Modelling Underwater Sound Propagation Using the Finite-Difference Time-Domain Method

Abstract

Marine life in coastal regions is under environmental pressure from anthropogenic activities such as commercial shipping, offshore wind farms and leisure boats. As part of an ongoing research project to create underwater noise maps for recreational boats, IVL Swedish Environmental Research Institute has measured propagation loss in Kosterhavet marine protected area. These measurements show a variety of acoustic effects that are not captured by simple analytical models. The goal of this project is to produce a numerical model that can provide a more detailed understanding of how noise propagates underwater to the surrounding environment. A three-dimensional finite-difference time-domain (FDTD) model was developed in MATLAB. The model was validated by comparison to known analytical solutions of increasing complexity. First, it was confirmed that the model reproduces propagation loss due to spherical spreading, agreeing closely with analytical predictions. A nearly perfectly matched layer (NPML) was implemented to avoid unwanted reflections from the boundaries of a truncated domain. The decay factor and layer width were optimised empirically, achieving reduction of reflected wave energy up to 45 dB relative to a rigid boundary condition. Then, several boundary conditions were tested including a rigid wall boundary, a pressure-release condition and a finite-impedance boundary, with the latter two conditions representing the water-air interface and the water-seabed interface respectively. Analytical solutions for each case were calculated and show strong agreement with model output in both frequency and time domains. Finally, an attempt was made to reproduce real world measurements of propagation loss provided by IVL using different configurations of sea floor properties. Initial results show promise however require further investigation and fine-tuning of the model to accurately reproduce measurements.