Calculation of three-dimensional acoustic scattering from Gaussian rough under-ice surface using the Kirchhoff approximation method with modified reflection coefficient

The Kirchhoff approximation with a modified reflection coefficient is used to calculate the three-dimensional acoustic scattering of a Gaussian rough under-ice surface.The concept of a local statistical average reflection coefficient of an under-ice surface is proposed in the calculation model.The scattered sound field of a two-dimensional Gaussian rough under-ice surface is divided into coherent scattering and incoherent scattering.A formula is derived for the scattering coefficient of each scattering component,and the three-dimensional scattering intensity is obtained.The relationships between the scattering intensity and (i) the root-meansquare height of the Gaussian rough under-ice surface,(ii) the angle of incidence,and (iii) the sound frequency are analyzed.The scattering intensity of a Gaussian rough under-ice surface is measured in a laboratory water tank,and the calculation results of the theoretical model are verified.The experimental results are compared with those of the theoretical model using (i) the present local statistical average reflection coefficient of an under-ice surface and (ii) the mirror reflection coefficient of an under-ice surface from the literature.The calculation results of the model using the local statistical average reflection coefficient agree well with the experimental results.