Nonlinear Inversion in Electrode Logging in a Highly Deviated Formation with Invasion Using an Oblique Coordinate System.

摘要

Electrode logging as known in the oil industry is a method for determining the electrical conductivity distribution around a borehole or between two boreholes from the static field (dc) measurements in the borehole. In this paper we discuss the reconstruction of the three-dimensional conductivity around a borehole in a highly deviated formation with invasion. To solve this problem the full-vector analysis is required. In most available algorithms, for the forward and inverse modeling of the resistivity data, the dipping bed environment is approximated using the staircase discretization grid and/or the effect of dip is modeled by taking a linear combination of vertical and horizontal dipoles. In contrast, we have modeled the effect of dip by introducing an oblique (non-orthogonal) coordinate system such as the staircasing approximation for the dipping-bed environment can be avoided. Furthermore, the structure of the Contrast Source Inversion method in this non-orthogonal coordinate system allows us to include the a priori information about the conductivity distribution easily. Several numerical results are presented to demonstrate the performance of the inversion method using the synthetic 'measured' data which are generated by solving a forward scattering problem numerically with the help of the Conjugate Gradient Fast Fourier Transform method.