Geophysics and Geophysical Exploration ISSN:1229-1064(Print) 2384-051X(Online) 지구물리와 물리탐사

Apparent resistivity is one of the most fundamental quantities used in the processing and interpretation of electrical resistivity tomography (ERT) data, and is determined by the geometric factor. However, when survey lines are not straight or when non-collinear electrode configurations are used in three-dimensional (3D) surveys, a generalized definition of the geometric factor is required. In this study, a generalized geometric factor is proposed using primary field-aligned virtual points, which are defined to align 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 consistently regardless of electrode orientation or survey-line geometry. Analytical verification shows that, except in limited regions near the current electrodes where electric-field curvature is large, the proposed method yields apparent resistivity values that are nearly identical to the true resistivity under homogeneous conditions. The proposed method provides a generalized basis for apparent resistivity calculations in 3D ERT with arbitrary electrode configurations.