Layer-stripping and parameter reconstruction for a hyperbolic equation in a three-dimensional inhomogeneous half-space

A time domain wave-splitting approach to the inverse problem for a hyperbolic differential equation in an inhomogeneous half-space is considered (the wave velocity is assumed to be constant). A layer stripping method is used to reconstruct the parameter in a non-iterative way, using the reflected field which is produced by an exterior step-function point source. Local continuation formulas of the field are used, and in particular the continuation formulas for the field in the vicinity of a discontinuous wavefront are derived. Numerical results for data continuation and the reconstruction of the dissipation coefficient are presented.