Beam Displacements for Media with Monotonic Sound-Speed Profiles with Discontinuous and with Continuous First Derivatives

Abstract

A ray representation for some of the diffraction phenomena encountered in underwater sound propagation in media with nonmonotonic sound-speed profiles [E. Murphy, J. Davis, and J. Doutt, J. Acoust. Soc. Amer. 50, 101 (A) (1971)] leads to beam displacements that remove the sensitivity or pathology of ordinary ray analysis when first derivatives of the sound-speed profile are discontinuous. In this modified ray theory, diffraction phenomena take the form of frequency-dependent beam displacements for rays with vertexes near the sound-speed profile extremum. Unlike ordinary ray theory results, modified range-versus-source-angle curves are well-behaved (continuous derivatives). The analysis has been extended to monotonic profiles with discontinuous and continuous derivatives; the analysis is somewhat more complicated than for the nonmonotonic extremum examples. Here also, beam displacements remove some of the pathology in the range-versus-source-angle curves. For the smooth monotonic profiles there are displacements if the curvature of the profile is too great. For the profile with discontinuous gradients there can be oscillations in the range-versus-source-angle curves.