Simple illustrations of range-dependence and 3-D effects by normal-mode   sound propagation modelling
  As is well known, the sound-speed profile has significant effects on underwater acoustic sound propagation. These effects can be quantified by normal-mode models, for example. The basic case is a laterally homogeneous medium, for which the sound speed and the density depend on depth only and not on horizontal position. Effects of horizontal medium-parameter variation can be quantified by coupled-mode models, with coupling between mode expansions for laterally homogeneous parts of the medium. In the present paper, these effects are illustrated for media with a particularly simple horizontal parameter variation such that mode shapes do not vary with horizontal position. The modal wavenumbers depend on horizontal position, however. At a vertical interface between regions with laterally homogeneous medium parameters, each mode is reflected as well as transmitted. For the media considered, reflection and transmission coefficients can be computed separately for each mode without mode coupling, and this is done recursively, stepping through the laterally homogeneous regions in appropriate order. Continuous-wave as well as pulse computations are used to illustrate frequency-dependent reflections from ridges and diffraction into shadow zones behind islands, for example. 
Sven Ivansson
physics.ao-ph physics.comp-ph