Single Scattering Theory Versus Numerical Modelling In 2‐D Random Media: Single scattering theory versus numerical modelling

Abstract

The scattering of acoustic waves in random media is investigated numerically by a finite difference method and is compared with the predictions of single scattering theory. the random media are characterized by autocorrelation functions which allow the construction of spatially anisotropic random structures with different correlation lengths a and b perpendicular and parallel to the propagation direction. If a equals b, the attenuation of the transmitted wave can be successfully explained by single scattering theory. the attenuation maximum occurs at kb≈ 1‐2, where k is the wavenumber. For media with a > b we observe a stronger attenuation than expected from single scattering theory for kb greater than 6. the attenuation peak is shifted to smaller kb values when the spatial anisotropy of the random fluctuations is increased. the investigation of the seismic coda shows that the single scattering theory cannot explain the time dependence of the coda. Coda Q, as determined from the coda decay rate under the single scattering assumption, does not describe the scattering attenuation. In 1‐D random media the decay rate of the coda observed in transmission decreases with increasing standard deviation of the impedance fluctuations. In the 2‐D case the decay rate increases slightly with the standard deviation. Copyright © 1993, Wiley Blackwell. All rights reserved