Intelligent meshing technique for 2D resistivity inverse problems

Abstract

In geophysical inverse problems, an a priori structured mesh is often used for inversion and mesh refinement is applied if needed by the user after observation of inversion results. We have developed a new intelligent self-adaptive unstructured finite-element meshing technique for electrical resistivity tomography inverse problems. This new approach uses Harris corner-and-edge detectors that are based on the local autocorrelation function of 2D distribution of pixels. This meshing technique optimizes the size of the inverse problem by refining areas where variations in the physical property structure are sensed to be important. The meshing technique also generates a more appropriate and optimum mesh for the inverse problem that is dependent on the problem itself. Tests on modeled data have demonstrated that the proposed intelligent meshing technique can reduce data misfit, produce a better reconstruction of the true physical properties, and minimize the size of the inverse problem. The synthetic model consists of a conductive dike in a resistive medium. By applying the proposed intelligent meshing technique, the inverse model of the dike is very similar to the inverse model produced using fine meshes, and it is also better reconstructed than the inverse model produced using conventional meshes. We have also applied the intelligent meshing technique to survey data collected for groundwater-saltwater mapping and characterizing the subsurface conductive structure with topography included. Our results indicate that the new meshing technique can produce solutions that are comparable with standard meshing and fine meshing techniques, while optimizing the size of the inverse problem.