A note on scattering operator symbols for elliptic wave propagation

Abstract

The ill-posed elliptic wave propagation problemscan be transformed into well-posed initial valueproblems of the reflection and transmission operatorscharacterizing the material structure of the givenmodel by the combination of wave field splittingand invariant imbedding methods. In general,the derived scattering operator equations areof first-order in range, nonlinear, nonlocal,and stiff and oscillatory with a subtlefixed and movable singularity structure.The phase space and path integral analysisreveals that construction and reconstructionalgorithms depend crucially on a detailedsymbol analysis of the scattering operators.Some information about the singularity structureof the scattering operator symbols is presentedand analyzed in the transversely homogeneous limit.