Wave propagation in stochastic fractals

Abstract

Wave propagation in random media has become a subject of increasing interest for a wide range of different research areas. The reason for this is that most insonified media clearly reveal a highly irregular behavior that can be quantified. A stochastic fractal yields a random process that displays a behavior similar to observations from, e.g., well-log and seafloor topology measurements. Considerations of wave propagation in random media indicate that the leading behavior of the coherent part of the wave field (the signature) is predominantly determined by the spatial autocovariance function of the medium. Dispersion is always present and the question is how to account for this in a global way, i.e., without local information. For the 1-D situation it can be shown that the signature gradually converges to a limiting solution that is determined by the stochasticexpectation of the power spectrum of the medium contrasts. The required globaleffective medium representation can be found after combination of the wave propagation operator with the stochastic fractals. In this way information on the complexity of the medium can be transferred to the description of wave propagation and vica versa. During the presentation the theory will be illustrated by examples.