Far-field Green's functions and azimuthal mode decompositions of the Helmholtz-Kirchhoff integral for axisymmetric scatterers buried in sediment

The Helmholtz-Kirchhoff integral with an appropriate Green's function is commonly used to calculate the far-field target strength of an acoustic emitter/scatterer based on a solution for the near-field emitted/scattered pressure. This paper presents approximate Green's functions for objects buried in the sediment layer based on the far-field assumption. These approximate Green's functions offer convenient analytical expressions for their value and normal derivative in the general three-dimensional case and permit a modal decomposition of the Helmholtz-Kirchhoff integral for axisymmetric geometries. The formulations assume the same mathematical form as in the free-field case, making them straightforward to implement and of similar computational complexity. The accuracy of the approximations is verified through comparison with published results for several benchmark problems.