The pseudo‐primary field due to a point‐source in a finely layered medium

Abstract

Using the theory of wave propagation in a finely layered medium which grew out of the work of O'Doherty and Anstey we calculate synthetic VSP traces and the slant stack of the transmitted waves. The present work may be regarded as an application of the method described by Burridge, White & Papanicolaou (1988), Burridge & Chang (1989), and De Hoop, Burridge & Chang (1990). The anisotropy (transverse isotropy) due to the fine layering is apparent in the pulse arrival times and the shear wave splitting. It can be shown that the arrival times agree with the effective medium theory of Schoenberg & Muir (1989). However, that effective medium theory does not predict the observed pulse broadening. Our results can be obtained by combining ray theoretic amplitudes in the average medium with a changing pulse shape evolving according to a certain integro‐differential equation governed by the medium statistics. Copyright © 1991, Wiley Blackwell. All rights reserved