Inverse problem for the dissipative wave equation in a stratified half-space and linearization of the imbedding equations

The invariant imbedding procedure with a modified planar wave-splitting process is applied to the dissipative wave equation for a smooth stratified medium. The imbedding equations for R 0 and R 2 , respectively the zeroth and second moments of the kernel of the reflection operator, are obtained. A linearization of the nonlinear imbedding equation for R 0 is given, which greatly simplifies the numerical procedure and improves the speed one order in the direct and inverse problems. Numerical results are given for the direct problem, and for the inverse problem where the zeroth and second transverse moments of the reflection data are given on one side.