequency/'• to the source radius of the
i th event following Brune (1970):
2.34[3 (12)
2e,
where r3 is shear velocity.
The subevents are distributed randomly on the fault
plane, and overlap of subevents is allowed. This is a major
difference from the model visualized in Frankel (1991), in
which boundaries of subevents do not intersect. Another
difference is that the total area of subevents exceeds the
area of the main event; the necessity for this is pointed out
by Tumarkin ½t al. (1994). Allowing overlap, subevents are
particularly easy to assign to the fault. Subevents are not
allowed to extend beyond the limits of the main fault, so
they are distributed uniformly over the area where overlap
of the main fault boundary will not occur. As an example,
Figure 1 shows the locations of the first 10% of subevents
generated for one realization. We then assumed a hypo-
center and a rupture velocity. The origin time of radiation
from each subevent is the time the rupture, propagating at
a uniform rupture velocity, reaches the center of the
subevent. Because the number of subevents is very large,
we do not compute the Green's function for all of them.
Rather, we divide the fault into a grid of approximately
square sub-faults, and sum the time functions for each
source in one grid element to obtain an effective time
function. This sum is performed adding in a delay for each
sub-event controlled by the rupture time and the geo-
metrical phase delay appropriate for the azimuth to the
station.
Synthetic seismogram
The Green's functions for this simulation are computed
using our code (see Zeng and Anderson, 1994) imple-
menting the generalized reflection coefficient method of
Luco and Apse1 (1983). The synthetic seismograms due to
the complex fault are obtained by convolving the Green's
function with the composite source time function gener-
ated above.
Example
We demonstrate this approach by generating synthetic
seismograms for a source - station geometry that has
previously produced strong motion accelerograms. In
particular, we chose to apply the method to two subduction
zone earthquakes recorded on the Guerrero, Mexico,
accelerograph network shown in Figure 2 (Anderson et al.,
1987, 1991). The simulated events are the M =6.9 earth-
quake on April 25, 1989 and the M =8.1 earthquake on
September 19, 1985.
For the M=6.9 event, we choose to simulate the
accelerograms at the station at La Venta, since Humphrey
and Anderson (1992) have demonstrated that there is a
nearly flat site response at that station. The source
geometry we used is as given by Anderson et al., (1991).
The hypocentral depth is 19 km, and the focal mechanism
is a low angle thrust, consistent with subduction, with dip
13 and strike 301. The seismic moment is
8.7 x 10 2s dyne - cm (Humphrey and Anderson,
unpublished data, 1993). Singh (personal communication)
found the aftershock zone to be roughly circular with radius
Figure 1. Spatial distribution of 10% of the subevents on
the fault for one simulation.
ZENG ET AL.: COMPOSITE SOURCE MODEL 727
19.5
19.0
18.5
18.0
17.5
17.0 i
165
16O
MEXICO CIT
.
O Accelerogroph site
I 0 ? i100 km
i i i
-103 -102 -101
I I
-100 -gg -98
Figure 2. Epicenter, fault size, and station locations for
the observed seismograms that are simulated in this paper.
about 10 kin, which we approximate with a rectangle. The
La Venta station is sited on a granitic outcrop on the
southern flank of the Sierra Madre mountains. The velocity
model used to compute the synthetic seismograms is given
by Anderson et al. (1987), but modified by addition of a
low velocity layer near the surface. Attenuation in this low
velocity layer has been set to assure that t* has a value about
equaling the spectral decay parameter, •:, estimated by
Humphrey and Anderson (1992).
Figure 3 shows observed (Anderson et al., 1991) and
computed acceleration, velocity, and displacement seis-
Acceleration (cm/sec '2 )
ao I- !'
60
40
ql , I i
0 to 20 30 40 50
Time (sec)
25=
20
16
I0
5
o
-5 o
Velocity (cm/sec)
i i ;0 i i
I o 20 40 60
Time(sec)
lO t
100
10-•
10 -2
Displacement (cm)
i i i i i
10 20 30 40 50
Time (sec)
Acceleration Spectra (cm/sec)
U E S
I 0 ø 10 ø I 0 ø
Frequency (Hz)
Figure 3. Observed (Anderson et al., 1991) and simulated
acceleration, velocity, displacement, and Fourier ampli-
tude spectra at the station La Venta. The observed time
series (left) and Fourier amplitude spectra (dashed) are
derived from accelerations recorded in the April 25, 1989
earthquake (Figure 2). The simulation uses D--2,
AO= 30 bars, and rupture velocity of 2.7 km/sec.
Component orientations are S: south; E: east; U: up.
