An approximation to the three-dimensional parabolic-equation method for acoustic propagation

We have reported previously [Ralph N. Baer, J. Acoust. Soc. Am. 69, 70–75 (1981)] on an algorithm, based on the parabolic approximation to the reduced wave equation, for the propagation of sound in three dimensions in the ocean. We present here a simpler algorithm: solve N two-dimensional problems and combine the results to form an approximate three-dimensional solution. Analytic and numerical results show that this N×2D approach is an excellent approximation to the original algorithm for realistic ocean environments, even those where fronts and eddies are present, provided redirection of energy in azimuth due to boundary interaction is not important. We compare the two computer models based on these algorithms for several test cases by considering how they distribute energy spatially, and by simulating the performance of a hypothetical horizontal array of hydrophones placed in the calculated complex-valued acoustic fields. In an example of propagation through a large and strong ocean eddy, the N×2D method predicts intensities and array performance parameters (such as array signal gain) which are typically within 8% of the values from the full 3D algorithm. In another example, with a large linear cross-range gradient on the index of refraction, the N×2D and 3D solutions are essentially identical out to a range of 120 km. The new method has made it practical to consider higher source frequencies and has reduced the substantial computer time of the three-dimensional program.