Wave propagation and profile inversion in lossy inhomogeneous media

Using the Lagrangian approach, a time-domain analysis of wave propagation in an inhomogeneous lossy medium is described. We consider a half-space problem (x ≥ 0) in which the medium is plane stratified in the direction of propagation and can be modeled by a piecewise uniform lossy transmission line. A method of profile inversion which is based directly upon quantities measured in time at the sending end boundary is presented. The problem of uniqueness is discussed. For a given medium, computer simulation results obtained by using the known reflected waves at the boundary x = 0 are shown.