Benchmark calculations for higher-order parabolic equations

Abstract

Benchmark solutions generated with parabolic equation (PE) models are presented for range-dependent underwater acoustic propagation problems involving both penetrable and perfectly reflecting ocean bottoms. The solution of the wide-angle PE of Claerbout [J. F. Claerbout, Fundamentals of Geophysical Data Processing (McGraw-Hill, New York, 1976), pp. 206–207] agrees with the outgoing coupled-mode solution for the problems involving penetrable bottoms. The solution of the higher-order PE of Bamberger et al. [Bamberger et al., ‘‘Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media,’’ SIAM J. Appl. Math. 48, 129–154 (1988)], which is a generalization of Claerbout’s PE, agrees with the outgoing coupled-mode solution for problems involving large variations in sound speed and propagation nearly orthogonal to the preferred direction. The computer code FEPE was used to generate the benchmark solutions and was found to run several times faster than the IFDPE computer code due to a tridiagonal system solver in FEPE that is optimized for range-dependent problems.