Enhanced backscattering of seismic waves from a highly irregular, random interface: P‐SV case

Abstract

We examine the scattering of P and SV waves incident on a highly irregular 2‐D interface separating two semi‐infinite elastic spaces to determine whether the enhanced backscattering, already identified for optical waves and SH waves, occurs. The Somigliana identity is used to derive exact integral expressions for the scattered displacement produced when an incident wave having Gaussian spatial distribution encounters a randomly irregular surface. These coupled integral equations are then solved using a discretization scheme where both slope and curvature of the interface are incorporated. The final set of linear equations, expressed in full analytical form, are then inverted to give the reflection coefficient from a given irregular interface. Using a statistical approach, we elucidate the average reflection coefficients for various irregular interfaces in the Earth's crust and mantle. This is accomplished by varying the height and length of the irregularities with respect to the incident wavelength and varying the incident angle and impedance contrast at the interface. This analysis shows that a well‐defined ‘retroreflective’ peak occurs for interfaces with steep slope and large impedance contrasts. This enhanced backscattering is observed only for P‐to‐P and SV‐to‐SV reflections, strongly supporting the idea that multiple scattering and time‐reversed paths are responsible for enhanced backscattering. Enhanced backscattering may be valuable in prospecting, as large‐amplitude waves can be scattered directly back at the source complicating interpretations based on small amounts of reflection data. In addition, we show that an irregular Mohorovičič discontinuity can destroy a specular reflection and create a large conversion of most incident waves into incoherent wide‐angle and post‐critical energy. This may partially explain the complexities of P coda observed in the continental crust. Copyright © 1994, Wiley Blackwell. All rights reserved