Borehole Resistivity Inversion

In this paper we perform the inversion of borehole resistivity data using the software package developed by Western Atlas Logging Services, Houston, TX. Direct current resistivity methods, namely lateral sounding and conventional laterolog methods, are the main interest in this paper. In resistive formations drilled with a conductive mud, where induction methods are not logged, it becomes imperative to combine these two methods in order to provide a reliable solution to the inversion problem. Lateral sounding provides comprehensive information about the resistivity distribution away from the borehole, while the higher resolution of the laterolog allows for detailed delineation of the formation. We perform the inversion computationally using the constrained least-squares Marquardt algorithm combined with singular value decomposition. The nonlinear inversion problem is linearized after each iteration of the Marquardt method. One of the main benefits of the algorithm is its ability to incorporate all resistivity/conductivity methods into a unique solution that is able to explain and satisfy all measurements. Several levels of inversion analysis are considered, from one-dimensional inversion to a rigorous and comprehensive two-dimensional approach. We demonstrate the method with multiple synthetic examples in which the algorithm successfully recovers the formation parameters. Different noise levels, resistivity contrasts, borehole conditions, and initial guesses are considered. We then apply the method to field data consisting of lateral sounding logs and laterologs. The inversion results are then checked against the available sampling data