The Use of Tessellation in Three-Dimensional Parabolic Equation Modeling

Abstract

A full three-dimensional parabolic equation model (MONM3D) has been developed that incorporates techniques that reduce the required number of model grid points and reduces computation time. The concept of tessellation is implemented in MONM3D, which allows the number of radial paths in the model grid to vary with range from the source, reducing the number of computational points in the horizontal plane. This design establishes a grid layout that is both numerically and computationally desirable. A benchmark test case is used to illustrate the accuracy and efficiency of the model. using two-dimensional models, in which the stratified environment is separated into locally range-independent segments where the environmental properties vary between segments. 1 For simplicity, many models make the assumption that environmental range-variability is omni-directional in the horizontal plane. In reality, ocean environments exhibit spatial variability in all directions and are better represented with the class of models commonly known as Nx2D, or pseudo-3D. Such models solve 2D fields in many different vertical planes that emanate radially from a sound source, each with uniquely defined range-dependent environmental parameters. These Nx2D models assume that the influence of any cross-range environmental gradients is too weak to divert sound from range-depth planar propagation, and are not fully three-dimensional (3D) since they neglect any potential sound coupling between adjacent planes. Fully 3D models include terms to account for the out-of-plane propagation that can occur in some environments. These models represent most accurately the true acoustic field in environments with complex spatial variability, but are computationally more intensive than 2D or Nx2D models. 2,3Parabolic equation (PE) models are suitable for computing sound fields in complex, range-dependent environments and can be set up in a 3D formulation involving partial differential equations in azimuth as well as in depth. 3-5 Full 3D solutions are computationally demanding and efforts in 3D-PE model design often focus on maximizing efficiency. Model efficiency can be improved through a strategic definition of the under-lying model grid to reduce the number of computation points while maintaining accuracy of the solution. In a cylindrical coordinate system, an arrangement of grid points with consistent areal coverage at all ranges (such that the grid is neither too coarsely nor too densely sampled at any range) can be called a tessellation. a This paper focuses on a 3D PE model, MONM3D, that has been developed as an extension of JASCO Applied Sciences' Nx2D Marine Operations Noise Model (MONM) that is used to characterize underwater sound fields surrounding marine industrial noise sources, mainly for environmental impact assessment purposes. The 3D extension was undertaken to allow more accurate MONM estimations for environments in which 3D propagation effects are important. A key design requirement was to consider efficiency in order to make the 3D versi...

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