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quake Engineering
ake Engineering
ake Engineering
ake Engineering
ake Engineering
Resear
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Resear
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Research Center
ch Center
ch Center
ch Center
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PEER Utilities Program
PEER Utilities Program
PEER Utilities Program
PEER Utilities Program
PEER Utilities Program
Report No. 2000/01
Report No. 2000/01
Report No. 2000/01
Report No. 2000/01
Report No. 2000/01
Evaluation of Numerical Procedures for
Simulating Near-Fault Long-Period Ground
Motions Using Zeng Method
Yuehua Zeng
John Anderson
University of Nevada, Reno
A report to the PEER Program of
Applied Earthquake Engineering Research on
Lifeline Systems
The financial support of the sponsor organizations including
the Pacific Gas & Electric Company (PG&E),
the California Energy Commission (CEC), and the
California Department of Transportation (Caltrans) is acknowledged. Final Technical Report on Near Fault Ground Motions

Phase II, Task 5: Near-fault ground motions

Yuehua Zeng and John Anderson
Seismological Lab, University of Nevada - Reno

Introduction

Over the past several years, we have developed theories and methods for modeling synthetic strong ground
motion using a composite source model (Zeng et al., 1994). The method has been successful in generating realistic
strong motion seismograms. The realism is demonstrated by comparing synthetic strong motions with observations
from the recent California earthquakes at Landers, Loma Prieta (Su et al., 1994a,b) and Northridge (Zeng and
Anderson, 1996; Anderson and Yu, 1996; Su et al., 1998), earthquakes in the eastern US (Ni et al., 1999) and
earthquakes in Guerrero, Mexico (Yu, 1994; Johnson, 1999), Turkey (Anderson et al., 1997) and India (Khattri et al,
1994; Zeng et al, 1995). We have also successfully applied the method for earthquake engineering applications to
compute the ground motion of scenario earthquakes. During the process of continuing development, we have
included scattering waves from small scale heterogeneity structure of the earth, site specific ground motion
prediction using weak motion site amplification, and nonlinear soil response using the geotechnical engineering
model.

In this report, we investigate the effect of rupture directivity from large damaging earthquakes. First we
will find the earthquake source models that best describe the ground motion waveform recorded at the strong motion
stations. Then we will use those earthquake source models to simulate near fault ground motion and compared them
with the recorded strong motion seismograms. Finally, we will use the near-fault directivity model of Somerville et
al. (1997) to test the synthetic prediction of the rupture directivity effect from those earthquake ground motions in
term fault normal and fault parallel components.
Method
Composite Source Model

We have developed a composite source model (Zeng et al., 1994) for realistic synthetic strong ground
motion seismograms computation. This method uses synthetic Greens functions, which characterize wave
propagation in a flat-layered medium, convolved with the composite source time functions. The source is a
superposition of circular subevents with constant stress drop. The number of subevents and their radius follows a
power law given by

dN
d(ln R)
=
pR D

where D is the fractal dimension that equals twice the b-value, N is the number of subevents, and p is a constant of
proportionality. The random nature of the heterogeneities on a complex fault is simulated by distributing the
subevents randomly on the fault plane. Rupture propagates from the hypocenter at a constant velocity, and each
subevent initiates the radiation of a displacement pulse of a crack model. The heterogeneous nature of the
composite earthquake faulting is apparently characterized by the maximum subevents size and the subevents stress
drop, which can be constrained by other independent geophysical data.

