Through the use of perturbation theory, Kuo has previously introduced a joint surface roughness/volumetric model in order to characterize bubbly sea surface reverberation based on volumetric wave spectra, surface roughness wave spectrum, and correlation of volumetric wave spectrum and surface roughness wave spectrum. Due to the lack of undetermined volumetric scattered wave number Kv, Kuo obtained backscattering strengths using only Pierson-Moskwitz wave spectrum. In this paper, the reformed integral equation of authentic Helmholtz-Kirchhoff-Fresnel is discussed in which volumetric scattering is involved. By applying the reformed Helmholtz-Kirchhoff-Fresnel, volumetric scattered acoustic pressure field Pv is obtained. Using Helmholtz wave equation and the obtained pressure field Pv, the wave number vector of volumetric scattered field Kv is calculated, and this used to compute the volumetric wave spectrum and the joint surface roughness/volumetric wave spectrum. The obtained spectra are then used to compute scattering strengths. Comparison of the obtained results against the results of experimental Critical Sea Tests shows good agreement. Finally, a parametric study is conducted to examine the effects of wind speeds, grazing angles, and frequencies on the scattering strengths.
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