Rapid Simulation of Triaxial Induction Logging Responses in Layered Biaxial Anisotropic Media

This letter presents a concise and efficient method for simulating triaxial induction logging (TIL) responses in layered biaxial anisotropic (BA) media. Initially, a modified global amplitude propagation matrix algorithm is developed for the derivation of spectral scattered fields using a novel virtual boundary scheme. This innovation eliminates the necessity to separately handle the source-related and source-free boundaries, thereby simplifying the recursion. Subsequently, a polar coordinate based integral method is developed for the dual inverse Fourier transform. This method converts the original dual infinite integrals into a semi-infinite integral with a definite one. By leveraging the smoothness of spectral fields along the polar angle direction, the definite integral is accurately computed with minimal integral points in conjunction with linear interpolation technique. The semi-infinite integral is then calculated utilizing quadrature-with-extrapolation (QWE) algorithm, resulting in reduced integral points and controllable precision. Compared to traditional methods, the new method significantly improves the simulation speed of TIL responses in layered BA media, laying a solid foundation for the rapid inversion.