The synthetic Green's function has been modified to consider the effect of the random lateral heterogeneity
of the earth by adding scattered waves into the Green's function (Zeng, 1995). The solution is then convolved with a
plane wave propagation function through a near surface 1-D velocity layering as complex as that suggested by sonic
well logs. Thus the complex high-frequency waveform of our simulation is generated from a combination of a
heterogeneous source (Figure 1), wave reverberation in a stratified crustal structure (Figure 2) and scattering from
lateral inhomogeneity of the earth (Figure 3). Earthquake source Imaging Using Genetic Algorithm

Zeng and Anderson (1996) used a Genetic Algorithm to find a specific composite source model that best fit
the observed waveform data for the Northridge earthquake. The Ge netic Algorithm works by mimicking the process
of natural selection principle of survival of the fittest. By analogy with the natural behavior, it starts with an initial
"population" of "individuals" (e.g., models of the subevent locations), each representing a possible solution. A
fitness score is assigned to each individual. Individuals with higher fitness are given better opportunities to
"crossbreed" with others in the population to produce "offspring" that form a new population the same size as the
original. The algorithm iterates by taking those offspring as a new generation and repeats the process until a
satisfactory solution is obtained.

The fitness function in our waveform inversion is defined as








=
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components
and
stations
s
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)
,
max(
)
,
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max

where
i
m
is the i</i>th individual;
o
l
u
is the observed seismogram;
s
l
u
is the corresponding synthetic seismogram; and
o
u
max
and
o
u
max
are the corresponding peak values of the observed and synthetic seismograms, respectively. The
representation in the parentheses gives the cross-correlation coefficient of the synthetic with the data. The weights
given to the correlation coefficients penalize seismograms with similar waveforms but different amplitudes. Each
individual is assigned a fitness value based on the above equation.

Next, we pick two individuals as "parents" for a reproduction event using the so-called roulette wheel
selection scheme. The two parents are used to generate two offspring by recombining their "chromosomes" using
the mechanisms of cross-over and mutation. The chromosomes in our case are the subevent locations on the rupture
plane. The subevents of both models are divided randomly into 10 groups exactly, and their positions are copied
into their offspring according to a randomly generated "cross-over mask." Mutation is applied to each offspring
individually after cross-over. It is done by randomly altering the location of each subevent with a probability of
0.01.
Modified Source Radiation

Motivated by the fact that we do not observe any distinct radiation pattern and wave polarization at high
frequency, we introduced an effective high frequency source radiation term. This source radiation consists of
energy contributions from an angular cross section centered at the direction from the source to receiver in order to
simulate high frequency wave reflection and scattering at the fault zone. The total source radiation then equals *effective-source-radiation + (1-

)*double-couple-source-radiation,
where is a continuo function of frequency. It equals 1 above a high frequency threshold and tapers to 0 at low
frequency since this reflection and scattering at the source zone has less an effect at lower frequencies (Figure 4).
The results were validated with the Northridge strong motion observations. We have compared the results with the
observed and regression prediction (Abrahamson and Silva, 1997) of the PGA and SA at 3 second. The synthetic
simulations clearly predict the trends of the observed ground motion parameters better than the regression. The
scatter in the data is presumably caused by local site and basin response effects.
Data and Analysis

We selected several important earthquakes for the validation study of the composite source model. These
events are selected through PEER and PG&E project coordination meeting. A list of those events is given in Table
1.
Table 1. Earthquakes used for the model validation
Event year
Event name
Epicenter
Latitude
Epicenter
Longitude
Hypocenter
Depth 1979
Imperial Valley earthquake, CA
32.6435
115.3088
8.0
1989
Loma Prieta earthquake, CA
37.0407
121.8829
17.6
1992
Landers earthquake, CA
34.2000
116.4300
7.0
1994
Northridge earthquake, CA
34.215
118.538
17.5
1995
Kobe earthquake, Japan
34.5948
135.0121
16.9
Near field strong motion seismograms from those events within about 40 km of the fault planes were
selected. Table 2a, 2b, 2c, 2d and 2e list the station names, locations for the strong motion data analysis of the 5
earthquakes listed in Table 1, respectively. The total number of strong motion stations selected for Imperial Valley,
Loma Prieta, Landers, Northridge, and Kobe earthquakes are 28, 34, 13, 33 and 15, respectively.
Table 2a
Station names and locations for the Imperial Valley earthquake
Name Latitude Longitude Description
.

AEPI 32.6510 -115.3320 Aeropuerto Mexicali
AGRI 32.6210 -115.3010 Agrarias
BCRI 32.6930 -115.3380 Bonds Corne