地震波走时场模拟的快速推进法和快速扫描法比较研究

A comparative study on the fast marching and fast sweeping methods in the calculation of first-arrival traveltime field

地震波走时信息在叠前偏移、叠前速度分析、地震层析成像、走时反演及地震定位等中都有重要应用.快速推进法因其理论完善、精确灵活,无条件稳定,近年来已在走时计算领域得到广泛应用.快速扫描法作为求解一阶非线性双曲型偏微分方程的高效方法,已在图像处理、计算机视图、控制论等领域得到有效应用,且在走时计算方面有所应用且展现了广泛的应用前景.本文介绍了两种方法的基本原理且(通过均匀介质模型、局部低速体模型和Marmousi模型)把两种方法做了详细对比.研究结果表明:1)基于逆风差分格式的快速推进法和快速扫描法对纵横向速度变化很大的不均匀介质依然有很好的稳定性和适用性,均可以准确地计算地震波初至走时;2)对于相同的模型和在相同的计算条件下,两种方法的精度相当,但快速扫描法所耗的CPU时间较快速推进法明显减少,效率显著提高.

Traveltime calculation plays an important role in many areas of seismology such as pre-stack migration,traveltime inversion,earthquake location and seismic tomography.The fast marching method has been widely used in traveltime calculation as it is accurate,flexible,and unconditionally stable.As an efficient tool in computing the numerical solution of a first order non-linear hyperbolic partial differential,the fast sweeping method has already had effective applications in optimal control,computer vision,geometric optics,path planning and seismology,etc.In this paper,we give a brief summarization on the fundamental theories of the two methods and make a comparative study（of the two methods） on the calculation of first-arrival traveltime field.Numerical examples show both the fast marching method and fast sweeping methods are applicable to media with strong velocity contrast;the accuracy of the two methods is considerable,but the CPU time consumed by the fast sweeping method is more less than that of the fast marching method,which may reveal that the efficiency has been improved significantly.