Frequency Content of Randomly Scattered Signals

The statistical properties of acoustic signals re ected by a randomly layered medium are analyzed when a pulsed spherical wave issuing from a point source is incident upon it. The asymptotic analysis of stochastic equations and geometrical acoustics is used to arrive at a set of transport equations that characterize multiply scattered signals observed at the surface of the layered medium. The results of extensive numerical simulations are presented, illustrating the scope of the theory. A number of inverse problems for randomly layered media are also formulated where we recover large scale properties of the sound speed pro le from the statistics of re ected signals.