Source-dependent variations of M7 earthquakes in the Los Angeles Basin

Deterministic earthquake scenario simulations are playing an
increasingly important role in seismic hazard and risk estimation.
The numerical calculation of the complete 3D wavefield in the
observed frequency band for a seismically active basin remains a
computationally expensive task. This expense restricts
seismologists either to calculating source models with homogeneous
media (e.g., Gallovic and Brokesoová, 2004, 2007a,b), or to
calculating single source scenario in 3D media (e.g., Olsen and
Archuleta, 1996; Olsen, 2000; Ewald et al., 2006) while the complex
effects of the media and the source on the ground motion are
getting more and more attention. At the same time, with the
development of the instrument, ground rotation introduced by an
earthquake becomes a more and more important topic. Our aim is to
provide a tool with which we can calculate a large number of
different finite-source scenarios for a particular fault or fault
system located in a 3D structure which will enable us to estimate
ground motion (translation and rotation) variations due to source
and 3D structure. In order to avoid having to run numerical
expensive 3D code for each kinematic source scenario we propose the
concept of “numerical Green’s functions” (NGF): a large seismic
fault is divided into sub-faults of appropriate size for which
synthetic Green’s functions at the surface of the seismically
active area are calculated and stored. Consequently, ground motions
from arbitrary kinematic sources can be simulated for the whole
fault or parts of it by superposition. To demonstrate the
functionalities of the method a strike-slip NGF data base was
calculated for a simplified vertical model of the Newport-Inglewood
fault in the Los Angeles basin. As a first example, we use the data
base to estimate variations of surface ground motion (e.g., peak
ground velocity (PGV)) due to hypocentre location for a given final
slip distribution. The results show a complex behavior, with
dependence of absolute PGV and its variation on asperity location,
directivity effect and local under-surface structure. Hypocentral
depth may affect peak ground velocity in a positive or negative way
depending on the distance from the fault and the receiver location
with respect to basin structure. Finite-fault source inversions
reveal the spatial complexity of earthquake slip over the fault
plane. In this study, several possible earthquake scenarios of Mw
7.0 are simulated with different quasi-dynamic finite source models
for the Newport-Inglewood fault in the Los Angeles basin. We
investigate the effects of the various slip histories on peak
ground velocities and the related variations in ground motion
prediction for our study area. The results confirm that the fault
perpendicular components of motion are dominated by directivity
effects while the fault parallel component is influenced both by
the slip distribution and the basin structure. There are
theoretical considerations suggesting that
observations/calculations of the rotation part of
earthquake-induced ground motions may provide additional
information for earthquake risk hazard analysis after reports on
rotational effects on structures (like twisting of tombstones or
statues). For the first time, we carry out a systematic study of
earthquake scenario simulations in 3D media with a specific focus
on the rotational part of the motions. We simulate several M7
earthquakes with various hypocentre locations and slip histories on
the Newport-Inglewood fault embedded in the 3D Los Angeles Basin.
We investigate source and basin structure effects on the rotational
components of ground motion (e.g., peak ground rotation rates and
their variation, horizontal gradients) and compare with the effects
on translations. Igel et al. (2005) shows a similarity of the
observed waveforms between transverse acceleration and the vertical
rotation rate in the teleseismic range benefiting from the recently
developed ring laser instruments. The vertical rotation rate is
found to be surprisingly similar to the horizontal translations in
waveform which is explained with the plane wave propagation in the
global range. That condition could not be hold any more in the
near-field range, but some information could be extracted from the
comparison between the translations and the rotation rate. As a
final application, we investigate the source-dependent variations
on rotational ground motions and compare with the results for
translations. The thesis is structured as follows: Chapter 1: An
insight into the present standard procedures carried out in the
Seismic Hazard Assessment (SHA) is shown and then the different
methodologies for predicting ground motions are described and
compared, which are working individually or cooperate with each
other. In recent years, one of those methods – deterministic
calculations have been used widely and its consumption both in
terms of CPU time and memory motivated the development of one new
tool. We name that tool Numerical Green’s Function (NGF) method.
