Nonlinear inversion of the electrode logging measurements in a deviated well

We develop a nonlinear inversion method for reconstructing the 3-D electrical conductivity in a highly deviated well with invasion using electrode logging (static field) measurements. The integral equation is formulated in an oblique polar coordinate system so that the dipping-bed environment can be modeled without approximations. The computation time is dramatically reduced by using a nonuniform discretization grid in the direction away from the borehole. Moreover, the contrast source inversion method, which has been successfully applied to the electrode logging problem using a homogeneous background, has been modified so that the inhomogeneous background can be used without introducing a borehole Green's function. Numerical examples have shown that the present inversion method formulated in an oblique polar coordinate system can be used as an interpretation technique for the electrode logging measurements.