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Electromagnetic field response of triaxial induction logging tools in 1-D multi-layered anisotropic formations

As thick-layered oil reservoirs are gradually getting exhausted, detection and exploration of thin laminated reservoirs are becoming more and more important. Thin laminated sand-shale layers can be treated as transverse isotropic in bulk, characterized by the horizontal and vertical resistivity. The recently developed triaxial induction tool can detect formation anisotropy. In a traixial tool, three orthogonal transmitter and receiver coils oriented at three directions are used. The formation anisotropy responds to different components of the transmitter–receiver combinations, therefore the tool is able to measure formation resistivities with anisotropy. The measured data must be converted to the formation resistivities by inversion. Since the inversion process requires a repeated computation of the forward modeling, a fast forward modeling is essential to the inversion procedure. In this paper, we presented an 1D analytic method for the efficient simulation of traixial induction tools in multilayered transverse isotropic formations. This work is based on the previous work [1] with appropriate modifications and improvements. The coefficient propagator method is used to obtain the generalized reflection and transmission coefficients in each layer. The fast Hankel transform integration method is implemented to evaluate the highly oscillating integrals of the Bessel functions. The developed code has been verified by comparison with published data and is proved to work stably and accurately for dipping angles up to 89.9o and larger than 90o. For lower dipping angles, we further improve the efficiency of the code by using a modified Gauss-Laguerre quadrature with less sampling points instead of the fast Hankel transform to evaluate the integration without loss of accuracy.