Application of transition matrix to scattering of elastic waves in half-space by a surface scatterer

A transition matrix formulism for the scattering problems of elastic waves using a surface scatterer of three-dimensional half-space is derived by applying Betti's third identity and orthogonality conditions. The basis functions and their corresponding regular parts are derived from Lamb's singular solutions. The new orthogonal functions are constructed based on the linear transform. The intrinsic properties of the scattering and transition matrices derived in this paper are investigated. Numerical results for verification are presented and discussed.

Research Highlights
► The T-matrix method for the scattering of a surface scatterer was proposed.
► A new set of orthogonal basis functions have been constructed.
► The properties of the scattering and transition matrices were investigated.
► Surface responses have been calculated numerically for some cases.