A general approach for DC apparent resistivity evaluation on arbitrarily shaped 3D structures

This paper presents a general and comprehensive way to evaluate the geometric factors used for the computation of apparent resistivities in the context of DC resistivity mapping and non-destructive investigations, in laboratory or in the field. This technique enables one to consider 3-dimensional objects with arbitrary shape. The expression of the geometric factor results from the early definition of apparent resistivitiy. It is expressed as the ratio of the resistances obtained from measurements to the resistances induced in the medium with unitary resistivity considering the same object geometry and electrode set-up. In this work, a finite element code is used for the computation of the geometric factor. In this code, the electrodes do not need to be located on the nodes of the mesh. This option makes the finite element mesh generation task easier. A first synthetical example illustrates how the present approach could be applied to apparent resistivity mapping in an environment with a complex underground topography. A second example, based on real data in a water tank, illustrates the simulation of a resistivity survey on a structure with finite extent, e.g. a laboratory sample. In both examples, topographic artefacts and effects of material sample shapes are successfully taken into account and reliable apparent resistivity descriptions of the structures are obtained. The effectiveness of the method for the detection of heterogeneities in apparent resistivity maps is highlighted.