Mitigation of installation-related effects for small-scale borehole-to-surface ERT

Abstract

Small-scale resistivity inhomogeneities can result from the local distribution of water and the water and nutrient uptake of plants. Measuring small-scale Electrical Resistivity Tomography (ERT) in the field comes with a set of particularities, especially when including borehole electrodes for a better resolution with depth. We apply small-scale borehole-to-surface ERT over a palaeochannel. Combining surface ERT with detailed borehole-to-surface ERT profiles along the measurement line allows a delineation of finer layering within the coarser lithology. Our field setup includes a borehole electrode tool with 20 ring electrodes, electrically coupled to the ground via a conductive mud. Two main points are addressed in this publication: (1) In the field, we electrically coupled the borehole electrodes to the ground by filling the cavities around the tool with a soil mud, i.e., we need to account for the unknown conductive borehole filling in the inversion. If not incorporated, the mud has a considerable influence on the resistivities close to the borehole tool, but also on the region around the surface electrodes. Consequently, alongside with a 3D inversion scheme representing the electrodes with the Complete Electrode Model (CEM), we include the mud as a separate and uncoupled region. We model the geometry of the mud layer around the tool and do not allow an influence of this region on the rest of the model. (2) Due to the small electrode distances and the overall small-scale nature of the array, the depth of installation of the borehole electrode tool must be known accurately in the inversion model. However, it is not easy to measure the tool depth in the field with the required accuracy, due to small-scale surface roughness, e.g., from a weathered loose soil layer at the surface or from vegetation. We also investigate the influence of a tilted tool installation and optimise for the depth and installation angle of the borehole tool before inverting for resistivities. An accurate knowledge of the borehole electrode positions is crucial for a reliable and precise inversion result. The surface electrodes establish a coordinate system around the borehole tool on the surface, with an angle φ describing the direction around the tool in the top view. The sensitive plane (in-plane) is defined as the x-z plane cutting through φ=0° and φ=180°. A tilting of the tool from the vertical direction is described by a tilting angle θ. A tilting of the borehole tool within the sensitive plane manifests in an increased misfit between data points on both sides of the tool, i.e., at φ=0° and φ=180°. We use this difference to optimise on the tool angle. The true depth of the borehole tool is found by searching for a minimum of the objective function, describing the goodness of the found model, while assuming different tool depths in each inversion. We see a minimum of the objective functionwhich can be attributed to the correct depth range, as shown by a synthetic study. Through our optimisations, we can determine a tilting of the tool, i.e., the angle θ, with an accuracy of 2° to 3° and the tool depth with an accuracy of a few centimetres, depending partially on the subsurface resistivities, i.e., our optimisation works mainly in predominantly horizontally layered soils. A tilting in directions out of the sensitive plane (out-of-plane) can be projected onto the sensitive plane, since the out-of-plane tilt has a negligible influence on the data. After this optimisation, we can determine layer resistivities from our field data.