椭球坐标系下多震相地震射线追踪

Multiple-phase seismic ray tracing in ellipsoidal coordinates

地震射线追踪方法技术在地震学领域有着较为广泛的应用,然而大多数算法建立在直角坐标系或球坐标系下,实际地球并非完美的球体,而是两极略扁的椭球体,因此,球坐标系下计算结果与真实情况存在一定误差.传统的做法一般是在球坐标系下进行计算,而后进行椭球校正.本文提出了一种直接在椭球体模型中采用分区多步最短路径算法进行多震相地震射线追踪的方法技术,实现了椭球坐标系下多震相地震波射线路径追踪和走时计算.与解析解的对比表明:该算法具有较高的计算精度,适用于任意形状的椭球体,且不需要进行额外的走时校正.数值模拟结果表明,计算所得P波和PcP反射波的走时与AK135走时表的误差小于0.1 s.当震中距较大时,使用球对称模型和椭球体模型计算所得的走时差异显著,说明采用椭球坐标系的必要性.

Seismic ray tracing technology is widely used in seismology, and most of the algorithms are executed in Cartesian coordinates or spherical coordinates system. However, the actual earth is not a perfect sphere but rather an ellipsoid, which caused that the result calculated in spherical coordinate system is different from the actual situation. In general, traveltime was calculated in spherical coordinates, and then ellipsoid correction should be done. In order to overcome the deficiency of current algorithms, models were described in ellipsoidal coordinate system and the multistage shortest-path method was adopted to trace raypath and calculate traveltime of multi-phase seismic wave.The algorithm is suitable for any shape ellipsoid, and it does not need to carry out additional traveltime correction, which can reduce the calculation. The results of numerical simulation show that the difference between traveltimes of P/PcP wave and AK135 traveltime tables is less than 0.1 s. Furthermore there is a significant difference between the results of the spherically symmetric model and the ellipsoidal model when the epicenter distance is large, which further reflects the necessity of adopting the ellipsoidal coordinates system.