A hybrid eikonal solver for accurate first-arrival traveltime computation in anisotropic media with strong contrasts

TL;DR

This paper introduces a stable, high-accuracy hybrid eikonal solver for 2D and 3D anisotropic media with strong contrasts, improving traveltime computation near sources and in complex structures.

Contribution

The paper presents a novel hybrid eikonal solver combining factorization, third-order Lax-Friedrichs scheme, and a new base traveltime method for anisotropic media.

Findings

The solver is stable in complex TTI media with strong contrasts.

It achieves high-order spatial accuracy in traveltime computation.

Results match full-wavefield solutions, confirming accuracy.

Abstract

First-arrival traveltime computation is crucial for many applications such as traveltime tomography, Kirchhoff migration, etc. There exist two major issues in conventional eikonal solvers: the source singularity issue and insufficient numerical accuracy in complex media. Some existing eikonal solvers also exhibit the stability issue in media with strong contrasts in medium properties. We develop a stable and accurate hybrid eikonal solver for 2D and 3D transversely isotropic media with a tilted symmetry axis (TTI, or tilted transversely isotropic media). Our new eikonal solver combines the traveltime field factorization technique, the third-order Lax-Friedrichs update scheme, and a new method for computing the base traveltime field. The solver has the following three advantages. First, there is no need to assign exact traveltime values in the near-source region, and the computed traveltime field near the source location is accurate even for TTI media with strong anisotropy. Second, the computed traveltime field is high-order accurate in space. Third, the solver is numerically stable for 2D and 3D TTI media with strong anisotropy, complex structures, and strong contrasts in medium properties. We verify the stability and accuracy of our hybrid eikonal solver using several 2D and 3D TTI medium examples. The results show that our solver is stable and accurate in 2D and 3D complex TTI media, producing first-arrival traveltime fields that are consistent with full-wavefield solutions.