A proposal for a horizontal vector approach in 3D electrical resistivity tomography and its associated geometric factor

Churl Hyun Jo 

Electrical resistivity tomography (ERT) is commonly implemented with collinear electrode arrays that measure only electric-field components along the survey line, neglecting horizontal variations in other directions. While this limitation is acceptable in 2D ERT, it can be significant in 3D settings with complex geometry and strong resistivity contrasts. To address this issue, we propose an approach to determining the total magnitude and direction of the horizontal electric field. Access to such vector information may provide a more representative characterization of the local surface response in complex 3D settings. Because this requires non-collinear measurements, a corresponding basis for consistent apparent-resistivity calculation is also needed. We therefore introduce a generalized geometric factor based on field-aligned virtual points (FAViPs), defined by the primary-field direction in a homogeneous medium, to provide a physically consistent basis for non-collinear horizontal measurements. Because these points are defined at an arbitrary measurement location, the resulting geometric factor can be applied to non-collinear electrode arrays in irregular survey geometries. By formalizing these basic physical principles, this work provides a theoretical basis for horizontal-vector measurements in 3D ERT. While practical implementation may be limited by current field logistics, this approach offers a theoretical option for 3D surveys involving complex environments where more flexible electrode configurations may be beneficial.