Two-dimensional forward modeling of direct current resistivity method with line source based on one-dimensional finite difference method

Abstract We proposed an improved two-dimensional (2D) direct current (DC) resistivity numerical modeling method based on line sources. By applying a one-dimensional (1D) Fourier transform along the profile direction, we reduce the full 2D problem to a set of independent 1D partial differential equations in the wavenumber domain. These equations are solved with a finite-difference method accelerated by a tight-operator iterative scheme that significantly enhance computational efficiency and convergence velocity. A suite of numerical experiments confirms that our algorithm not only maintains the accuracy of simulation results but also exhibits superior convergence characteristics. Apparent-resistivity curves for a model of a circle in a half-space agree with analytical solutions to within 0.73%, and the algorithm remains stable for resistivity contrasts spanning 1:1000. Line-source responses exhibit systematically larger anomaly amplitudes than equivalent point-source responses, providing sharper detection of both high- and low-resistivity targets. Additionally, by comparing the anomaly responses of point-source and line-source models in both high-resistivity and low-resistivity geophysical scenarios, we demonstrate the line-source model’s heightened sensitivity to anomalies. The method delivers true 2-D line-source solutions with near-analytic precision and computational effort comparable to 1-D simulation, offering both an efficient field interpretation tool and new theoretical guidance for distinguishing line-source from point-source data.