Three-Dimensional Ray Tracing and Geophysical Inversion in Layered Media

Abstract

In this paper the problem of finding seismic rays in a three-dimensional layered medium is examined. The "layers" are separated by arbitrary smooth interfaces that can vary in three dimensions. The endpoints of each ray and the sequence of interfaces it encounters are specified. The problem is formulated as a nonlinear system of equations and efficient, accurate methods of solution are discussed. An important application of ray tracing methods, which is discussed, is the nonlinear least squares estimation of medium parameters from observed travel times. In addition the "type" of each ray is also determined by the least squares process—this is in effect a deconvolution procedure similar to that desired in seismic exploration. It enables more of the measured data to be used without filtering out the multiple reflections that are not pure P-waves.

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