Linear approximation of underwater sound speed profile: Precision analysis in direct and inverse problems

Sound speed is one of the key sources of uncertainty in an underwater environment. The wave equation for a complex sound speed profile (SSP) cannot be analytically solved and numerical solutions generally involve high computational costs. A relatively simple way is to approximate the SSP by assuming it as horizontally stratified, vertically multi-layered and linearly varied with respect to water depth in each layer. This approximative model leads to a fast computation of the sound propagation. However, the error of SSP results in an inaccurate sound field computation, thus the model accuracy in terms of error propagation in both direct and inverse problems should be investigated. Rapidly developing numerical techniques are currently able to accurately simulate the sound propagation in a complex configuration, such that the difference between a real case with a complex SSP and its approximation can be precisely quantified. In this paper, the sound propagation with a complex SSP is simulated via a full wave numerical approach, known as the spectral element method. The efficiency of SSP linear approximation with various layer number (corresponding to different sound speed error) is quantified via transmission loss forecast (direct problem) and sound source localization error (inverse problem), respectively. The precision analysis is able to guide the choice of optimal approximate model for different scenarios, which is a trade-off between the computational cost and the model accuracy.