射线追踪方程与程函方程的初至旅行时层析对比

Ray-tracing equation-based first-arrival traveltime tomography and eikonal equation-based first-arrival traveltime tomography

初至旅行时层析反演是目前应用最广泛的近地表建模方法。按照反演中正演算子的不同,可将基于射线理论的层析反演方法分为基于射线追踪方程与程函方程两类。本文分别从理论及数值测试上对两种方法在反演精度、计算效率等方面进行了系统的对比分析。结果表明:①两种方法可在统一的反演框架下推导得到,两者主要的差别均是由反演中正演算子的不同引起的;②两者具有相似的反演精度,由于后者的核函数是带限的,在复杂地区的层析反演中更加稳定;③前者的计算效率、内存占用等依赖于检波点个数,后者则依赖于模型大小,检波点稀疏时优选前者,否则优选后者;④前者具有射线密度等质控手段,后者缺少类似的质控手段。

The first-arrival traveltime tomographic inversion is the most widely used near-surface modeling method.According to the forward modeling operator in the inversion,the tomographic inversion based on the ray theory can be divided into two kinds of methods:based on the ray-tracing equation and based on the eikonal equation.In this paper,a detailed contrastive analysis of the two methods in terms of inversion accuracy and computational efficiency are carried out respectively in theory and numerical tests.The following observations are obtained:(1)The two methods can be deduced from the unified inversion framework.The main differences between the two methods are caused by the differences of the forward-modeling operators in the inversion;(2)The two methods have similar inversion accuracy.The kernel function of the second method is band-limited,so it is more stable in complex areas;(3)The computational efficiency of the first method depends on the number of receivers and the second method depends on the size of the model.So the first method is preferable when receivers are sparse.Otherwise,the second method is preferred;(4)The first method has lots of quality controls such as ray density,while the second method lacks similar quality controls.