Direct and inverse scattering in the time domain for a dissipative wave equation. Part IV: Use of phase velocity mismatches to simplify inversions

For pt.III see J. Math. Phys., vol.28, p.260 (1987). The one-dimensional inverse scattering problem is considered for lossy inhomogeneous media for the case in which the phase velocities at the two boundaries of the scatterer do not match that of the host medium. The model problem involves electromagnetic wave propagation in a medium of unknown thickness with spatially varying permittivity and conductivity. An inversion algorithm which is capable of simultaneously reconstructing both the permittivity and conductivity is derived and tested numerically. It is shown that the discontinuity in phase velocity simplifies the data requirements for the inverse problem in that only one scattering experiment needs to be performed, rather than two. The input data for the inversion algorithm consist of a finite time trace of the reflected field or, alternatively, portions of the reflected and transmitted fields.