OPTIMAL WAVE FOCUSING FOR SEISMIC SOURCE IMAGING
Abstract
In both global and exploration seismology, studying seismic sources provides geophysicists
with invaluable insight into the physics of earthquakes and faulting processes. One way to
characterize the seismic source is to directly image it. Time-reversal (TR) focusing provides
a simple and robust solution to the source imaging problem. However, for recovering a well-
resolved image, TR requires a full-aperture receiver array that surrounds the source and
adequately samples the wavefield. This requirement often cannot be realized in practice. In
most source imaging experiments, the receiver geometry, due to the limited aperture and
sparsity of the stations, does not allow adequate sampling of the source wavefield. Incomplete
acquisition and imbalanced illumination of the imaging target limit the resolving power of
the TR process. The main focus of this thesis is to offer an alternative approach to source
imaging with the goal of mitigating the adverse effects of incomplete acquisition on the
TR modeling. To this end, I propose a new method, named Backus-Gilbert (BG) source
imaging, to optimally focus the wavefield onto the source position using a given receiver
geometry. I first introduce BG as a method for focusing waves in acoustic media at a desired
location and time. Then, by exploiting the source-receiver reciprocity of the Green function
and the linearity of the problem, I show that BG focusing can be adapted and used as a
source-imaging tool. Following this, I generalize the BG theory for elastic waves. Applying
BG formalism for source imaging requires a model for the wave propagation properties of
the earth and an estimate of the source location. Using numerical tests, I next examine the
robustness and sensitivity of the proposed method with respect to errors in the earth model,
uncertainty in the source location, and noise in data. The BG method can image extended
sources as well as point sources. It can also retrieve the source mechanism. These features of
the BG method can benefit the data-fitting algorithm that is introduced in the last part of
this thesis and is used for modeling the geometry of the subducting slab in South America.
The input to the proposed data-fitting algorithm are the depth and strike samples inferred
from the location and focal mechanism of the subduction-related earthquakes in the South
American subduction zone.