Accelerated Computation of Triaxial Induction Tool Response for Arbitrarily Deviated Wells in Planar-Stratified Transversely Isotropic Formations

In this letter, a new formulation for calculating an induction logging tool response in a multilayered transversely isotropic (also called uniaxial anisotropic) dipping formation is proposed. Using transmission line theory, only five independent integrals are necessary to form all the components of the dyadic Green's function in order to calculate the tool response, resulting in a more succinct and efficient formulation. The fast Hankel transform (FHT) is then employed to calculate these spectral integrals efficiently. In special cases, such as horizontal and vertical wells where the direct FHT fails, alternative approaches are proposed. A singularity extraction is implemented to handle the divergent integrals for a horizontal well, whereas the double-exponential integration rule is implemented for a vertical well. In order to speed up the computation, the spectral transmission line currents and voltages are precalculated and then stored in memory, and parallel computing using OpenMP is employed. Numerical examples demonstrate a speedup factor of more than two orders of magnitude compared with other reported results based solely on the FHT.