Seismograms are bandpass fiRered between 0.03 and 10
Hz.
mograms and Fourier amplitude spectra of acceleration.
The initial impression is that the synthetic seismograms
have a realistic appearance and about the correct ampli-
tudes. Peak values are consistent to within a factor of two.
The phases do not match in detail, of course, since there
is no attempt to achieve this in the source function. We
conclude that the method described here has been very
successful in generating a synthetic time series that is
appropriate for this geometry.
The second application is for a source - station geometry
that was observed in the M =8.1 earthquake on Sept 19,
1985. The station selected is at Caleta de Campos, which
is almost directly above the hypocenter (Figure 2). The
hypocentral depth is 21 km, and the focal mechanism is
again a low angle thrust, consistent with subduction, with
dip 18 and strike 301. The seismic moment is nearly
1.1 x 10 28 dyna-cm (Anderson et al., 1986). The
hypocenter is at the downdip limit in the northwestern part
of the fault. The velocity model used to compute the
synthetic seismograms is a given by Anderson et al. (1987),
but modified by addition of a low velocity layer near the
surface, constrained to have the P- and S- velocities of a
short baseline refraction experiment (Anguiano Rojas,
1987). Attenuation in this low velocity layer has again been
set to assure that t* has a value about equaling the spectral
decay parameter, •0, estimated by Humphrey and
Anderson (1992), 0.04 sec in this case.
The results of this simulation are shown in Figure 4.
Once again, we are impressed by the realism of the syn-
thetics, especially in acceleration and velocity. All the
synthetics have about the correct duration and amplitude.
Predominant frequencies on acceleration and velocity are
consistent with the data. The displacement, which is
band-pass filtered, shows about the correct amplitudes, but
has two somewhat higher-frequency pulses than the
observations This is a result of the stochastic placement,
by chance, of smaller asperities near the station rather than
Acceleration (cm/sec 2 ) Velocity (cm/sec)
500[ ,t.,l•l• •[],LI ...... s
t .
200 E
,, ,;,,
I I i i i
0 20 40 60 80 100
Time (sec)
120
100
80
40
o
-2.0
0 20 40
I i I
60 80 l oo
Time (sec)
Displacement (cm)
40 E
20
0 20 40 60 80 1 O0
Time(sec)
Acceleration Spectra (cm/sec)
U If'
10
lO 0
1,0 -• I I
I 0 ø I 0 ø
Frequency (Hz)
s
lO 0
Figure 4. Equivalent of Figure 4 for the September 19,
1985 earthquake recorded at Caleta de Campos. ^ccel-
erograms are described by Anderson et al. (1987). Seis-
mograms are bandpass filtered between 0.03 and 10 Hz.
728 ZENG ET AL.' COMPOSITE SOURCE MODEL
a single large one that is inferred, from waveform inver-
sions, to have ruptured there (Campillo et al., 1989).
Campillo et al. proposed that the "ripples" that are visible
on the displacement and conspicuous on the velocity result
from acceleration and deceleration of the rupture from.
Figure 4 suggests that failure of randomly sized and places
asperities is an alternative hypothesis to explain this effect.
Discussion and Conclusions
This paper proposes the hypothesis that the composite
source model provides a kinematic description of the
earthquake source time function that, when combined with
a realistic Green's function, leads to the synthesis of real-
istic strong ground motions. The initial trials give synthetic
seismograms that appear to be quite realistic, with
appropriate amplitudes, durations, and frequency content.
These trials were selected to be cases where site effects are
believed to be minimal, and thus the Green's functions are
relatively simple and the source effect dominates the
ground motions. Considering the fundamental difficulties
of separating source and site effects, this simple situation
seemed most appropriate. This is not a fundamental
limitation, as the composite source model can be combined
equally well with synthetic Green's functions for a more
complicated 2-D or 3-D structure, or even with empirical
Green's functions if they are available.
As a kinematic description of an earthquake source, the
composite source model is easy to implement. All the
parameters involved are potentially constrained by physical
phenomena. Fault mechanism, dimension and slip, and
R max are constrained from geology. Rupture velocity can
be taken from the relatively narrow range of prior obser-
vations. The appropriate stress drop of the subevents needs
to be investigated more, but the value of 30 bars used here
is a typical stress drop for large earthquakes. Finally, fractal
dimension is, according to Frankel (1991), related to the
b-value of earthquakes.
One of the fundamental problems in seismology has
been the inverse problem of describing the seismic source
from observed strong motion accelerograms and other
data. The success in using this composite source model as
a source description for generating realistic ground
motions suggests the idea that there might be some kinship
between the actual earthquake source and a power-law
distribution of random-sized asperities. It will thus be
interesting to see if it is possible to perform an inverse
problem for location and size of main subevents, as a
supplement to the present procedure of estimating slip time
functions as a function of location on the fault.
