Surface variations effect on electrical resistivity measurement: Aroughness based approach

Electrical Resistivity Imaging technique requires accurately taking surface geometry into account during the inversion process to avoid artefacts. Some terrains (for example volcanology) or materials (at low scale) present important high frequency topography variations that common inversion software cannot take into account. Recent Digital Elevation Model (DEM) tools offer a high resolution that permit to image some characteristics of these rough surfaces. The aim of this paper is to examine the effect on the electrical measurement of different surface topography features at different DEM resolutions. For this purpose, we evaluate the effects on a micro and macro scale. We define mathematical criteria (based on geometrical roughness parameters) to analyse and generate surfaces and we simulate electrical measurements with a Finite Element Analysis code. An initial numerical study shows that roughness parameters play a key role in resistivity measurement. A second study performed on 30 limestone samples shows that a DEM resolution trade-off can be found based on geometrical roughness parameters. This study gives a rule of thumb to determine a resolution threshold for real survey data.