Multiple scattering by topographic relief with application to the core-mantle boundary

Some striking features on seismic sections and on earthquake seismograms are thought to be caused by scattering by topographic relief of the Earth's surface and internal discontinuities. In the past, first-order approximations have been applied to try and quantify the topographic features, even in circumstances where multiple scattering might be significant. The present method is also an approximation since a perturbation series is used to evaluate generalized reflection and transmission coefficients representing the scattered field, but multiple scattering is included and there are no restrictions on surface topography other than those implied by the condition of convergence of the series solution. The solution is obtained by recursion and is therefore relatively easy to calculate and interpret. Scattering coefficients and the energy flux are given for a solid-solid interface, a free surface and a solid-liquid interface. The method makes possible a comparison with previous single-scattering results. Examples of scattering by a rough core-mantle boundary are included. The examples demonstrate that multiple scattering tends to widen the wave-number spectrum of the scattered field. Higher-order terms are also needed to obtain the correct phase shift of scattered waves. The numerical results are consistent with an energy conversion theorem stating that the diffuse part of the scattered flux equals the drop of the specular part. The results do not necessitate a reinterpretation of available scattering data. © 1988 RAS.