Echo, Reverberation, and Echo-to-Reverberation Ratio for a Short Pulse in a Range-Dependent Pekeris Waveguide

In shallow water, active sonar performance is typically limited by reverberation, making the prediction of target echo, reverberation, and echo-to-reverberation ratio an important part of sonar performance prediction. In range-dependent shallow-water environments, the echo is often calculated without considering the effect of dispersion, and reverberation predictions are often limited to Lambert's rule for seabed scattering. In this paper, analytical formulae are derived for the echo, including the effect of time dispersion, and for reverberation for non-Lambert scattering laws. More specifically, the method for calculating the short-pulse echo intensity developed by Harrison and Nielsen is extended to a range-dependent bathymetry. For reverberation, the Zhou-Harrison method is also generalized to cover an arbitrary power law for the seabed scattering coefficient, combined with a range-dependent bathymetry. These formulae are applied to range-dependent test cases from an international workshop, and compared with predictions using a normal mode sum. Neglect of time dispersion is found to result in an error of up to 16 dB. Results for a cylindrically symmetric bathymetry differ by up to 14 dB from the corresponding results with a Cartesian symmetry.