Evaluation of the integrals of target/seabed scattering using the method of complex images

In this paper the integrals which arise in target/seabed scattering problems are examined. These are the integrals which express the propagation of a spherical harmonic term in a fluid above or below a half-space and the integrals which compute the conversion coefficients of outgoing spherical harmonics into incident spherical harmonics after a seabed reflection. A very efficient and accurate method of computing these integrals, using the method of complex images, is derived. Numerical comparisons with the exact integral expressions show the accuracy of this approach.