ELASTIC-WAVES IN RANDOMLY STRATIFIED MEDIUM - ANALYTICAL RESULTS

Propagation of elastic harmonic waves through a stratified slab is investigated. It is assumed a nonzero angle of inclination of an incident wave. The equation for the amplitudes of reflected and transmitted waves are presented in the form useful for simulation. Then a limiting case where the density of stratification of the slab tends to infinity is analysed and the equations for the amplitudes of the waves in a homogenized medium are obtained. Finally, the law of large numbers for noncommuting random products is applied to the randomized equation for amplitudes showing its convergence to some deterministic effective one for increasing density of stratification. © 1990 Springer-Verlag.