中文摘要：

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.

英文摘要：

In the seismic wave field,the first arrival travel-time plays an important role in the field of seismology,which is due to the first arrival phases can be easily traced and identified.The seismic first arrival travel-time field is widely used in seismic prestack migration,velocity analysis,seismic traveltime tomography and earthquake location.This paper mainly introduces four typical seismic first arrival travel-time calculation methods,that is,（1）seismic ray method based on the high-frequency approximation,the commonly used methods are Shortest Path Method（SPM）and Modified Shortest Path Method（MSPM）;（2）the method based on the numerical solution of eikonal equation,which mainly include Finite Difference Method（FD）,Fast Marching Method（FMM）and Fast Sweeping Method（FSM）;（3）Wavefront Construction（WFC）method based on the Huygens principle;and（4）the method based on the frequency domain wave equation（FWQ）.The first one has higher computational accuracy and better stability,while it needs more grid points,which may result in low computational efficiency.The calculation of ray paths is not required in the second one,so it has advantages in computational efficiency,stability and realization,but the computational accuracy is lower,which can be improved by introducing the high-order finite difference scheme.The third one can calculate traveltime with high accuracy and stability,while it requires the grid transition between ray grid and regular grid,which may result in low computational efficiency.The last one can adapt any complex medium,but the computational accuracy and efficiency are lower.