Rapid 2-D/3-D crosshole resistivity imaging using the analytic sensitivity function

We develop a method to obtain 2-D/3-D resistivity images for crosshole dc electric measurements. This imaging procedure consists of two steps: (1) an approximate resistivity image is obtained using a simple projection based on the analytic form of the sensitivity function for the specified electrode array and a modified version of an inversion formula: (2) a final image may be obtained by nonlinear regularized inversion using the approximate resistivity image as the starting model. The imaging procedure is sufficiently flexible to handle different crosshole resistivity applications. Numerical experiments for 2-D and 3-D synthetic models show that the first step can give a satisfactory image of the target between the boreholes or underground when the background medium is uniform. For an inhomogeneous background, the approximate resistivity image is not as good but still conveys a reasonable outline of the resistivity structure. The procedure has no limitation on choice of electrode array (pole-pole, pole-bipole, bipole-pole, bipole-bipole) or field surveying configurations (surface-to-surface, surface-to-borehole, multiborehole crosshole). It may be applied in a routine way for processing crosshole electric data in various applications.