Spreading of a Pulse Travelling in Random Media

Abstract

This paper investigates the deformation of an acoustic pulse travelling in a slab of random medium when its width is large compared to the size of the random inhomogeneities of the medium. A limit theorem is shown that explains how the shape of the transmitted pulse can be obtained as a result of a deterministic Gaussian convolution of the initial pulse. Since the random fluctuations are not supposed to be small, this gives a new rigorous formulation of the O'Doherty-Anstey result, which is well known in geophysical literature theory.