各向异性强反差介质中初至走时精确计算的混合程函求解器
A hybrid eikonal solver for accurate first-arrival traveltime computation in anisotropic media with strong contrasts
摘要：
初至走时计算在走时层析成像、克希霍夫偏移等应用中具有重要意义。传统程函求解器存在两个主要问题：震源奇异性问题和复杂介质中数值精度不足。一些现有的程函求解器也表现出在介质中的稳定性问题，在介质属性的强烈对比。我们开发了一个稳定和准确的混合程函求解器的二维和三维横向各向同性介质与倾斜对称轴（TTI，或倾斜横向各向同性介质）。我们的新程函求解器结合了走时场分解技术，三阶Lax-Friedrichs更新方案，和一种新的方法来计算基走时场。求解器具有以下三个优点。首先，不需要在近源区域分配精确的走时值，并且即使对于具有强各向异性的TTI介质，源位置附近的计算走时场也是准确的。其次，计算的旅行时场在空间上具有高阶精度。第三，求解器对于具有强各向异性、复杂结构和介质性质的强对比的2D和3D TTI介质是数值稳定的。我们验证了我们的混合程函求解器的稳定性和准确性，使用几个二维和三维TTI介质的例子。结果表明，我们的求解器是稳定和准确的二维和三维复杂TTI介质，产生的初至走时场是一致的全波场解决方案。
英文摘要：
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.
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