The theory of a direct inversion method to obtain the P and S wave seismic velocities and the density of a horizontally, finely layered elastic medium from vertical and horizontal component plane wave seismograms in the tau-p (slant stacked) domain has been developed. The method is based on the downward continuation method of Bube and Burridge (1983), but plane wave seismograms with a range of ray parameters are used simultaneously to obtain the velocity and density profiles. A corrected acoustic approximation of the elastic case has also been developed with which one may obtain a model of the P wave velocity and density from vertical component seismic recordings. However, it requires the S wave velocity to be estimated a priori, for instance as a fixed fraction of the P wave velocity. Many direct inverse methods, including the Bube and Buridge procedure followed here, may lack stability when implemented numerically, specially when they are applied to real data which necessarily are band limited at both low and high frequencies.

The possibility of a stable implementation of our methods has been investigated, firstly by using synthetic data for layered acoustic media containing a full range of low frequencies. In this case, the inverted velocity and density profiles are in good agreement with the test models. Secondly, the indeterminacy associated with the lack, in practice, of low frequencies has been studied, and a method has been devised to estimate the missing low-frequency data from travel time information. Finally, the inversion algorithm has then been applied to high-quality marine seismic reflection data obtained by the North Atlantic Transect (NAT) group in the deep ocean using an expanding spread profile (ESP). In this test, only the P wave velocity profile was estimated independently, because the move-out data cannot provide low-frequency information about density. Also, the ''source wavelet'' of the seismic system had to be estimated from the seismic recordings. A stable and plausible estimate of the velocity variation was obtained. Unfortunately, no independent measurement of this velocity structure is available with which to verify the method's accuracy. ¿ American Geophysical Union 1989