Acknowledgements. We benefitted from helpful discus-
reviewers. This research was supported by the Southern
California Earthquake Center and National Science
Foundation Grant BCS 9120027.
References
Aid, K. and P. G. Richards, Quantitative Seismology:
Theory and Methods, Volume I, 557 pp., W. H. Freeman
and Co., New York, 1980.
Anderson, J. G., Strong Motion Seismology, Reviews of
Geophysics, Seisrnology Supplement, U.S. National
Report to the International Union of Geology and Geo-
physics 1987-1990, 700-720, 1991.
Anderson, J. G., P. Bodin, J. Brune, J. Prince, S. Singh, R.
Quaas, M. Onate, and E. Mena, Strong ground motion
and source mechanism of the Mexico earthquake of Sept.
19, 1985, Science 233, 1043-1049, 1986.
Anderson, J. G., R. Quaas, D. Almora, J. M. Velasco, E.
Guevara, L. E. dePavia, A. Gutierrez, and R. Vasquez,
Guerrero, Mexico Accelerograph Array: Summary of
data collected in 1985, Report GAA-2, Instituto de Inge-
nieria, Universidad Nacional Autonoma de Mexic,
Mexico City, Mexico, 1987.
Anderson, J. G., R. Quaas, R. Vasquez, D. Almora, J. R.
Humphrey, J. M. Velasco, R. Castro, and C. Perez,
Guerrero, Mexico Accelerograph Array: Summary of
data collected in 1989, Report GAA-11, Seismological
Laboratory, Mackay School of Mines, University of
Anguiano Rojas, R. A., Exploracion sismica del subsuelo
en los sitios de ubicacion de las estaciones acelerograficas,
Geophysical Engineering Thesis, 129 pp., Universidad
Nacional Autonoma de Mexico, Mexico City, 1987.
Brune, J. N., Tectonic stress and the spectra of seismic
shear waves from earthquakes, J. Geophys. Res. 75,
4997-5002, 1970.
Boore, D. M., Stochastic simulation of high-frequency
ground motions based on seismological models of the
radiated spectra, Bull. Seisrn. Soc. Am. 73, 1865-1894,
1983.
Campillo, M., J. C. Gariel, K. Aki, F. J. Sanchez-Sesma,
Destructive strong ground motion in Mexico City: source,
path, and site effects during great 1985 Michoacan
earthquake, Bull. Seisrn. Soc. Am. 79, 1718-1735, 1989.
Frankel, A., High-frequency spectral falloff for earth-
quakes, fractal dimension of complex rupture, b-value,
and the scaling of strength on faults, Jour. Geophys. Res.
96, 6291-6302, 1991.
Hartzell, S. H., Earthquake aftershocks as Green's func-
tions, Geophys. Res. Letters 5, 104-107, 1978.
Humphrey, J. R. Jr. and J. G. Anderson, Shear wave
attenuation and site response in Guerrero, Mexico, Bull.
Seisrn. Soc. Am. 82, 1622-1645, 1992.
Hutchings, L. and F. Wu, Empirical Green's functions from
small earthquakes: a waveform study of locally recorded
aftershocks of the 1971 San Fernando earthquake, J.
Geophys. Res. 95, 1187-1214, 1990.
Keilis Borok, V., On estimation of the displacement in an
earthquake source and of source dimensions, Ann.
Geofis. (Rome) 12, 205-214, 19959.
Luco, J. E. and R. J. Apsel, On the Green's functions for
a layered half-space. Part I., Bull. Seisrn. Soc. Am. 73,
909-929, 1983.
Somerville, P.M. Sen and B. Cohee, Simulatio• of strong
ground motions recorded during the 1985 Michoacan,
Mexico and Valparaiso, Chile earthquakes, Bull. Seisrn.
Soc. Am. 81, 1-27, 1991.
Tumarkin, A., R. J. Archuleta and R. Madariaga, Scaling
relations for composite earthquakes, Bull. Seisrn. Soc.
Am., in press, 1994.
Zeng, Y. and J. G. Anderson, A method for direct com-
putation of the differential seismogram with respect to
the velocity change in a layered elastic solid, Bull. Seisrn.
Soc. Am., in press, 1994.
J. G. Anderson, Guang Yu, Yuehua Zeng, Seismological
89557.
(Received: September 16, 1993; Revised: December 17,
1993; Accepted: December 29, 1993.)
