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In this article, we are the first to formulate the direct and inverse problems of resistivity logging on determining the components of the electrical resistivity tensor of rocks from a set of high-frequency induction and lateral logging sounding measurements. Using a finite element approximation, high-order hierarchical basis functions, computationally efficient multilevel methods and a multistart algorithm with the DFO-LS local optimization method, we investigate the capability of reconstructing the horizontal and vertical resistivity components, as well as the tilt of the resistivity tensor principal axes with regard to the study of complex geological objects. A separate consideration is given to a realistic generalized geoelectric model of the unique hydrocarbon source with hard-to-recover reserves, the Bazhenov Formation.

journal of inverse and ill-posed problems

Joint inversion of high-frequency induction and lateral logging sounding data in earth models with tilted principal axes of the electrical resistivity tensor