Multiple scattering of seismic waves in multilayered structures

Abstract

We study the influence of higher-order multiple scattering in 1-D layered structures on the transmissivity and the reflectivity of normally incident delta-pulse plane waves. With this aim in view we combine the classical formalism of polynomial representations of z-transformed wavefields and methods of the statistical wave-propagation theory. Starting with the transmissivity we obtain an exact representation of the wavefield as well as an approximation which is very close, however generally, more accurate than the familiar O'Doherty-Anstey formula (ODA in the following). This approximation describes the main part of the transmitted signal (primaries) as well as an earlier part of its coda. For stochastic stratifications our analysis shows that whereas the primaries are controlled by the second statistical moments of the reflection-coefficient series, the coda is controlled by its fourth statistical moments. Based on these results we reach the main aim of our study: an approximation of the reflectivity taking into account the multiple scattering. Finally, we show how our results have implications for seismogram inversion.