3-DIMENSIONAL NONLINEAR INVERSION IN CROSS-WELL ELECTRODE LOGGING

Electrode logging as known in the oil industry is a method for determi ning the electrical conductivity distribution around a borehole or bet ween two boreholes from the static field (dc) measurements in the bore hole. In this paper we discuss the reconstruction of the conductivity in a three-dimensional domain between two boreholes. The electric curr ent density integral equation will be taken as point of departure to d evelop a nonlinear inversion scheme based on a new inversion method, t he so-called contrast source inversion method (CSI). The CSI method co nsiders the inverse scattering problem as an inverse Source problem in which the unknown contrast sources in the object domain are reconstru cted by minimizing the object and data error using a;conjugate gradien t Step, after which the contrast is updated by minimizing only the err or in the object. The robustness and the abilities of this full-vector three-dimensional inversion method have been demonstrated with a numb er of numerical examples where the synthetic ''measured'' data used we re generated by solving a forward scattering problem using the conjuga te gradient fast Fourier transform method.