Semi-coherent image method to estimate propagation loss in shallow water for measuring surface vessel source level

The source level (SL) of an underwater sound source can be determined by measuring sound pressure level (SPL) at a known distance from the source, modelling propagation loss (PL) to that distance, and calculating SL as the sum of PL and SPL. For a surface vessel, while modelling PL in deep water has been standardized (ISO 17208-2:2019), the calculation of PL in shallow water is complicated by the occurrence of multiple reflections from the seabed. To address multipath propagation in shallow water, the method of images is considered, including fully coherent and semi-coherent sums. The fidelity of the coherent image sum is verified by comparison with wavenumber integral and parabolic equation solutions. The semi-coherent image sum is proposed for use in shallow water and is shown to simplify to the deep-water result in the limit of infinite water depth.