Coordinate-free Formulation and Evaluation of Tensor Green’s Functions for General Homogeneous Uniaxial Anisotropic Media

A coordinate-free formulation of four tensor Green’s functions for the general homogeneous uniaxial anisotropic lossless and/or lossy media is developed with the Fourier transformations. In the derivation of these formulas, the product to sum approach is introduced to evaluate the Fourier integrations. For the lossy media, the double-value problem, which is existed in calculating formula of Green’s functions, is effectively avoided by the radiation condition. With a way of finding limit, the pseudo-singularities problem of four Green’s functions, which has to be treated, is discussed deeply and resolved briefly. The robust and efficient computational procedure of Green’s functions is achieved with C++ operator overloading. Modeling results of the triaxial induction well-logging demonstrate efficiency of the computation of the coordinate-free formulas.