A fast sweeping method based on discontinuous Galerkin method for the 3D factored eikonal equation

• Published in: Journal of applied geophysics Vol. 241; p. 105829
• Main Authors: Chen, Xin, Cao, Danping, Zhu, Zhaolin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2025
• Subjects: 3D factored eikonal equation; Discontinuous Galerkin method; Superconvergence phenomenon; The fast sweeping method; The fast sweeping method; Discontinuous Galerkin method; Superconvergence phenomenon; 3D factored eikonal equation
• ISSN: 0926-9851
• DOI: 10.1016/j.jappgeo.2025.105829

First-arrival traveltime calculation is a crucial matter of seismic processing and imaging. However, the large computational scale and complex velocity structures in 3D media challenge both the accuracy and efficiency of traveltime calculations. Particularly for the point-source conditions, source singularity can lead to inaccurate traveltime obtained by the eikonal solver, affecting its practical application effectiveness. To overcome these shortcomings, we construct a fast sweeping method (FSM) with the discontinuous Galerkin (DG) method and the factorization idea to calculate first-arrival traveltime accurately and efficiently. Under the fast iteration strategy of FSM, we first use the finite difference (FD) solver to calculate the traveltime, and then obtain the traveltime with second-order precision by using DG method. The advantage of DG solver is that it can obtain high-order accurate traveltime solutions on a more compact template by utilizing appropriate basis functions. For ease of calculation, we leverage the superconvergence phenomenon, where the numerical solution of FD solver is first-order accurate on its value and gradient, to simplify the formula of the DG solver, thereby obtaining an efficient second-order scheme. To overcome numerical error caused by source singularity, we use the addition factorization principle to decompose the unknown traveltime into two factors. One factor is specified to capture the source singularity, while the other is the correction term that is differentiable near the source. Numerical examples demonstrate that the proposed method can accurately and effectively solve the 3D eikonal equation, and the computational cost is lower than conventional FSM for a given accuracy. •A discontinuous Galerkin (DG) solver was constructed to solve eikonal equation.•The formula of DG solver was simplified using the superconvergence phenomenon.•Combining factorization idea to eliminate errors caused by source singularity.•The computational cost is lower than conventional FSM for a given accuracy.