Fast Multiparameter Reconstruction of Multicomponent Induction Well-Logging Datum in a Deviated Well in a Horizontally Stratified Anisotropic Formation

Abstract

In this paper, we advance a fast iterative inversion algorithm of multicomponent induction well-logging (MCIL) datum to simultaneously reconstruct a total model vector in a deviated well in the horizontally stratified transversally isotropic (TI) formation (TI medium) with the case-neglecting borehole. The model vector consists of the horizontal and vertical conductivities, the interface depth of each bed, and a borehole dipping angle. Because an electromagnetic field emitted by a horizontal magnetic dipole is no longer axially symmetrical, we first decompose the horizontal magnetic dipole located at borehole axis as the sum of two harmonics only so that the computation of MCIL responses can be entirely transformed into three axially symmetrical problems. Therefore, we solve them through the numerical mode matching method and obtain the semianalytic (SA) solution of an EM field in an arbitrary bed. Then, based on the perturbation principle and spatial distribution of formation conductivity related to the model vector, we set up an efficient SA algorithm of Frechet derivatives of the MCIL response with respect to the model vector. Then we extract an initial model from synthetic logs for the inversion through a special blocking technique. Finally, we give an iterative process to simultaneously reconstruct all model parameters from the logs through a combination of a normalization and singular value decomposition technique. Numerical tests validate the algorithms.