A self-consistent perturbation method for three-dimensional acoustic scattering due to sound speed and density fluctuations is developed below. This method allows calculation of mean-field attenuation due to scattering, as well as second-moment statistics of the scattered field. Scattering from an inhomogeneous sediment bottom in shallow water is considered as an application. The power spectral density of the scattered field is calculated and used to study the effects of fluctuation statistics. Modal attenuation due to scattering is then calculated for several shallow-water scenarios. The scattering loss calculation is straightforward and is suitable for use with standard normal-mode codes. Numerical results show the influence of the statistical model used to represent bottom randomness and demonstrate the importance of scattering into the continuous spectrum. Scattering loss predictions are shown to agree well with a previous wave number-integration approach.
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Tracey et al. (1999) studied this question.
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