Seismic Waves in a Laterally Inhomogeneous Layered Medium, Part I: Theory

[+] Author and Article Information
Ruichong Zhang

Department of Civil Engineering, University of Southern California, University Park, Los Angeles, 90089-2531

Liyang Zhang

Weidlinger Associates, Inc., New York, NY 10001

Masanobu Shinozuka

Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089-2531

J. Appl. Mech 64(1), 50-58 (Mar 01, 1997) (9 pages) doi:10.1115/1.2787293 History: Received June 27, 1995; Revised October 11, 1996; Online October 25, 2007


Seismic waves in a layered half-space with lateral inhomogeneities, generated by a buried seismic dislocation source, are investigated in these two consecutive papers. In the first paper, the problem is formulated and a corresponding approach to solve the problem is provided. Specifically, the elastic parameters in the laterally inhomogeneous layer, such as P and S wave speeds and density, are separated by the mean and the deviation parts. The mean part is constant while the deviation part, which is much smaller compared to the mean part, is a function of lateral coordinates. Using the first-order perturbation approach, it is shown that the total wave field may be obtained as a superposition of the mean wave field and the scattered wave field. The mean wave field is obtainable as a response solution for a perfectly layered half-space (without lateral inhomogeneities) subjected to a buried seismic dislocation source. The scattered wave field is obtained as a response solution for the same layered half-space as used in the mean wave field, but is subjected to the equivalent fictitious distributed body forces that mathematically replace the lateral inhomogeneities. These fictitious body forces have the same effects as the existence of lateral inhomogeneities and can be evaluated as a function of the inhomogeneity parameters and the mean wave fleld. The explicit expressions for the responses in both the mean and the scattered wave fields are derived with the aid of the integral transform approach and wave propagation analysis.

Copyright © 1997 by The American Society of Mechanical Engineers
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