Plane Wave Method for Elastic Wave Scattering by a Heterogeneous Fracture

摘要

A plane-wave method for computing the three-dimensional scattering of propagating elastic waves by a planar facture with heterogeneous fracture compliance distribution is presented. This method is based upon the spatial Fourier transform of the seismic displacement-discontinuity (SDD) boundary conditions (also called linear slip interface conditions), and therefore, called the wavenumber-domain SDD method (wd-SDD method). The resulting boundary conditions explicitly show the coupling between plane waves with an incident wavenumber component (specular component) and scattered waves that do not follow the Snell's law (non-specular components) if the fracture is viewed as a planar boundary. For a spatially periodic fracture compliance distribution, these boundary conditions can be cast into a linear system of equations that can be solved for the amplitudes of individual wave modes and wavenumbers. We demonstrate the developed technique for a simulated fracture with a stochastic (correlated) surface compliance distribution. Low and high-frequency solutions of the method are also compared to the predictions by low-order Born series in the weak and strong scattering limit.