多层垂直对称轴横向各向同性介质精确走时计算

Exact traveltime computation in multi-layered transversely isotropic media with vertical symmetry axis

给出了计算多层垂直对称轴横向各向同性(VTI)介质精确射线路径和走时的方法,所用的体波相速度公式、群速度公式和Snell定律都是严格的显式解析公式.任意基本波的射线路径和走时计算问题都可以转化成一个等效的透射问题,再用文中的公式来计算,具体实现方法用一个多次波和一个首波的实例给出.最后分别用精确公式和Thomsen近似公式计算了相同模型相同基本波的走时曲线.比较两者计算结果可发现,近似公式反复使用会使误差积累,同时揭示了近似公式适用范围的局限性,强调了使用近似公式需要注意其适用范围的重要性.

An approach to calculate accurate ray-paths and traveltimes in multilayered VTI media （transversely isotropic media with a vertical symmetry axis） is proposed. The expressions of phase velocity, used for computation are all explicit and exact, group velocity and Snell＇s law For a given elementary wave, the calculation of ray-paths and travettimes can be transformed into an equivalent refraction problem, which is easy to solve, The process of implementation is introduced by a multi-arrival example and a head-wave example. Finally, traveltime curves for the same models and same elementary waves are calculated by using the exact formulae and the Thomsen＇s approximations, respectively. A comparison between the two results shows the effect of increasing errors arising from the repeated use of approximations and reveals the limitation in applicable range of the approximation approach. It is stressed in this paper that researchers should pay much attention to the applicable range of an approximation approach.