Enhanced Backscattering of Seismic Waves From A Highly Irregular, Random Interface: Sh Case

In this paper we study the scattering of SH waves from a highly irregular random interface between two elastic half-spaces to determine whether the ‘enhanced backscattering’ observed in optics can also occur for seismic waves. We approach this problem by combining the elastic representation theorem with the extinction theorem to develop a surface integral representation of the total scattered displacement. the scattered displacement is then expressed quantitatively in terms of a differential reflection coefficient (DRC). Statistically, the incoherent and coherent contributions to a mean DRC are calculated by averaging over many realizations of randomly irregular surfaces. We find that the incoherent field forms the major contribution to the total mean DRC, clearly showing an ‘enhanced backscattered’ or ‘retro-reflective’ peak which results directly from multiple scattering. the character of the peak varies strongly as a function of impedance contrast, incident angle, and rms slope of the interface. In each case, the peak height decreases dramatically with the decrease in impedance contrast and with the increase in incident angle. In addition, the longer the wavelength of the incident wave relative to the correlation length of the interface, the wider the retro-reflective peak. Overall, this study provides a more intuitive yet quantitative understanding of multiple scattering both as a function of frequency and interface properties.