Linear time-variant space-variant filters and the WKB approximation

Abstract

Wave propagation in a random, inhomogeneous ocean is treated as transmission thru a linear, time-variant, space-variant, random communication channel. A consistent notation (vis-a-vis ad hoc), fundamental input-output relations, and various time-space transformations for both deterministic and random linear, time-variant, space-variant, filters are established. Using the method of separation of variables and the W.K.B. approximation, a time-invariant, space-variant, random transfer function of the ocean volume is derived. The ocean volume is characterized by a random index of refraction which is a function of depth. The index of refraction is decomposed into a deterministic component and a zero mean random component. In addition, two example calculations are made