Finite Difference Resistivity Modeling on Unstructured Grids with Large Conductivity Contrasts

The 3-D geo-electrical forward problem solved with a finite difference approach faces several difficulties. Besides the singularity at the source location, major issues are caused by the definition of the computational domain to match a particular topography, and by high conductivity contrasts. To address these issues, we combine here two methods. First, we implement a specific finite difference method that takes into account specified interfaces in elliptic problems. Here, the contrasts are defined along grid lines. Second, we extend the method to unstructured meshes by integrating it to the generalized finite difference technique. In practice, once the conductivity model is defined, the approach does not need to explicitly specify where the large contrasts are located. Several numerical tests are carried out for various Poisson problems and show a high degree of accuracy.