A Robust Geometric Factor for 3D ERT Based on a Field-Aligned Approach

Abstract

Apparent resistivity is a fundamental concept in electrical resistivity tomography (ERT), governed by the geometric factor. For non-collinear electrode configurations, especially in 3D surveys, a more consistent and robust formulation of the geometric factor is needed. We propose a generalized method using field-aligned virtual points—theoretical positions aligned with the electric field direction in a homogeneous half-space. These points are defined on a circle centered at the midpoint of a potential electrode pair, allowing the geometric factor to be formulated independently of electrode alignment. This method yields apparent resistivity values consistent with the true resistivity under homogeneous conditions, except near current electrodes where electric field curvature is significant. The proposed framework extends naturally to arbitrary and highly non-collinear electrode configurations, providing a robust foundation for apparent resistivity calculations in 3D ERT.