Accounting for azimuthal coupling in long-range ocean acoustics calculations

The parabolic equation method is an accurate and efficient approach for solving nonseparable problems in ocean acoustics in which there are horizontal variations in the environmental parameters. Many range-dependent problems may be solved using 2-D parabolic equation models that ignore coupling of energy between planes of constant azimuth. When azimuthal coupling must be taken into account, the splitting method may be used to efficiently solve a 3-D parabolic equation that handles the depth operator to higher order but handles the azimuth operator only to leading order. Despite the fact that this approximation provides a favorable combination of accuracy and efficiency for 3-D problems, run times have generally been regarded as prohibitive for the long-range problems that are often of interest in ocean acoustics. It is demonstrated here that, when propagation paths from source to receiver are confined to a relatively narrow neighborhood of the vertical plane containing the source and receiver, it is practical to solve 3-D problems out to long ranges by using nonuniform azimuthal sampling, with fine sampling near the vertical plane and extremely coarse sampling elsewhere.