3-D Modeling of Resistivity Devices
Resistivity logging plays a fundamental role in distinguishing between oil-saturated and water-saturated rocks. Accurate modeling of resistivity devices with complex electrode configurations in complicated borehole environments must take into account 3-D geometries. We present an efficient finite-difference solution to the dc modeling problem that can simulate resistivity devices in 3-D media. The algorithm uses a conjugate gradient solver with preconditioning. Examples indicate that the code is very accurate in the presence of very large contrasts in conductivity (up to 1011). Convergence of our iterative solver is excellent, but it is a function of conductivity contrast in the model. We present some applications of practical importance, including the response of a microresistivity tool to a tilted layer.