Inversion of electromagnetic logging measurements using an oblique coordinate system

Electromagnetic logging methods as known in the oil industry are methods for determining the electrical conductivity distribution around a borehole from the low frequency field measurements (either electrode or induction logging). The authors study the reconstruction of the three-dimensional (3D) conductivity around a borehole in a highly deviated formation with invasions. In most available methods, the dipping bed environment is approximated using the staircase discretization grid. In contrast, they have modeled the dipping bed environment using an oblique coordinate system. This coordinate system has a vertical axis, which is defined to coincide with the borehole axis. By using this oblique coordinate system, they have obtained some advantageous above the usual approaches. Firstly, the use of staircase discretization grid can be avoided. This means that the discretization errors can be reduced, and the authors can suffice with less discretization grid to obtain the results with the same degree of accuracy of the problem formulated in the Cartesian coordinate system. Secondly, the contrast source inversion (CSI) method based on the integral equation formulated in the oblique coordinate system allows us to include some a priori information about the conductivity distribution in a simple fashion