Peak surface motion due to scattering of a plane harmonic SH wave by a randomly corrugated scatterer

Abstract

Scattering of a plane harmonic elastic SH wave by a rough elastic inclusion embedded within an elastic half space is investigated for an anti-plane strain model by using a direct boundary integral equation method. The scatterer’s interface is assumed to be of an elliptical shape perturbed in a random fashion. The perturbations are assumed to have either uniform or normal probability distributions. The peak perturbation amplitude is assumed to be arbitrary. Surface displacement spectral amplitude is evaluated for different scatterers, impedance contrasts, angles of incidence, and range of frequencies. Corresponding contour plots are used to identify the frequencies of the peak surface spectral amplitudes for each model. The results clearly demonstrate that the presence of small roughness in the inclusion’s interface may change significantly the peak surface motion frequencies. These changes depend upon the inclusion geometry, the nature of the interface roughness, and the impedance contrast of the materials. For certain frequencies, the presence of the inclusion roughness is important for the surface response and modeling may require detailed description of the corrugated inclusion. Lack of such analysis may result in considerable error in the surface motion amplification estimates.