Three-dimensional inversion technique in ocean and seabed acoustics using the parabolic equation method

Abstract

A three-dimensional parabolic equation (PE) and perturbation approach is used to invert for the range-dependent geoacoustic characteristics of the seabed. The model assumes that the sound speed profile is the superposition of a known range-independent profile and an unknown depth and range-dependent perturbation. Using a Green’s function approach, the total measured pressure field in the water column is decomposed into a background field, which is due to the range-independent profile, and a scattered field, which is due to the range-dependent perturbation. When the Born approximation is applied to the resulting integral equation, it can be solved for the range-dependent profile using linear inverse theory. For simplicity, the sound speed profile in the water column is assumed to be known, and the range-dependent perturbation is added to the index of refraction n(x,y,z), rather than the sound speed profile c(x,y,z). The method is implemented in both Cartesian (x,y,z) and cylindrical (r,θ,z) coordinates with the forward propagation of the field in x and r, respectively. Synthetic and experimental data are used to demonstrate the validity of the method. Keywords: Three-dimensional parabolic equation method, geoacoustic inversion, range-dependent sound speed profile, linear inversion, Born approximation, and Green’s functions.