An improved numerical scheme for predicting sound propagation in a vertically stratified medium

Abstract

Propagation of sound in a stratified medium has been studied for many decades. The ray tracing method, which is one of the most popular ways to solve this kind of problems, involves identifying the sound rays connecting the source with the receiver. However, the ray method does not yield accurate solutions when either the source or the receiver is placed near a turning point. Under these circumstances, it is found necessary to use a wave-based approach leading to a more accurate solution for predicting the sound fields. Typically, the solution is written in a form of a highly oscillatory integral that can be evaluated numerically. High computational times are required to obtain accurate solutions. There have been significant developments in the numerical approximation of highly oscillatory integrals. An improved scheme, which is known as Levin’s collocation method, has low computational costs but it gives accurate numerical solutions for high-frequency sound fields. In this paper, the propagation of sound in a stratified and unbounded medium is considered where there is only one turning point. The Levin collocation method is explored for calculating the sound fields efficiently. In addition, an asymptotic solution is also derived for comparison with the Levin collocation method.Propagation of sound in a stratified medium has been studied for many decades. The ray tracing method, which is one of the most popular ways to solve this kind of problems, involves identifying the sound rays connecting the source with the receiver. However, the ray method does not yield accurate solutions when either the source or the receiver is placed near a turning point. Under these circumstances, it is found necessary to use a wave-based approach leading to a more accurate solution for predicting the sound fields. Typically, the solution is written in a form of a highly oscillatory integral that can be evaluated numerically. High computational times are required to obtain accurate solutions. There have been significant developments in the numerical approximation of highly oscillatory integrals. An improved scheme, which is known as Levin’s collocation method, has low computational costs but it gives accurate numerical solutions for high-frequency sound fields. In this paper, the propagation of sound...