Evaluation of Numerical Techniques for Accurate Solution of the Eikonal Equation in a 3D Subsurface Medium: A Basis for Training Machine Learning Models

Abstract

This work presents the numerical techniques FMM (Fast Marching Method) and FSM (Fast Sweeping Method), along with their high-accuracy versions: HAFMM (High Accuracy Fast Marching Method) and HAFSM (High Accuracy Fast Sweeping Method), for solving the Eikonal equation. The accuracy of the classical and high-accuracy methods is compared using a proposed quantitative metric. The performance of the methods is evaluated on two three-dimensional models: one homogeneous and another heterogeneous with sharp interfaces, allowing for an analysis of the robustness and accuracy of each approach in contexts of varying complexity. Finally, the generalization capability of machine learning models is assessed by approximating the solution of the Eikonal equation using the most accurate method found in a three-dimensional heterogeneous subsurface medium when trained on artificially perturbed data.