Perturbation approximation of 3‐D seismic scattering

Abstract

A method is presented for computing 3‐D seismic wave scattering from a rough interface. The matrix method used is appropriate for direct implementation in existing propagator matrix‐based seismogram synthesis programs. It is derived using a perturbation approach which requires interface height perturbations to be small relative to the wavelengths of scattered waves, and interface slope perturbations to be much less than unity. These validity conditions are based on an order‐of‐error analysis of the truncation of the perturbation series. These conditions are numerically investigated by comparison of frequency‐wavenumber‐domain and time domain perturbation results with those generated by a second‐order finite difference method for several rough interface models with Gaussian autocorrelation functions. In the ω‐k domain comparisons, the perturbation method is accurate for rms interface height deviations of less than about 10 per cent of the smallest wavelength in the scattered field. This result is independent of rms interface slope in the tested range of 0.037‐0.99. Comparisons of seismograms generated by the two methods show that error does increase with increasing rms slope, but at half the rate of error growth with increasing height. Time‐domain error is acceptable for rms height deviations of less than about 20 per cent and rms slopes of less than about 0.25. A 3‐D scattering kernel is defined which facilitates analysis of 2‐ and 3‐D scattered field results. Copyright © 1990, Wiley Blackwell. All rights reserved