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在地震波场中,初至波到时信息由于初至震相可追踪、易识别性,在地震学领域占有重要的位置,广泛地应用于叠前偏移、叠前速度分析、地震走时层析成像及地震定位等.本文主要介绍了四类具有代表性的计算初至波走时的方法:(1)基于高频近似射线理论方法,如最短路径方法(SPM),及修正后的最短路径方法(MSPM);(2)基于程函方程的数值解方法,如有限差分方法(FD)、快速推进法(FMM)和快速扫描法(FSM);(3)基于惠更斯原理的波前构建法(WFC);(4)基于频率域波动方程数值解法(FWQ).最短路径方法计算精度较高,稳定性较好,但其需要采用更多的网格节点,因此计算效率低;程函方程数值解法无需计算射线路径,具有计算效率高、稳定性较好、易于实现等优势,但其计算精度较低,可以通过引入高阶差分格式得到提高;波前构建法计算精度高,稳定性好,但其需要在射线网格和规则网格之间做网格转换,因此计算效率较低;频率域波动方程方法能适应任意复杂介质,但其计算精度和计算效率较低.
In the seismic wave field, the information of the first arrivals arrives at the first arrivals due to its traceability and identifiability during the first arrival. It occupies an important position in seismology and is widely used in prestack migration, prestack velocity analysis, seismic traveltime tomography Imaging and seismic location, etc.This paper mainly introduces four representative methods of calculating the first-arrival traveltime: (1) Based on the high-frequency approximate ray theory, such as the shortest path method (SPM) and the modified shortest path method (MSPM); (2) numerical solution methods based on the equation of equations, such as finite difference method (FD), fast forward method (FMM) and fast scanning method (WFC); (4) Numerical solution of wave equation based on frequency domain (FWQ). The shortest path method has higher accuracy and stability, but it needs more mesh nodes and therefore has lower computational efficiency. Numerical solution of equations does not need to calculate the ray path, which has the advantages of high computational efficiency, good stability and easy to implement, but its computational accuracy is low, which can be improved by introducing high-order difference scheme. The wavefront construction method has high computational accuracy and stability Well, but it requires a grid of rays and a regular grid Between the mesh do conversion, thus a lower computational efficiency; frequency-domain method for the wave equation can adapt any complex medium, but its low accuracy and computational efficiency.