Earth Resources Laboratory :: Abstracts

Seismic Wave Scattering From Rough Interfaces

Michael D. Prange

Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on September 1, 1989 in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Abstract

In this thesis I present a perturbation method which can model three-dimensional scattering from an arbitrary elastic-elastic rough interface with great computational efficiency. Using this method, I examine the changes introduced into the scattered wavefield by the presence of interface roughness. 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 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. Error is acceptable for RMS height deviations of less than about 20 percent and RMS slopes of less than about 0.25. A three-dimensional scattering kernel is introduced which represents the scattered field response to a delta function interface height function. This must be convolved with an interface height function in order to produce a scattering coefficient, but by itself illustrates the general scattering behavior of an interface contrast and source configuration independent of any particular interface roughness function. These scattering kernels show that waves are maximally scattered in directions for which the scattered wave particle motion coincides with that of the incident wave. Scattering kernels also show that the critical angles in rough interface scattering, i.e., those angles at which amplitude maxima or minima appear, correspond to the critical angles of the mean planar interface problem with one qualification: since the spectrum of the interface height function modulates the scattering kernel, an interface whose spectrum does not contain energy at the critical angles will not have these maxima or minima in its scattering coefficient. By assuming material contrasts across the interface are small, further approximations can be made, yielding simple equations for the scattering coefficients which separate the influence of contrasts in P and S velocities and density on the scattered wavefield. Form these forms it is seen that the scattered field wavelet is the time derivative of the source field wavelet. Scattering coefficients and seismograms for normally incident waves illustrate the relative contributions of the separate material contrasts on the scattered wavefield. Scattering coefficients for obliquely incident waves show that the scattered wave amplitudes, excluding the background specular field, are not necessarily maximum in the direction of specular scattering. Finally, I present seismic data from a vertical seismic profile experiment which contains evidence of rough interface scattering. By generating scattering coefficients and seismograms for several rough interface models, I explore the particular scattering mechanism at work at this site.