ELASTIC-WAVES SCATTERING AND RADIATION BY FRACTAL INHOMOGENEITY OF A MEDIUM

I obtain the Born approximation for the scattered intensity I, the differential cross-sections sigma(d), and the total scattering cross-sections sigma of elastic wavefields scattered by a mass fractal, an object with a fractal surface and a fragment of a turbulent medium. The results for I and sigma(d) are valid for an arbitrary anisotropic random discrete or continuous inhomogeneity and they are in agreement with the well known results for discrete inclusions (Gubernatis, Domany & Krumhansl 1977b). For fractal inhomogeneities I show that: (1) for small angle scattering I is-proportional-to omega-4+omega(sin theta/2)nu, where theta is a scattering angle and the constant nu depends linearly on the fractal dimension; (2) sigma(d) is-proportional-to omega-4+omega; (3) sigma is-proportional-to omega-4+nu if nu > -2 and sigma is-proportional-to omega-2 if nu < -2; and (4) the Fourier transform of the correlation function of the wavefield-GAMMA, which is coherently radiated by white noise point sources distributed on fractal objects obeys \GAMMA\ is-proportional-to omega(nu). Applying the results for sigma(d) I show that the model of inhomogeneities with a fractal surface is in agreement with the fractal dimensions of some fault systems.