This paper presents a method for using surface loss as a function of angle in a parabolicequation (PE) model. In this method, the complex pressure field in a layer near the surface is transformed to vertical wavenumber space where a loss function is applied. The field is then transformed back to depth space and merged with the field outside the layer in preparation for the next range step in the PE model. Test cases show the method to be computationally efficient as well as accurate.
Solving the parabolic approximation to the acoustic wave equation by the split-step algorithm is one of the principal methods for estimating the acoustic-pressure field in a range-dependent underwater environment. The algorithm is computationally intensive and is usually practical only at low frequencies. A modification to the split-step algorithm is provided (the calculation-frequency method), which allows rapid calculation of transmission loss at high frequency, includes surface and bottom loss, and provides for the redistribution of surface-scattered energy in wavenumber space.
A PE model has been used to compare 2D cw acoustic fields p(x,z) propagating in sound-speed fields c(x,z) to a reference acoustic field pr (x,z) propagating in the reference sound-speed field cr (x,z). Samples of the range- and depth-dependent sound-speed difference fields, δc(x,z) = c(x,z) − cr (x,z), were generated from physical models of (1) instrumental errors, (2) internal waves, and (3) baroclinic waves (mesoscale). The square modulus of the normalized inner product over depth, called ρ(x), with ρ = 1 corresponding to δc = 0, was used as a measure of the distance between ρ and ρr. Results are presented as curves of ρ(x) in dB units for various frequencies, depending on the magnitude of δc. It was found that ρ(x) decreases monotonically with range, on the average, and saturates in range at a value that decreases with increasing frequency at the rate of about 3 dB/oct. The range to saturation, called the “predictability horizon,” is surprisingly short for most frequencies of interest for moderate δc.
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