Efficient algorithm for long-range monostatic reverberation in shallow water using geometrical ray-bundle

An efficient algorithm for long-range monostatic reverberation is developed using geometrical ray-bundle as its propagation model. In the standard approach for reverberation modeling, scattered signals are numerically integrated along the rough surface. In this work, the integration along the rough surface is converted to an integration along the delay time of source signal. It can be expressed in an analytic form under the assumption of ignoring time-dispersion effect. Repetitive eigen-ray searches for calculating scattered signals are avoided by using a split-step marching algorithm for the range based on the geometrical ray-bundle. When the bottom is range-dependent, arrival times of scattered signals from the rough bottom at same range is different according to azimuthal angles and they cannot be directly summed in time domain. The reverberation signals along the azimuthal angles are interpolated to obtain new reverberation signals at certain times. They are summed to compute a time series reverberation signal from the rough sloping bottom. The algorithm is applied to problems of reverberation modeling workshop, and its results are compared with those from the standard reverberation algorithm.