Intelligent Meshing For Geophysical Inverse Problems Using Unstructured Meshes

Mesh generation to solve geophysical forward problems is a thoroughly studied area that has seen the development of many methods and techniques. In geophysical inverse problems, a priori structured mesh is often used for inversion because the geometry of the underlying subsurface structures is unknown and mesh refinement is applied if needed by the user only after observing the inversion results. We present an intelligent meshing approach for an electrical resistivity tomography inverse problem. This new approach uses the Harris corner and edge detectors that are based on the local autocorrelation function of a signal (Harris and Stephens, 1988). The process optimizes the size of the inverse problem by refining areas where the boundaries of physical structure seems to be important and generates a more appropriate and optimum mesh for the inverse problem. The performance and robustness of the proposed algorithm are determined through a series of tests using 2D ERT modelled data and survey data. Tests on modelled data have demonstrated that the proposed meshing technique can reduce data misfit, produce a better model reconstruction, minimize the size of the inverse problem and reduce computational resource requirement. Tests on survey data from application such as ground water mapping have demonstrated that this new meshing approach produced data fit and inverse solutions that are comparable to conventional meshing and fine meshing techniques while minimizing the size of the inverse problem.