Direct and inverse scattering in the time domain for a dissipative wave equation. Part 3: Scattering operators in the presence of a phase velocity mismatch
The direct scattering problem for an inhomogeneous lossy medium is examined for the one-dimensional case in which the phase velocity profile is discontinuous at the boundaries of the medium. Scattering operators (or impulse responses) and propagation operators are defined and equations that govern their behavior are developed. Knowledge of the scattering kernels for one round trip in the medium im