A three-dimensional propagation algorithm using finite azimuthal aperture

The use of three-dimensional (3-D) propagation models is becoming increasingly common in current underwater acoustics applications. Such models typically treat the propagation as a function of range, depth, and bearing, consistent with previous multibearing two-dimensional (N×2-D) models. However, to obtain accurate 3-D solutions at long ranges, many bearings must be computed in order to maintain the necessary cross-range resolution between bearings. In this paper, a 3-D parabolic equation (PE) model is developed with a marching algorithm based on the split-step Fourier technique in both depth and azimuthal bearing. The algorithm includes a scheme to compute the solution for only a finite azimuthal aperture rather than the full 360° of bearing. The success of this algorithm allows for increased cross-range resolution at long range without increasing the number of bearings needed in the calculation. Results of this technique are compared to results from a suggested benchmark case.