... Finally, the wave propagation problem, essentially formulated by the wave equation, can be solved using multiple numerical methods: finite element (FE), 19,20 finite difference (FD), 21,22 spectral element (SE) 23,24 and discontinuous Galerkin (DG). 25,26 Ever since the seminal contribution of Zeng et al. 27 to the first ever GMS method based on a kinematic rupture representation on a finite fault, physics-based GMS have acquired significant growth over the last two decades, mainly due to the explosive development of high-performance computing techniques and resources. Table 1 summarizes some representative studies on 3D physics-based GMS. ...
... As seen, the BD scenario, in which the direction of rupture propagation is away from the station, produces weaker ground motions compared to the ND and FD scenarios. [26][27][28]. It can be concluded that even among scenarios having the same magnitude, significant variabilities can be found for IMs. ...
Article
Physics‐based earthquake ground motion simulations (GMS) have acquired significant growth over the last two decades, mainly due to the explosive developments of high‐performance computing techniques and resources. These techniques benefit high/medium seismicity regions such as the city of Istanbul, which presents insufficient historical ground motion data to properly estimate seismic hazard and risk. We circumvent this reality with the aid of the Texas Advanced Computing Center (TACC) facilities to perform a suite of 57 high‐fidelity broadband (8–12 Hz) large‐scale physics‐based GMS for a region in Istanbul, Turkey. This paper focuses on the details of simulated GMS: (i) validation of the GMS approach against recorded ground motions produced by the 2019 Mw5.7$M_{w}\nobreakspace 5.7$ Silivri earthquake; (ii) characteristics of 57 different source models, which aim to consider the uncertainties of many fault rupture features, including the length and width, dip, strike, and rake angles of considered fault planes, as well as hypocenter locations and earthquake magnitudes ranging between Mw$M_{w}$ 6.5 and 7.2; (iii) high‐resolution topography and bathymetry and seismic data that are incorporated into all GMS; (iv) simulation results, such as PGAs and PGVs versus Vs30$V_{s30}$ and distances to fault ruptures (Rrup$R_{\text{rup}}$), of 2912 surface stations for all 57 GMS. More importantly, this research provides a massive database of displacement, velocity and acceleration time histories in all three directions over more than 20,000 stations at both surface and bedrock levels. Such site‐specific high‐density and ‐frequency simulated ground motions can notably contribute to the seismic risk assessment of this region and many other applications.
... The different-sized sub-events can describe the complex rupture process during earthquakes. These sub-events constitute a composite source model used by Frankel (1991), Zeng et al. (1994), andYu et al. (1995). In this technique, the source model's complexity is assumed, according to which randomly distributed sub-events of constant stress drop in the entire fault plane constitute a mainshock. ...
... Finally, SGM simulation is achieved when the convolution is applied between the composite source generated from the contribution from all sub-events and the synthetic Green's functions. The reliability of this technique for the generation of realistic time histories has been confirmed by Zeng et al. (1994). The main limitation of this method lies in the requirement of the Q-structure of the region, source mechanism, and velocity structure of the region. ...
Article
Full-text available
The strong Hualien earthquake (Mw 6.1) occurred along the suture zone of the Eurasian Plate and the Philippine Sea Plate, which struck the Hualien city in eastern Taiwan on April 18, 2019. The focal mechanism of this earthquake shows that it is caused by a rupture within a thrust. In the present study, the rupture plane responsible for this earthquake has been modeled using the modified semi-empirical technique (MSET). The whole rupture plane is assumed to be composed of strong motion generation areas (SMGAs) along which the slip occurs with large velocities. The spatiotemporal distribution of aftershocks of this earthquake within identified rupture plane suggests that there are two SMGAs within the rupture plane. The source displacement spectra (SDS) obtained from the observed records have been used to compute the source parameters of these two SMGAs. The MSET efficiently simulates strong ground motion (SGM) at the rock site. The shallow subsurface shear wave velocity profile at various stations has been used as an input to SHAKE91 algorithm for converting records at the surface to that at the rock site. The simulated records are compared with the observed records based on root-mean-square error (RMSE) in peak ground acceleration (PGA) of horizontal components. Various parameters of the rupture plane have been selected using an iterative forward modeling scheme. The accelerograms have been simulated for all the stations that lie within an epicentral distance ranging from 5 to 100 km using the final rupture plane parameters. The comparison of observed and synthetic records validates the effectiveness of the simulation technique and suggests that the Hualien earthquake consists of two SMGAs responsible for high-frequency SGM.
