Applications of 3D time domain wave splittings to direct and inverse scattering

Abstract: The three-dimensional direct and inverse scattering problems in the time-domain are considered in the present thesis. The direct problem is to find an explicit or numerical solution of the transient reflection for given physical parameters. The inverse problem is to reconstruct the physical parameters in the scattering region, using the reflection data generated by a known incident field. The method used is based on the concept of wave-splitting. To make the thesis more instructive, wave-splitting and the Green function approach are fimt described for the the plane wave case. For stratified half-space with a point source, a spatial Han kel transform is used to obtain a one-dimensional wave equation. The explicit expression for the reflection kemel in the Hankel-transformed space for an expo nential density profile is obtained. Closed-form solution of the transient reflected pressure in physical space is obtained through an inverse Hankel transform. The time domain Green func:ion approach is used to solve the inverse probelm. For a 3D inhomogeneous ha&space in a Cartesian coordinate system, wave-splitting to the three-dimensional wave equation is used. By introducing a lotal continuation and a wave-splitting approach, one can propagate the transient wave field and its normal derivative to the next layer, so that parameter reconstruction can be achieved in a layer-stripping manner. From the up and down-going wave conditions, one can obtain the exact absorbing boundary conditions. Wave-splitting and corresponding absorbing boundary conditions for 3D scattering problems in spherical coordinate system are also discussed in this thesis.