Three-Dimensional Sound Propagation Models Using the Parabolic-Equation Approximation and the Split-Step Fourier Method

Abstract

The split-step Fourier method is used in three-dimensional parabolic-equation (PE) models to compute underwater sound propagation in one direction (i.e. forward). The method is implemented in both Cartesian (x, y, z) and cylindrical (r, θ, z) coordinate systems, with forward defined as along x and radial coordinate r, respectively. The Cartesian model has uniform resolution throughout the domain, and has errors that increase with azimuthal angle from the x axis. The cylindrical model has consistent validity in each azimuthal direction, but a fixed cylindrical grid of radials cannot produce uniform resolution. Two different methods to achieve more uniform resolution in the cylindrical PE model are presented. One of the methods is to increase the grid points in azimuth, as a function of r, according to nonaliased sampling theory. The other is to make use of a fixed arc-length grid. In addition, a point-source starter is derived for the three-dimensional Cartesian PE model. Results from idealized seamount and slope calculations are shown to compare and verify the performance of the three methods.

Modeling and Forecasting Ocean Acoustic Conditions

“…It must be emphasized that with accurate knowledge of the sound speed in any 3D ocean volume, 2D modeling can be done with a choice of established codes. Fewer implementations are available for 3D, among them parabolic equation (PE) one-way codes (Lin et al 2013a;Heaney and Campbell 2016), coupled normal mode codes (Shmelev et al 2014;Ballard et al 2015), adiabatic (uncoupled) normal mode codes, and ray-based models such as Gaussian beams.…”

“…Three-dimensional sound at 100 Hz is simulated using a Cartesian 3D split-step Fourier code (Lin et al 2013a) within a volume of synthetic ocean environment Inside the shallowest (200-m) contour enclosing the area 0 < y < 4 and 0 < x < 8 km, the 250-m depth sound is in the attenuating seabed and is very low level (see Fig. 1).…”

Three-Dimensional Shallow Water Acoustics

“…A 3-D normal mode method has been used to study canonical environmental models of shelfbreak front systems [1] and nonlinear internal wave ducts [2][3]. 3-D parabolic-equation (PE) wave propagation models with improved split-step marching algorithms [4][5][6] are used to study sound propagation in realistic environments. When the acoustic mode coupling can be neglected, a vertical-mode horizontal-PE model is used.…”

“…REPORT TYPE 3. DATES COVERED 00-00-2013 to 00-00-2013 4. TITLE AND SUBTITLE Three-Dimensional Shallow Water Acoustics 5a.…”

“…A 3-D PE model [4] is employed to explain the underlying physics. The acoustic data show a significant decrease in sound intensity as the source crossed over the canyons (see Figure 3), and the numerical model produces comparable results due to this shadowing effect.…”