Introduction

Wave propagation in a marine environment can be separated into two parts: the propagation through the water, in which the acoustic wave equation applies, and the propagation in the subsurface strata, in which the elastic wave equation applies. Propagation in the water is described by the scalar pressure wavefield recorded by the hydrophones; in solid layers the displacement vector, or elastic field separation should be used. The coupling of the two potentials can be achieved by the application of the continuity of the normal components of stress and displacement at the liquid-solid interface.

The conversion of the scalar recorded field into the elastic wavefield at the ocean floor and the subsequent separation of the converted wavefield can be achieved by the application of successive steps.

First the recorded pressure field is decomposed into the upcoming and downgoing wavefields (Claerbout, 1971), and since the downgoing wave at the cable is just the upcoming wave reflected at the water surface (or ghost), it is possible to express the upcoming wavefield as a function of the recorded wavefield. Then, the principle of survey sinking (Schultz and Sherwood, 1980; Claerbout, 1985) is used to extrapolate the upcoming pressure field down to the ocean floor. The next step is the conversion of the scalar pressure field into the displacement amplitude field of the P waves in the water; this conversion is accomplished through a simple relation in the w-k_x domain. Finally, a slowness filter is used to obtain the displacement amplitudes of P and SV waves below the water bottom interface. This filtering process shows to be more effective if a prior separation of the data into P wave Snell rays domains is performed, so that a different filter can be used for each domain.