Factorization of a dissipative wave equation and the Green functions technique for axially symmetric fields in a stratified slab

The time domain scattering problem for axially symmetric fields and a dissipative stratified slab is considered. Explicit representations are derived for the wave splitting operators that factorize the dissipative Hankel transformed wave equation. The Green functions approach associated with this splitting is developed. Partial differential equations (PDEs) for the Green functions are derived and used to derive the imbedding equations for the reflection and transmission kernels. Numerical results for the internal fields are given in the direct problem, and the phase velocity is reconstructed in the inverse problem.