Range Dependent Propagation Codes Based on Wave Field Factorization and Invariant Imbedding

摘要

In the absence of range variation the Helmholtz equation can be exactly factored into two one-way equations. These factored equations provide the bases for a number of computationally efficient codes, the most familiar of which is the ordinary parabolic wave theory. This paper discusses the reintroduction of range dependence to enable analysis of media with arbitrary variation. Two calculations will be presented. One is the reflection and transmission of an arbitrary variation. Two calculations will be presented. One is the reflection and transmission of an arbitrary field at an interface separating two transversely inhomogeneous media. The second is the reflection and transmission of an arbitrary field by a transition region separating two transversely inhomogeneous media. The second problem is addressed by an invariant imbedding procedure and taken together the solutions to the two problems represent an exact and complete generalization of Kennett's method, in the context of scalar waves.