Effects of horizontal refraction on underwater sound propagation in deep and shallow water are considered within geometrical acoustics and adiabatic normal modes approximations. Several distinct formulations of the adiabatic approximation have been proposed in the literature on modal propagation. These formulations differ in the predicted values of mode amplitudes and, hence, in their reciprocity and energy-conserving properties. The formulations are compared with respect to their accuracy and domain of validity, assuming small and smooth variation of mode propagation constants characteristic of underwater acoustic waveguides. Perturbation theory for horizontal (modal) rays is used in the analysis. An approximate expression for the adiabatic mode amplitude in 3-D problems is derived which requires environmental information only along the source-receiver radial and which has greater accuracy than previous formulations. It is shown that the uncoupled azimuth approximation, also known as the N × 2-D approximation, overestimates travel times of ray arrivals as well as phases of adiabatic normal modes in a horizontally-inhomogeneous ocean. The travel time and phase biases rapidly increase with the value of cross-range environmental gradients and propagation range. Simple and explicit expressions for leading-order corrections to the travel time and the phase are found in terms of path-averaged cross-range environmental gradients. Implications on applicability of the uncoupled azimuth approximation for sound propagation modeling in a horizontally-inhomogeneous ocean are discussed. A perfect-wedge model of the coastal ocean is chosen to illustrate the importance of the travel-time and phase biases due to horizontal refraction.
A Chebyshev-Tau spectral method for normal modes of underwater sound propagation with a layered marine environment
