Attenuation of the coherent component of sound propagating in shallow water with rough boundaries is studied. Normal-mode theory is used in conjunction with a boundary perturbation method. The inclusion of surface and bottom scattering cause the eigenvalues to become complex and explicit mathematical expressions for the imaginary parts of these eigenvalues are derived. These expressions correspond to the individual normal-mode attenuation coefficients due to scattering. Numerical results are presented for sample shallow-water environments with depth-dependent sound-speed profiles and lossy bottom sediments. The profile structure and the acoustic properties of the bottom sediment have a significant effect on the total attenuation due to scattering.
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Kuperman et al. (1977) studied this question.