... Platform) has been used. A total of 9 broadband ground motion simulation schemes have been reported (Zeng et al., 1994;Motazedian and Atkinson., 2005;Graves and Pitarka., 2010;Mai et al., 2010;Schmides et al., 2010;Morikawa et al., 2011;Song, 2015;Iwaki et al., 2016a;Iwaki et al., 2016b;Pitarka et al., 2017). Three simulation schemes are based on the "Recipe" scheme proposed by Irikura and Miyake. ...
Article
Full-text available
Three destructive earthquakes occurred in Pingwu and Songpan, Sichuan Province, China, between August 16 and 23, 1976. Due to the seismic monitoring capability at that time, the ground motion characteristics of these earthquakes are very vague. Realistc and reliable strong ground motion input plays an important role in seismic building design and urbanscale earthquake damage simulation. This study reproduces the main broadband ground motion characteristics of the 1976 Ms7.2 Songpan earthquake in densely populated areas of Pingwu. The empirical Green’s function method and finite difference method are used to simulate highfrequency and low-frequency ground motion, respectively, and the broadband ground motion is obtained by superposition within the frequency range. In addition, in combination with the “Recipe” source parameter scheme, various uncertainties in the source parameters are considered, including the source mechanism, source depth, asperity parameters, etc. We obtain 36 kinds of broadband ground motion at six typical locations in the Pingwu area. Moreover, we test the rationality of the obtained broadband ground motion by ground motion prediction equations(GMPEs), and the broadband ground motions are consistent with the local ground motion characteristics. The results show broadband ground motions obtained from the scenario earthquake in this paper can meet the destructive capacity of earthquakes of this magnitude. The hybrid method can effectively compensate for the lack of long-period components of the original empirical Green function method. This research also proves that the peak ground acceleration (PGA) of ground motion is mainly contributed by high-frequency ground motion components and that highfrequency and long-period ground motion contributes most to the peak ground velocity (PGV). Concerning the Chinese seismic intensity scale (GB/T 17742-2020) and China Seismic Ground Motion Parameter Zoning Map (GB18306-2015), the basic fortification intensity in the Pingwu area is VIII. In this paper, the seismic intensity of PWN is VI-VII, indicating that the buildings at this location are less likely to be damaged after the earthquake. The seismic intensity of other regions is VII-IX and buildings are more likely to be damaged during the earthquake at these locations. There are many mountains and valleys in the Pingwu area, and the probability of landslides, debris flows, and other disasters after an earthquake is very high, and we should give special attention to the impact of secondary disasters caused by earthquakes. It is necessary to prevent dammed lakes and other disasters caused by landslides and debris flows.
... Ground-motion simulation is a main part of regional disaster crisis management and seismic design of engineering structures, which can effectively reproduce historical seismic records. There are usually several methods for ground-motion simulation: empirical Green's function method (Hartzell 1978;Irikura and Kamae 1994), composite source modeling method (Somerville et al. 1991;Zeng et al. 1994;Yu et al. 1995), and stochastic method (Boore 1983(Boore , 2003(Boore , 2009Beresnev and Atkinson 1997;Motazedian and Atkinson 2005). Based on small earthquake records, the empirical Green's function method can synthesize low-frequency ground motions, but has defects in high-frequency simulation. ...
Article
Full-text available
Accurate simulation of ground motion is an important basis for the seismic design of engineering structures. The stochastic finite-fault method, which takes into account the source, path, and site effects, is comprehensively applied in simulating ground motion. However, the uncertainty in path and site parameters can affect the reliability of the simulation results. Therefore, it is of great significance to accurately determine these parameters. In this study, a parameter calibration process based on historical seismic data was proposed, where the genetic algorithm was adopted and the optimal combination of parameters was obtained through the best fit between the observed and simulated 5%-damped pseudo-spectral acceleration. Based on the 2019 Changning Ms 5.6 earthquake records, the calibrated parameters were obtained. In addition, a model bias analysis was performed and the simulation results were compared with those predicted by the ground motion prediction equations, which verified the effectiveness of the parameter calibration process. Furthermore, the ground motion of Changning Ms 6.0 earthquake was synthesized using the calibrated parameters, and the blind simulation was carried out at Gongxian middle school where ground motion was not recorded. The results show that in the area with complex terrain, the parameters reflecting the geological conditions are obtained through calibration, which forms effective input conditions in the stochastic finite-fault method, so that the ground motion can be well reproduced. Additionally, it also provides a theoretical basis for disaster prevention planning and implementation.
