Shallow water acoustic modeling over a sloping bottom

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Ray theory with beam displacement gives an approximate method of finding the acoustic field in shallow water. It was shown to be quite accurate for a horizontally stratified two fluid (Pekeris) model by comparison with normal mode results. [C. T. Tindle, J. Acoust. Soc. Am. 73, 1581–1586 (1983)]. The method is extended to the sloping bottom situation by simple geometric arguments and without further approximation. Results show that even small bottom slopes have a dramatic effect on the sound field. The results are compared with those for the adiabatic normal mode approximation and agreement is good for higher frequencies. At lower frequencies differences are attributed to normal modes passing through cutoff, a process which is ignored in simple adiabatic mode theory.