A two-way integral equation approach to a shelf break problem

Abstract

Benchmark solutions play an important role in the development, testing, and application of numerical models for range-dependent problems in underwater acoustics. To produce benchmark accuracy propagation solutions requires careful attention to both the theoretical formalism and numerical implementation. The focus of this research is a ‘‘benchmark’’ solution for a two-dimensional (2-D) shelf-break problem in ocean acoustics. The method employed to construct a solution is a two-way energy-conserving coupled mode approach in the form of coupled inhomogeneous integral equations. Solutions of the coupled equations are obtained using a powerful approach originally introduced in nuclear theory and also used to solve simple nonseparable problems in underwater acoustics. The basic integral equations are slightly modified to permit a Lanczos expansion to form a solution. The solution of the original set of integral equations is then easily recovered from the solution of the modified equations. Benchmark quality demands that the errors in each step of the numerical calculation be well quantified, so that the resolution in the transmission loss can be determined. Consistency checks are made in the form of using different numerical schemes to compute the adiabatic or free propagator and mode coupling matrix operator.