hp-HGS strategy for inverse 3D DC resistivity logging measurement simulations

In this paper we present a twin adaptive strategy hp-HGS for solving inverse problems related to 3D DC borehole resistivity measurement simulations. The term “simulation of measurements” is widely used by the geophysical community. A quantity of interest, voltage, is measured at a receiver electrode located in the logging instrument. We use the self-adaptive goal-oriented hp-Finite Element Method (hp-FEM) computer simulations of the process of measurements in deviated wells (when the angle between the borehole and formation layers are < 90 deg). We also employ the hierarchical genetic search (HGS) algorithm to solve the inverse problem. Each individual in the population represents a single configuration of the formation layers. The evaluation of the individual is performed by solving the direct problem by means of the hp-FEM algorithm and by comparison with measured logging curve. We conclude the paper with some discussion on the parallelization of the algorithm.