A hybrid topography-dependent eikonal solver for accurate and efficient traveltime computation in heterogeneous media with acoustic tilted orthorhombic anisotropy

Abstract

Accurate traveltime computation in 3D acoustic tilted orthorhombic (TOR) media is more challenging than in transversely isotropic media with a tilted symmetry axis (TTI), requiring enhanced numerical stability and precision for complex geological scenarios. We propose a hybrid eikonal solver for 3D traveltime calculation that effectively handles TOR anisotropy and complex topography through several numerical strategies. Our approach first employs boundary-conforming grids to precisely represent irregular surface geometries and then applies a systematic coordinate transformation to derive a topography-dependent eikonal equation (TDEE) in curvilinear coordinates. To address the inherent numerical instability caused by the sixth-order nonlinearity in TOR eikonal equations, we develop a comprehensive solution framework integrating (1) a fixed-point iteration mechanism that transforms the TDEE into a series of tilted elliptical anisotropic subproblems; (2) a secondorder Godunov upwind discretization enhanced by a locking sweeping strategy for efficient wavefront propagation; and (3) a factorization scheme to reduce numerical errors near the source singularity. Through systematic verification on challenging 3D models, our method demonstrates high computational accuracy and stable performance for the range of anisotropy parameters considered in the main numerical examples, including cases with rugged topography and strong heterogeneity.