Scattering and diffraction by a single crack: an accuracy analysis of the rotated staggered grid

Abstract

SUMMARY Scattering and diffraction of elastic waves by many cracks or inclusions have a significant influence on the waves behaviour (e.g. velocity, attenuation). As a result of the lack of an analytical solution for scattering caused by complex crack structures, numerical methods have to be used to compute the wave field. The numerical error of such methods has to be controlled. In this paper, we present an accuracy analysis of the rotated staggered grid (RSG)—finite difference (FD) scheme. It is designed, amongst other things, to model wave propagation in multiple cracked rocks with high contrasts in their elastic moduli without implementing explicit boundary conditions and without averaging elastic moduli (e.g. at free surfaces like crack boundaries). The problem of a plane SH wave scattered by a single finite crack has a known analytical solution. This solution provides a chance to validate the special abilities of the RSG–FD scheme. The calculation precision is examined by comparing numerical and analytical results. We observe a very good agreement for the single finite crack. Because the RSG is not restricted to the single crack case only, we conclude that this approach is an accurate tool to study wave propagation in media with many cracks.