The passage of elastic waves through an anomalous region — III. Transmission of obliquely incident body waves

A variational method is set up, which has been previously applied to problems of scalar wave transmission, reflection and scattering. The method is that of Schwinger and Levine and was originally constructed to deal with wave problems in Atomic Physics. The problem of a wave normally incident on a layer whose elastic properties vary in a fairly complex way is studied in this paper. Trial functions for the displacements in the layer are used to get transmission coefficients with only a second-order error. Results are obtained which are consistent with the known properties of the system at long and short wavelengths, and which are consistent with each other at intermediate wavelengths. 1