Numerical study of the diffraction of elastic waves by fluid‐filled cracks

The diffraction of P ‐ SV waves by one or several fluid‐filled cracks is simulated numerically. The method used is based on the integral representation of the diffracted field. We establish the integral representation for fluid‐filled cavities embedded in elastic media, and we compute the boundary integral equation by discretizing the diffracting surface and by evaluating Green's functions by the discrete wave number method. We compare the effects of the diffraction by a single crack versus a fracture system consisting of several shorter cracks, for low and high frequencies, with and without the single scattering (Born) approximation. At low frequencies the cracks interact individually; the energy diffracted is weak compared with the incident energy and exhibits a large dependence with respect to the crack length. For higher frequencies, interactions between cracks are predominant; the single crack and multiple cracks present similar radiation and amplitude patterns for diffracted waves. The effects are close to the ray theory results if the first Fresnel zone is of the same order as the crack extension.