A numerical comparative study of wave propagation in inhomogeneous and random media

Continuous media through which acoustic or elastic waves propagate often exhibit inhomogeneities of various types which are difficult to describe, either due to paucity of detailed physical measurements or to the vast complexity in both space and time of these inhomogeneities. The introduction of stochasticity in the description of a continuous medium offers an attractive alternative, due to the fact that randomness is able to reproduce the wave scattering phenomena associated with a naturally occuring medium. In this work, the phenomenon of acoustic or elastic wave propagation under time harmonic conditions is used as the vehicle through which the assumption of randomness in an otherwise homogeneous medium is validated against a deterministic, inhomogeneous medium whose properties vary with depth. The range of applicability of the former model is identified through a series of parametric studies and the results are followed by a discussion on the appropriateness of the various correlation functions that can be used for representing the medium randomness. The numerical methodology employed for both deterministic and random models is a Green's function approach for waves propagating from a point source, while techniques to account for the presence of boundaries are also discussed.

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