垂向非均匀介质中的地震波旅行时近似

 地震反射波旅行时通常可用炮检距的各种级数形式近似表示，其精度随炮检距与深度比的增大而减小。本文讨论了四种垂向非均匀介质中地震波的时距曲线方程，分析比较了四类层状介质模型在不同速度函数近似下的射线路径和走时曲线误差；证明双曲线拟合的射线路径均方根误差远远大于其他几种速度模型拟合的射线路径的误差。慢度随深度线性变化和慢度随垂直单程旅行时线性变化的两种速度模型的旅行时近似式，适合于描述低速层速度变化较慢及高速层速度变化较快的地层结构；而速度随深度线性变化和速度随垂直单程旅行时线性变化的两种速度模型的旅行时近似式，适合于描述速度变化率较为平稳的地层结构。理论记录动校正结果表明：上述四种拟 合方式的动校正结果优于四次曲线拟合方式动校正结果。

Travel-time approximation of seismic waves in vertical heterogeneous media

The seismic reflection travel-times are often represented approximately by various progression forms of offsets and its precision decreases along with the increase of offset-to-depth ratio. The paper discussed four time-distance curve equation of seismic waves in vertical heterogeneous media; analyzed and compared the errors of ray paths and travel-time curves under the approximation of different velocity function in four layered media models;demonstrated that the mean-square-root errors of hyperbolic-fitted ray paths are much greater than that fitted by other several velocity model. The travel-time approximations in two kinds of velocity models: slowness being linear change with depth and with vertical one-way travel-time are suitable to describe the formation structure with slowly-changed velocity in low velocity layer and fast-changed velocity in high-velocity layer; but the travel-time approximations in two other kinds of velocity models: velocity being linear change with depth and with vertical one-way travel-time are suitable to describe the formation structure with stable change of velocities. The NMO results of theoretical records showed above mentioned NMO results of four fittings are superior to that by four-order curve fitting.