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.