Fast and accurate traveltime computation for quasi-P waves in anisotropic media is an essential ingredient of many seismic processing and interpretation applications such as Kirchhoff modeling and migration, microseismic source localization, and traveltime tomography. Fast-sweeping methods are widely used for solving the anisotropic eikonal equation due to their flexibility in solving general equations compared to the fast-marching method. However, it has been observed that fast sweeping can be much less efficient than fast marching for models with curved characteristics and practical grid sizes. By representing a tilted transversely isotropic (TTI) equation as a sequence of elliptically isotropic (EI) eikonal equations, we determine that the fast-marching algorithm can be used to compute fast and accurate traveltimes for TTI media. The tilt angle is absorbed into the description of the effective EI model; therefore, the adopted approach does not compromise on the solution accuracy. Through tests on benchmark synthetic models, we test our fast-marching algorithm and discover considerable improvement in accuracy by using factorization and a second-order finite-difference stencil. The adopted methodology opens the door to the possibility of using the fast-marching algorithm for a wider class of anisotropic eikonal equations.

中文翻译：

---

倾斜横观各向同性介质的快速行进本征求解器

各向异性介质中准P波的快速准确行进时间计算是许多地震处理和解释应用程序（如Kirchhoff建模和偏移，微震源定位和行进时间层析成像）的重要组成部分。由于快速求解方法与快速行进方法相比具有求解通用方程的灵活性，因此广泛用于求解各向异性方程。但是，已经观察到，对于具有弯曲特征和实际网格尺寸的模型，快速扫描的效率可能比快速行进的效率低得多。通过将倾斜的横向各向同性（TTI）方程表示为椭圆各向同性（EI）方程方程的序列，我们确定了快速行进算法可用于计算TTI介质的快速且准确的传播时间。倾斜角被吸收到有效EI模型的描述中；因此，采用的方法不会影响求解精度。通过在基准综合模型上进行测试，我们测试了快速行进算法，并通过使用分解和二阶有限差分模板发现了准确性的显着提高。所采用的方法为将快速行进算法用于更广泛的各向异性各向异性方程组打开了可能。