Full reconstruction of a layered elastic medium from P-SV slant-stack data

Summary. We develop a méthod of reconstructing the elastic paraméters as functions of depth, for a horizontally stratified, isotropic elastic half-space. Unlike previous schemes, which have been able to retrieve the shear wave speed and density from SH seismograms slant stacked at two angles, our méthod makes use of P - SV data at a single stacking paraméter to obtain all three elastic constants. The data required are the elements of the full reflection matrix at the surface, corresponding to measurements of two separate components of the response to two independent sources, one explosive, the other generating shear waves.
In developing this inverse scheme fundamental differences emerge between the acoustic or SH problem, and the coupled P - SV case, the most important being in the nature of the interfacial scattering matrix. We show that it is not possible to make use of the downward reflection data for an interface to determine directly the remaining reflection and transmission coefficients, but that the scattering data may be completed by applying a simple iterative procedure at each interface.
We show the result of applying our inverse scheme to seismograms generated for a six-layered model, including a low-velocity layer. We are able to reconstruct both wave speeds and the density as functions of depth, all quantities being in close agreement with the original model.