... Based on the magnitude-area scaling relationship, the fault dimensions of each earthquake in the catalogue can be simulated and it is allowed to take place anywhere inside the maximum size fault plane. Various levels of complexities can be invoked at this stage if needed e.g., placing the simulated faults in the catalogue in a volume enclosing the maximum fault to simulate the width of the fault gauge (e.g.,Papageorgiou 1988, Zeng et al. 1994, Halldorsson & Papageorgiou 2012, varying the faults' strike and dip slightly, etc., to simulate some of the observed variability that for simplicity is not considered by the model. Then, for each earthquake fault in the synthetic catalogue, multiple slip distributions can be generated (e.g.,Mai & Beroza 2002), and for each of them different hypocentral locations are proposed (e.g.,Mai et al. 2005). ...
Article
The largest earthquakes in Iceland occur in the South Iceland Seismic Zone (SISZ) and the Tjörnes Fracture Zone in the Northeast. With the latter being primarily offshore, the seismic risk in Iceland is highest in the relatively densely populated SISZ. Past probabilistic seismic hazard assessment (PSHA) efforts in Iceland have however been based on statistical analyses of various historical earthquake catalogues, and limited ground motions models (GMMs), all subject to varying types and degrees of uncertainties. Moreover, they relied on simplistic source descriptions and largely ignore that the unique ‘bookshelf’ strike-slip fault system of the SISZ extends along the plate margins towards the West and over the entire Reykjanes Peninsula Oblique Rift (RPOR) zone. Namely, the bookshelf fault system in Southwest Iceland is twice as long as previously thought and it dominates the strain release of transcurrent plate motion in Southwest Iceland, having potentially important implications for PSHA. In this study therefore, we propose a new 3D finite-fault model of the Southwest Iceland bookshelf transform zone. The model has been calibrated on the basis of first principles to the rate of transcurrent plate motions across the transform zone and constrained by the salient features of the fault system geometry as reported in the literature. We model the systematic spatial variability of the seismogenic potential along the zone by its provisional subdivision into six distinct zones. The fault system model allows both for deterministic and random fault locations, with each realization completely specified in terms of the maximum expected magnitude of each fault, its maximum dimensions, and its long-term slip rate. The variability of the model has been estimated through sensitivity analyses of its key parameters. The total seismic moment rates produced by the fault system model are completely consistent with those reported in the literature. The new model allows the derivation of simple but self-consistent zone-specific Gutenberg-Richter (GR) relationships, and the total long-term seismic activity predicted by the new 3D fault system model effectively explains the historical earthquake catalogue of the SISZ-RPOR transform zone in Southwest Iceland. We are therefore confident that the model can serve as the foundation for future time-independent physics-based PSHA for Southwest Iceland. Moreover, the consistency and versatility of the model allows its application in conventional approaches to PSHA, which has the potential of bridging the gap between physics-based and conventional approaches to PSHA in Southwest Iceland. Such efforts will improve our understanding of the key elements that affect the hazard, thus improving the reliability of hazard estimates, with important practical implications for the optimized assessment of seismic risk.
... The finite-fault kinematic model can be divided into deterministic source model (asperity model), random source model (k 2 model), and Hybrid Source Model (HSM). The deterministic source model (Olson and Aspel, 1982) is chiefly used to define the high slip momentum area on the fault plane, whereas the random slip model (Andrews, 1981;Zeng et al., 1994) is used to describe the irregular complex phenomena in slip distribution. The HSM is the combination of the asperity model at lower wavenumbers and the k 2 model (Herrero and Bernard, 1994) at higher wavenumbers. ...
Article
Full-text available
Based on the finite-fault model, combined with the empirical relationship or semiempirical relationship between the moment magnitude and the global source parameters (GSP) and the local source parameters (LSP), the Hybrid Source Model (HSM) of the Yangbi earthquake has been predicted. Considering the regional seismotectonic, crustal structure, seismicity, and semiempirical relationships, the GSP (fault size, average slip, etc.) used in the simulation are given. The LSP primarily includes two parts, one is the asperity parameters describing the deterministic slip, and the other is the k2 model describing the random slip. LSP is determined based on the empirical or semiempirical relationship, and the average value and standard deviation of the GSP are calculated according to the empirical relationship. To generate a series of source parameters that meet the mean and standard deviation, an improved truncated normal distribution function is used. The pseudospectral acceleration (PSA; damp = 5%) of four stations satisfying different geological conditions and orientations are simulated by the stochastic finite-fault approach. The group with the smallest residual error with the average PSA is selected as the final selected focal parameters using the principle of minimum residual error. Eventually, the reliability of this method is verified by comparing it with the inverted source model, and it can be concluded that this method can quickly predict the source model of a given magnitude.
