Finite-Difference Simulations of Time Reversed Acoustics in a Layered Earth Model

Abstract

Traditionally an earthquake is located by using the arrival times of P and S phases. This uses only a limited portion of the information on a seismogram. A large part of the information carried by the waveform is not used. In this study we investigate the applicability of the Time Reversed Acoustics (TRA) technique, and thus the whole waveform of the recorded signal, for earthquake locations and source characterization. The basic concept involved in TRA is the fundamental symmetry of time reversal invariance. Injecting the recorded signal, with time running backwards, reconstructs the whole wave field within the medium and can focus the wave field to the source. TRA has emerged as an important technique in acoustics with applications to medicine, underwater sound, and many other disciplines. The objective of this paper is to demonstrate the feasibility of applying TRA to seismological data by means of simulating the relevant features using a finite-difference approach. The following subjects are investigated: (1) Locating the earthquake hypocenter; (2) finding the source space-time function; and (3) characterizing the direction of fault rupture during an earthquake. The results show that the TRA technique can focus back to the source reasonably well in a layered earth model and can recover the source time function. The results also show that TRA has a good tolerance to noise. For efficient applications, calculation time can be reduced by generating a medium response library. The source location and source time function can then be determined by convolving the medium response library with the time-reversed signals recorded at the seismic stations.