Chapter 2: An introduction to the different solutions of the wave
propagation is given and the state-of-the-art technologies are
described. We will introduce in detail the techniques adopted. We
show how to implement the source, how to solve the wave propagation
problem, and how to efficiently absorb the energies outgoing from
the working area, or reflect them at the free surface boundary. To
correctly account for the rupture process, which has been found to
be the most important contributor to the ground motion in the
near-source region, different tools are developed which can be
divided into two groups: kinematic description and dynamic
description of the source. These two descriptions are briefly
compared. Then we focus on the “quasi-dynamic” method developed by
Guatteri et al. (2004) which combines, to some extent, the two
different approaches. This method is used to provide us the rupture
processes we will consider. Chapter 3: Green’s function stands for
the response on the surface due to an impulse dislocation at the
source. A large earthquake rupture can be represented with a group
of impulse dislocations, and thus the ground motion on the surface
can be achieved by the superposition of its Green’s functions. In
this chapter, we follow the representation theorem published in Aki
and Richards (2002) to give the theoretical basis of that method
and briefly describe the two groups of that method: composite
method and integral method. Finally we introduce our new method –
Numerical Green’s Function, present the basic equations and analyze
its relationship with the representation theorem and empirical
Green’s function method. Chapter 4: Discretization of the fault
plane into elements and assumption the source parameters identical
inside each element will introduce errors in the calculated seismic
motions and these errors are expected to depend on some few
parameters such as the fault geometry, the rupture velocity, the
sub-fault size, the cut-off frequency for low-pass filtering the
ground motions, the directivity effect, etc.. In this chapter we
design a hypothetic velocity structure and investigate how the
errors introduced by the fault discretization will change with
those parameters. The results are considered to provide some clues
for our next step – selecting a seismic active fault and
discretizing it into pieces with optimal sizes for which the
Green’s functions will be calculated and stored. Chapter 5: The
working area of this study, the Newport Inglewood fault embedded in
the Los Angeles basin is introduced. The Los Angeles basin is
chosen as our working area because of the high seismicity and that
the most reliable information about the subsurface structure could
be achieved. One active fault, the Newport-Inglewood fault inside
this region is considered as a possible place where an M7.4
earthquake could happen in the future decades. Also its near
vertical straight fault plane facilitates the implementation of
this fault into the finite difference method. After choosing the
fault and velocity structure, we re-address the optimal size of
sub-fault by simulating a few M7 earthquakes and investigate the
peak ground velocity and the waveform difference introduced by the
different discretizations. The importance of the directivity effect
on the ground motion in the near-source region has been recognized
and is one of the main targets of the next generation of the
attenuation relationship. A brief introduction to the physics of
wave propagation is given in order to make the following
discussions and illustrations of our results understandable for
readers without previous knowledge. We analyze the different
directivity effect supposed to happen between different component,
or different kinds of motion (translation and rotation). Chapter 6:
This chapter addresses the problem of the variations of surface
ground motion (e.g., peak ground velocity) due to hypocentre
location for a given final slip distribution. A complex behavior
about the dependence of absolute PGV and its variation on asperity
location, directivity effect and local structure is presented.
Hypocentral depth may affect PGV in a positive or negative way
depending on the distance from the fault and the location with
respect to the basin structure. The directivity effect is found to
control the seismic motion generation for a specific final slip
distribution. Chapter 7: Inversions of the spatial and temporal
evolution of earthquake slip on fault planes provide compelling
evidence that fault displacement is spatially variable at all
resolvable scales. Investigations of strong ground motion also
indicate the spatial variability of the rupture velocity. This
source physics complexity appeals for thorough description of the
source process when calculating seismic motion. The method
developed before hand allows efficient simulation of arbitrary slip
histories. In this chapter, we investigate how the various slip
histories affect peak ground velocities and the related variations
in ground motion prediction for our study area. The fault
perpendicular components of motion are confirmed to be dominated by
directivity effects while the fault parallel component is
influenced both by the slip distribution and the basin structure.
Chapter 8: The rotational motions excited by earthquakes are
believed to be capable of providing more information for the aim of
earthquake hazard analysis. But to the present time, those
information are hard to be acquired. The first reason is that the
spacing of the accelerograph recording sites is too large to get
the indirect rotational motion measurement from the accelerograph
recordings. The second reason is that the small amplitude of the
rotational motion is beyond the recording capability of the present
instruments. At the present time, the answers lie in the numerical
simulation. In this section, for an M7.0 earthquake which is
considered to happen on the Newport-Inglewood fault embedded in the
Los Angeles basin, different parameters responsible for the ground
rotation variation, like the hypocentre location, directivity
effect and slip history, are systematically investigated. In the
teleseismic range where plane wave assumption can be made, Igel et
al. (2005) investigates the relationship between the translation
and the rotation in terms of the amplitude ratio and waveform
similarity. In this section, we find the waveform similarity
between one horizontal acceleration and the vertical rotation rate
even in the near-source region. We also calculate the amplitude
ratio between the acceleration and the rotation rate and compare
the results with the medium properties. That ratio is found to be
somehow correlative to the basin depth. Chapter 9: The most
important results in this work are briefly summarized. Future
promising prospectives are also described. Appendix A: The
individual peak ground velocity distributions corresponding to the
varying hypocentres of the grid presented in chapter 6 are
presented as a table for better illustration in case of interest.
Three components of velocity and rotation rates are summarized
here. Appendix B: The peak ground velocity distributions are
grouped into different tables corresponding to the varying slip
histories (chapter 7). Three components of velocity and rotation
rate are summarized here.