Forward modelling of direct-current resistivity data on unstructured grids using an adaptive mimetic finite-difference method

Abstract

The interpretation of the massive amount of direct-current (DC) resistivity data acquired by modern distributed systems demands forward solvers which are capable of dynamically adapting the grid to ensure accuracy and efficiency, as well as being able to handle complex geology and topography, and general, arbitrary electrode layouts. Here, we present preliminary results of the forward modelling of DC resistivity data using adaptive cell-based and vertex-based mimetic finitedifference schemes. The mesh adaptivity involves an iterative h-refinement that starts with an initial coarse tetrahedral mesh and uses goal-oriented error estimators to mark the elements for refinement. The refinement is performed by the regular subdivision of the elements where two levels of nonconformity between the adjacent cells are allowed. Since arbitrary polyhedra are naturally permitted in the mimetic finitedifference method, the added nodes are not regarded as hanging nodes, and therefore, any modification of the scheme or extra refinement is avoided. By generating perfectly embedded grids, the presented schemes facilitate the application of multi-mesh techniques in the inversion of DC resistivity data. We demonstrate the effectiveness of the presented adaptive mimetic schemes using a buried-sphere model with an analytical solution. The numerical results for electrical potential and apparent resistivity from both mimetic schemes accurately approximate the analytical values. Furthermore, on similar grids, the vertex-based mimetic scheme is found to be less expensive than the cell-based scheme in terms of computation resources.