Preprint
Full-text available
The 4th January 2016 Manipur earthquake (Mw 6.7) occurred along the Indo-Burmese wedge and ruptured towards NW direction causing severe damage to buildings/structures in North-East (NE) Indian region. A plausible earthquake (Mw 8.0) is simulated to estimate the ground motions and associated seismic hazard by means of the waveforms of 2016 Manipur earthquake (Mw 6.7) as an element earthquake considering the source in the subduction boundary of the Indo-Burmese wedge at an intermediate depth. The empirical greens function mechanism (EGFM) is adopted to accomplish the better utilization of the observed ground motions of the recorded earthquake as an element earthquake and to achieve the probable ground motions in order to acquire the appropriate path/site effects in the simulated ground motions. The obtained results demonstrate the impact of the comparable rupture directivity pattern in both element as well as the simulated earthquakes. The Peak Ground Acceleration (PGA) in NE India from element and simulated earthquakes vary from 3 cm/sec ² and 11 cm/sec ² to 103 cm/sec ² and 342 cm/sec ² at epicentral distances of 624 km and 53 km respectively. The high amplitude surface waves due to the interference of seismic waves along with the combined effects of rupture directivity and site amplification showcased the highest PGA value at Shillong (SHL). This site is located on Pre-Cambrian rock and situated at an epicentral distance of 214 km from the source zone, which is lying at an intermediate depth that might have propelled the direct seismic waves of higher intensity at a longer distance compared to other sites. The outcome of the present study highlights the significance of varied ground motion parameters among the observed sites to the extent of bearing the damage potential of strong ground motions. The related analysis also advocates for the simulated PGA variations and associated duration of the earthquake waveforms exposed on different geological formations that have strong bearings on the seismic risk involved with future probable great earthquake in the study region. Moreover, simulated ground motions of expected plausible disastrous earthquakes on numerous geological formations beneath the various sites have significant impacts on designing critical structures/buildings such as schools, hospitals, bridges, dams and nuclear power plants for NE India. Thus, the detailed investigations on ground motion parameters, simulation of ground motion and the influence of different geological/geomorphological conditions on duration, shape and maximum amplitude of ground motion may be supportive for implementing earthquake risk and mitigation plans in order to assess the seismic hazard of the study region.
Article
In this study, new empirical relations are proposed to determine the Fourier amplitude spectrum of acceleration. The FASAs form the white-noise spectrum in the stochastic ground motion simulation methods. So far, various analytical and experimental models have been proposed to determine the FASA. ω⁻² is among the most well-known models are used in the computational programs of ground motion simulation such as SMSIM or EXSIM. In this study, the relationship between the FASA, and the important seismological parameters such as moment magnitude, closest distance from rupture plane, site conditions and faulting mechanism is determined, and appropriate relations are presented. There are limited experimental models of FASA, and present models are mainly analytical. Therefore, the results of this research can be beneficial. To present models, the Iran Plateau earthquake catalog is used, including 2228 acceleration records of 749 earthquakes with magnitudes of 4.5–7.6 and rupture distance up to 200 km.
Chapter
This chapter explores the main types of data used today in seismic rupture imaging. It examines the forward problem, that is, the formulation to predict surface observations for a given seismic source. The chapter deals with the inverse problem, consisting of finding the slip distribution from surface data. It discusses certain implications of slip models on the dynamics of seismic ruptures. The chapter explains the main geophysical data used today to image the seismic rupture. Tsunami data can also bring significant constraints in rupture areas located offshore. The chapter introduces the formulation to relate the earthquake source to surface observations. Since data is affected by measurement errors and our limited knowledge of the Earth structure, the solution to the inverse problem is usually non‐unique. The slip models obtained using the methods present certain generic properties that are actively debated in the literature.
Article
Full-text available
We derived a method to compute the differential seismogram di-rectly in a layered elastic half-space. This method first computes a differential field caused by the velocity change in the layer and then multiplies it with the original elastic wave field. This product acts like a source, and the seismogram caused by this source term is the differential seismogram. The differential waves are propagated directly to the receiver in frequency/wavenumber domain using the generalized reflection and transmission coefficient method. In comparison with the typical finite-difference approach to compute a complete set of differ-ential seismograms at one station in an N-layered earth model, our method not only saves about N/2 folds of computation time but also leads to a more ac-curate solution. Thus, it provides an efficient and direct procedure to compute the differential seismogram for a complete waveform fitting in a layered elastic earth model.
