**Abstract:**

There are two basic approaches for discretizing the differential equations that are solved in propagation models: (1) Approximate the differential operator with a finite-difference formula; and (2) approximate the medium in terms of layers that may be treated analytically and solve for a set of coefficients. The analytic approach is more efficient for problems involving a small number of layers. Both approaches have been implemented for normal mode and wave-number integration models. The finite-difference approach has been implemented for parabolic equation models. This paper describes an analytic implementation of a parabolic equation model that is efficient for geoacoustic inversion problems [R. J. Cederberg and M. D. Collins, ``Application of an improved self-starter to geoacoustic inversion,'' IEEE J. Ocean. Eng. (in press)]. Using the finite-difference implementation, the self-starter can solve nonlinear inversion problems in minutes on a workstation (techniques that were developed previously require hours of run time). The analytic implementation reduces run times to seconds. [Work supported by ONR.]

ASA 133rd meeting - Penn State, June 1997