Mode-theory reflection coefficient

Abstract

Given the physical parameters of the ocean bottom, a plane wave reflection coefficient Rpw can be defined, e.g., the Rayleigh reflection coefficient. Rpw, or the equivalent bottom loss, is normally used in ray-theory calculations. A reflection coefficient, per se, is not an explicit parameter in a normal mode formulation. [See H. P. Bucker, J. Acoust. Soc. Am. 48, 1187–1194 (1971), for an exception to this.] For an inhomogeneous water column an effective plane wave reflection coefficient Re can be defined which plays the role of reflection coefficient in mode theory. Re and Rpw are equivalent only for an isovelocity water column. The phase of Re plays a direct role in determining the eigenvalues and contributes indirectly to the mode cycle or skip distance rC. The relationship between rC and the cycle distance arising from beam displacement rBD [E. L. Murphy, J. Acoust. Soc. Am. 61, 511 (1977)] is shown to be an approximate one. It is further shown that rBD is a fundamental constituent of mode theory and enters explicitly as a parameter in the mode amplitude. Several simple examples are selected to illustrate the various points. [Work supported by CNR/NORDA.]