Compressional‐shear wave coupling induced by velocity gradients in marine sediments

Abstract

The very high compressional and shear velocity gradients of marine sediments may result in continuous interconversion between P (compressional) and S (shear) types of motion at low frequencies. Since the ray theories commonly used in modeling acoustic interaction with the ocean bottom implicitly assume that P and S are decoupled, the importance of such phenomena must be assessed. The problem is investigated here through theoretical studies of the reflectivity function for representative models of the ocean bottom. The only practical approach for including all such wave phenomena in a determination of reflectivities involves numerical solution of the wave equation. For a depth‐varying structure, the most efficient numerical scheme is the classical approximation by homogeneous layers. This procedure can be readily modified to isolate the effects of gradient‐induced coupling by forcing the P‐ and S‐wave potentials to be independent and studying the effects of this on the reflectivity. Unfortunately, the results of this analysis, being in frequency‐wavenumber space, are so difficult to interpret that the physics of the coupling process is obscured. Some insight can be gained by transforming the frequency dependence of the reflectivity function to a time dependence. The resulting function (the plane‐wave response) is more amenable to physical interpretation and shows clearly that the principal consequence of coupling is the conversion of shear to compressional motion. As a result, coupling reduces the amplitude of shear arrivals and draws out the tails of compressional arrivals. Above 1 Hz, however, the effects of this coupling are extremely small, so for most marine acoustics applications, the phenomenon can be ignored.