Modeling and inversion of azimuthal lateral resistivity logging

The three-dimensional finite element method (FEM) is employed to simulate the response of an azimuthal lateral sonde in a borehole surrounded by inhomogeneous formations. The results demonstrate that, if the formation inhomogeneity is not significant, the measured resistivities at different azimuths are close to true formation resistivities. When the formation inhomogeneity is significant, however, the measured resistivity (R_t) distribution at different azimuths could be substantially different from the true distribution. The measured R_t distributions tend to smear the contrasts between the lowest and the highest R_t values. The responses at high resistivity areas are much lower than the correspondent true values. It is necessary to correct for the measured resistivities in these cases. As an improvement to the traditional linear correcting methods in the inversions, a nonlinear inversion scheme is developed in this paper to calculate the true R_t distribution. The numerical results demonstrate the feasibility of this nonlinear method.