Abstract
A decomposition of the solution of the dissipative wave equation into incoming and outgoing components across a smooth surface in a homogeneous region is presented. (The proof of the decomposition is given only for the plane surface.) This is then applied to the factorization of the dissipative wave equation into incoming and outgoing components in a planar-stratified medium. The Ricatti integral–differential equation for the reflection operator that relates the two components is obtained. It is shown how the zeroth and second moments (with respect to the transverse variable in a planar-stratified medium) of the reflection kernel can be used in the inverse problem to recover the velocity and dissipation coefficient from knowledge of the scattered field.
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