Fast simulation of triaxial borehole induction measurements acquiredin axially symmetrical and transversely isotropic media

摘要

We introduce and successfully test an efficient method tosimulate triaxial borehole electromagnetic EM inductionmeasurements acquired in axially symmetrical and transverselyisotropic TI media. The method uses a Fourier seriesexpansion to express the azimuthal dependence of EMfields and the source term whereby the essentially 3D problemcollapses to a series of independent 2D problems. Each2D problem is solved with a semianalytic method that usesnormalized Bessel functions and normalized Hankel functionsto express the radial dependence of EM fields, therebyimproving numerical stability. In addition, use is made of amplitudeand slope basis functions to describe the longitudinaldependence of EM fields to avoid grid refinement in the vicinityof horizontal formation boundaries. For validation, wecompare the new simulation method to two 1D analyticmethods in horizontally and radially layered formations, andto one 3D finite-difference method 3DFD in multilayeredformations that include borehole and invasion zones. Numericalresults indicate that the method is accurate in formationswith high conductivity contrasts compared to 1D methodsand is more than ten times more efficient than the 3DFDmethod in multilayer formations.