TIME-DOMAIN GREEN-FUNCTIONS TECHNIQUE FOR A POINT-SOURCE OVER A DISSIPATIVE STRATIFIED HALF-SPACE WITH A PHASE-VELOCITY MISMATCH AT THE SURFACE

A point source over a dissipative stratified half-space with a discont inuity for both the phase velocity and the dissipation coefficient at the surface is considered. The axial symmetry of the problem is exploi ted in a spatial Hankel transform. The Green functions technique based on wave splitting is used to solve both the direct and inverse proble ms in the time domain. A Green tensor is introduced which directly map s the physical incident field outside the inhomogeneous half-space to the internal split fields. The PDEs for the Green functions are derive d. In the direct problem, the internal fields are calculated as well a s the reflected field. The phase velocity is reconstructed in the inve rse problem. Simultaneous reconstruction of the phase velocity and dis sipation coefficient using two different values of the Hankel transfor m parameter is analyzed. Two special cases, namely a point source over a homogeneous non-dissipative half-space and over a homogeneous dissi pative half-space, are discussed and it is shown that the solution for the reflected fields is given by Volterra equations of the second kin d.