A Mimetic Finite-Difference Method for Two-Dimensional DC Resistivity Modeling

Nondestructive imaging and monitoring of the earth's subsurface using the geoelectric method require reliable and versatile numerical techniques for solving the governing differential equation. This work presents the first development of an algorithm for modeling two-dimensional direct current resistivity data based on the mimetic finite difference method. The mimetic finite difference method operator encompasses fundamental properties of the original continuum model and differential operator for a robust numerical algorithm. The proposed numerical scheme can simulate the response for an anisotropic model with irregular geometry having discontinuous physical properties. The developed algorithm's accuracy is benchmarked using the analytical responses of dyke models and a two-layer anisotropic model. The simulation result is compared with a published response for the variable topography case. The stability of the developed algorithm involving non-orthogonal grids is analyzed using a three-layer model. Non-orthogonal grids are generated by randomly perturbing the nodal coordinate of orthogonal grids. For these examinations, the maximum error in surface potential remains below 1.1% compared to the orthogonal grid simulation. Hence, the algorithm can simulate an accurate response of complex models such as rugged topography and anisotropic subsurface, and it is very stable concerning grid distortion.