Wave-Theoretical Properties of Cracked Media

Abstract

A large amount of cracks exist in the Earth's crust, especially in fault zones with high distribution densities. They can scatter seismic waves and influence their propagation. This paper reviews theoretical studies on elastic wave propagation in such cracked media. The focus is on the effects of crack scattering on coherent, or mean, waves. Inside regions with randomly distributed cracks, the scattering causes attenuation and dispersion of passing waves in a stochastic sense. For dilute distributions, they are analytically and approximately evaluated based on a traditional theory of multiple scattering. The theory cannot, however, treat scattering of higher than second order in practice. The effects of higher order scattering, that will be obvious for denser distributions, can be taken into account by numerical approaches. When the distributions of cracks are restricted on planes or within zones, reflection and transmission of waves occur. They are also evaluated using analytical as well as numerical approaches, in a stochastic and approximate sense except when the distributions are perfectly periodic. In the long-wavelength limit, the cracked media behave effectively as homogenous and, in general, anisotropic ones.