3D DC Modeling Based on PCG Using Background Field as Initial Value

This study addresses the issue of slow calculation in obtaining numerical solutions for 3-dimensional (3-D) Direct Current (DC) resistivity modeling. To improve the convergence rate of the traditional conjugate gradient (CG) method, we propose a new approach that uses back-ground potential as its initial value. By selecting an appropriate stopping criterion ε, our method achieves significantly faster convergence rates than the traditional CG method. We conducted experiments with several models and parameters, and found that the preconditioned CG method with initial value is more stable and requires fewer iterations to achieve the same level of precision. Moreover, when the stopping criterion ε is set to 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−5</sup>, our method achieves a computational speed increase of 2 to 5 times over the conventional method.