Article
Full-text available
We establish relations between seismic scaling parameters for gen- eral distributions of subevents in a composite (multiple event) model of faulting. The radiation from the main seismic event is presumed to be produced by a multitude of smaller earthquakes (subevents) with a range of source sizes. Under the composite earthquake hypothesis, the seismic moment scaling--the depen- dence of the seismic moment on the event's size--is the same for the large earthquake and all its components. If at lowest frequencies the subevent spectra add coherently, and at higher frequencies (above the corner frequency of the smallest subevent) the spectra add incoherently, then y = 6/2 and a > 1, where y is the high-frequency spectral fall-off, 6 determines the scaling of seismic moment M0 with source size R (such that MoR -~ is constant), and o~ is the frac- tion of the total rupture area occupied by subevents. In each particular case, these relations can be used to verify whether the studied large earthquake is a composite of smaller earthquakes. The goal of this article is to establish relations be- tween seismic scaling parameters for general distribu- tions of subevents in a composite (multiple event) model of faulting (Joyner and Boore, 1986; Boatwright, 1988). The radiation from the main seismic event is presumed to be produced by a multitude of smaller earthquakes (subevents) with a range of source sizes. Under the com- posite earthquake hypothesis, the seismic moment scal- ing-the dependence of the seismic moment on the event's size--is the same for the large earthquake and all its
Article
Full-text available
Seismograms from 52 aftershocks of the 1971 San Fernando earthquake recorded at 25 stations distributed across the San Fernando Valley are examined to identify empirical Green's functions, and characterize the dependence of their waveforms on moment, focal mechanism, source and recording site spatial variations, recording site geology, and recorded frequency band. Recording distances ranged from 3.0 to 33.0 km, hypocentral separations ranged from 0.22 to 28.4 km, and recording site separations ranged from 0.185 to 24.2 km. The recording site geologies are diorite gneiss, marine and nomarine sediments, and alluvium of varying thicknesses. Waveforms of events with moment below about 1.5×1021 dyn cm are independent of the source-time function and are termed empirical Green's functions. Waveforms recorded at a particular station from events located within 1.0 to 3.09 km of each other, depending upon site geology, with very similar focal mechanism solutions are nearly identical for frequencies up to 10 Hz. There is no correlation to waveforms between recording sites at least 1.2 km apart, and waveforms are clearly distinctive for two sites 0.185 km apart. The geologic conditions of the recording site dominate the character of empirical Green's functions. Even for source spatial separations of up to 20.0 km, the empirical Green's functions at a particular site are consistent in frequency content, amplification, and energy distribution. Therefore, it is shown that empirical Green's functions can be used to obtain site response functions. The observations of empirical Green's functions are used as a basis for developing the theory for using empirical Green's functions in deconvolution for source pulses and syntheis of seismograms of larger earthquakes.
Article
Spectra from moderate earthquakes are used to investigate shear-wave attenuation and site response for accelerographs located on rock outcrops in Guerrero, Mexico. The distance dependence of the spectral decay parameter as expressed by κ̄(r) is very weak in the Guerrero region in contrast to that in southern California. This difference may be due to greater shear strength of the top 20km of crust in the Guerrero subduction zone. Near-site attenuation, represented by κ 0(S), is greater in Guerrero compared to the stations in the Anza array of southern California. No obvious correlation with site geology was found. A combination of a deeper weathered layer of crystalline rock and varying subsurface lithology may be responsible for the greater mean values of κ 0(S) in Guerrero. The frequency-dependent site functions show significant amplification and deamplification effects for the hard-rock sites. No direct correlation with local topography is observed to explain these effects. -from Authors
Article
Simultaneous consideration of source, path, and site effects on ground motion during the Michoacan earthquake of 1985 allows us to draw coherent conclusions regarding the roles played for the disaster in Mexico City by the rupture process, the mode of propagation of the waves between the epicentral zone and Mexico City, and the local amplification. We examine two alternative source models associated with different crustal models to explain the characteristics of the vertical displacements recorded in Mexico City. Our preferred model attributes the cause of the enhanced 3 sec motion to the irregularity in the rupture propagation in addition to the effect of the local conditions in Mexico City. -from Authors
Article
The purpose of this study is to develop and test a procedure for simulating acceleration time histories of large subduction earthquakes. The ground motions of the large event are obtained by summing contributions from fault elements to simulate the propagation of rupture over the fault surface. The procedure has been tested against the recorded strong ground motions of the Mw = 8.0 Michoacan, Mexico, and Valparaiso, Chile, earthquakes of 1985. We find that models of heterogeneous slip in these events derived by other investigators from the analysis of teleseismic and near-source velocity seismograms also explain the shorter period motions of the recorded accelerograms. The procedure is applied in a companion paper to estimate strong ground motion characteristics in the Pacific Northwest region of the US from hypothesized Mw = 8 subduction earthquakes on the Cascadia plate interface. -from Authors