We incorporate topography into the 2D resistivity forward solution by using the finite-difference (FD) and finite-element (FE) numerical-solution methods. To achieve this, we develop a new algorithm that solves Poisson’s equation using the FE and FD approaches. We simulate topographic effects in the modeling algorithm using three FE approaches and two alternative FD approaches in which the air portion of the mesh is represented by very resistive cells. In both methods, we use rectangular and triangular discretization. Furthermore, we account for topographic effects by distorting the FE mesh with respect to the topography. We compare all methods for accuracy and calculation time on models with varying surface geometry and resistivity distributions. Comparisons show that model responses are similar when high-resistivity values are assigned to the top half of the rectangular cells at the air/earth boundary with the FE and FD methods and when the FE mesh is distorted. This result supports the idea that topographic effects can be incorporated into the forward solution by using the FD method; in some cases, this method also shortens calculation times. Additionally, this study shows that an FD solution with triangular discretization can be used successfully to calculate 2D DC-resistivity forward solutions.

In this study, we suggest the use of a finite difference (FD) forward solution with triangular grid to incorporate topography into the inverse solution of direct current resistivity data. A new inversion algorithm was developed that takes topography into account with finite difference and finite element forward solution by using triangular grids. Using the developed algorithm, surface topography could also be incorporated by using triangular cells in a finite difference forward solution. Initially, the inversion algorithm was tested for two synthetic data sets. Inversion of synthetic data with the finite difference forward solution gives accurate results as well as inversion with finite element forward solution and requires less CPU time. The algorithm was also tested with a field data set acquired across the Kera fault located in western Crete, Greece. The fault location and basement depth of sedimentary units were resolved by the developed algorithm. These inversion results showed that if underground structure boundaries are not shaped according to surface topography, inversion using our finite difference forward solution with triangular cells is superior to inversion using our finite element forward solution in terms of CPU time and estimated models.

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