A three-dimensional parabolic equation using non-uniform depth and horizontal grids in ocean acoustics

Three-dimensional parabolic equation models can be used to analyze three-dimensional (3-D) sound propagation effects in ocean acoustics. However, long calculation time and large computer memory must be consumed when the models are used to analyze 3-D sound propagation problems, which makes it very difficult to calculate long-range sound fields accurately. Therefore, a non-uniform depth and horizontal grid scheme is applied to a 3-D parabolic equation model in Cartesian coordinates. Some numerical examples show that the improved parabolic equation model can calculate long-range sound propagation problems at higher rate of speed and accuracy. To consider 3-D sound propagation problems where the environmental parameters are rauge-independent in short range but range-dependent in long range, the the computer code Kraken is used to build the starting sound field and is adopted to calculate the 3-D sound field recursively. A long-range wedge-shaped waveguide problem is considered in the rebuilt model to show an energy enhancement phenomenon.