A new semianalytical algorithm for rapid simulation of triaxial electromagnetic logging responses in multilayered biaxial anisotropic formations

A set of compact and stable formulas are developed for the computation of triaxial electromagnetic (EM) logging responses in multilayered formations with biaxial anisotropy. These formulas are based on a new global amplitude propagator matrix (GAPM) algorithm, which derives the amplitudes of upgoing/downgoing waves at the boundaries rather than the reflection/transmission coefficients of each layer. The kernel of the GAPM algorithm is assembling the local continuity equations into a global linear system, which has addressed the notorious overflow problems commonly encountered by the traditional coefficient propagator matrix approach. To fast and accurately convert the EM fields from the spectral domain into the spatial domain, an efficient twofold inverse Fourier transform (IFT) technique is established for the computation of triaxial EM logging responses. Two main techniques are developed to significantly improve the computation accuracy and speed of IFT. On the one hand, the spectral fields at the first integral quadrant can be used to express the fields at the other three quadrants. Consequently, the original twofold infinite integral is analytically simplified to a semiinfinite one and the computation cost can be reduced by three-fourths. On the other hand, a two-level subtraction scheme is developed to reduce the integral singularity. The first-level subtraction is achieved by separating the primary fields from the total fields. The second-level process includes subtracting the spectral scattered fields of an equivalent transverse isotropic (TI) layered medium, integrating the residual fields, and computing the spatial fields of the TI model. The subtractions on the primary and scattered fields can make the integral convergence increase by more than 10 orders of magnitude in favorable conditions. Numerical experiments demonstrate that the new semianalytical formulas are well suited for any dipping angle and an arbitrary number of layers, as well as for thin and thick formations. The modeling method is efficient and robust, which can provide a fast simulator for the interpretation of triaxial EM logging data.