Methods for interpretation of tensor induction well-logging data in three-dimensional inhomogeneous geological formations

The electromagnetic (EM) induction method is one of the most powerful techniques for formation conductivity (or resistivity) evaluation. For a long time the basic interpretation model for induction logging was a cylindrically symmetrical model of rock formations surrounding a borehole. Currently there is growing interest in developing borehole EM induction methods capable of characterizing three-dimensional (3-D) conductivity distribution in the near borehole space. A Tensor Induction Well Logging (TIWL) instrument, which detects three components of magnetic field due to each of three transmitters, is proposed for 3-D imaging from a single borehole. A method of fast 3-D inversion of TIWL data is developed in this work.; To verify capability of 3-D TIWL data interpretation, sensitivity of the method is examined. The presented sensitivity study not only verifies the directional sensitivity of TIWL, but also provides useful information for designing the geometry of the TIWL instrument.; The main goal of the current work is to develop a method of efficient 3-D inversion of TIWL data from a single borehole. The proposed technique is based on the localized Quasi-Linear (LQL) approximation. The LQL approximation makes it possible to run forward and inverse problems at once for all the transmitters, which makes the inversion of the well-logging data much more efficient. The iterative LQL inversion is further introduced to control and improve the accuracy of the original LQL inversion technique. Tikhonov regularization theory is used to make the solution of the inversion problem stable. Both smooth and focusing stabilizing functionals are implemented in order to influence the solution towards the most desirable type of the model recovered by the inversion. Two minimization routines are adopted for the inversion of the TIWL data: Regularized Conjugate Gradient Method (RCGM) and Spectral Lanzcos Decomposition Method (SLDM).; The developed method of 3-D imaging from a single borehole and the corresponding computer code has been tested on synthetic TIWL data. It has been shown that 3-D TIWL inversion is applicable to a number of synthetic models close to real well-logging situations. TIWL interpretation provides unique information, which may not be available from the interpretation of other well-logging data.