Efficient and Reliable Simulation of Multicomponent Induction Logging Response in Horizontally Stratified Inhomogeneous TI Formations by Numerical Mode Matching Method

An efficient and reliable numerical mode matching (NMM) method is developed to simulate the responses of multicomponent induction logging (MCIL) in the horizontally layered inhomogeneous transversally isotropic (TI) formations with the borehole and the invasion zone. The computation of MCIL responses is entirely transformed into three axially symmetrical problems on the Fourier harmonic components of the electromagnetic (EM) fields. The two extra singular differential operators about the horizontal EM components are introduced to describe the influence of the accumulation charge at the cylindrical interfaces on the EM fields excited by the horizontal magnetic dipoles. The first and second kinds of homogeneous boundary conditions of the different harmonic components of horizontal electrical fields near the borehole axis are derived to ensure that the EM problems become well posed in the cylindrical coordinate system. Then, the NMM is applied to solve the three axisymmetric problems with the extra singular differential operators. The numerical results demonstrate that the proposed method can accurately and efficiently simulate the MCIL responses in the horizontally layered TI formations with the large contrast resistivity.