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First-arrival traveltime computation is crucial for many applications such astraveltime tomography, Kirchhoff migration, etc. There exist two major issuesin conventional eikonal solvers: the source singularity issue and insufficientnumerical accuracy in complex media. Some existing eikonal solvers also exhibitthe stability issue in media with strong contrasts in medium properties. Wedevelop a stable and accurate hybrid eikonal solver for 2D and 3D transverselyisotropic media with a tilted symmetry axis (TTI, or tilted transverselyisotropic media). Our new eikonal solver combines the traveltime fieldfactorization technique, the third-order Lax-Friedrichs update scheme, and anew method for computing the base traveltime field. The solver has thefollowing three advantages. First, there is no need to assign exact traveltimevalues in the near-source region, and the computed traveltime field near thesource location is accurate even for TTI media with strong anisotropy. Second,the computed traveltime field is high-order accurate in space. Third, thesolver is numerically stable for 2D and 3D TTI media with strong anisotropy,complex structures, and strong contrasts in medium properties. We verify thestability and accuracy of our hybrid eikonal solver using several 2D and 3D TTImedium examples. The results show that our solver is stable and accurate in 2Dand 3D complex TTI media, producing first-arrival traveltime fields that areconsistent with full-wavefield solutions.

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