中文摘要：

在利用实际地震资料反演地球内部结构时，群速度往往比相速度更有意义．本文在水平层状均匀介质模型中，用快速广义反射透射系数方法（Pei，2008）计算了基阶瑞雷面波的群速度，并推导了Chen（1993）4×4层矩阵E的逆的解析表达式．文中用数值实验的方法合成了两个典型模型的群速度频散曲线，并与复合矩阵方法计算的结果进行了对比，结果表明本文的方法是切实可行的，与广义反射透射系数方法相比明显地提高了计算效率，尤其是在高频、层厚度大和层数多的情况下表现得更为突出．

英文摘要：

Group velocities of surface waves are more significative than phase velocities when we inverse the structure of the earth＇s interior by seismic data. In this study ,we calculate the group velocity of Rayleigh waves based on the Fast Generalized R/T coefficient Method （FGRT） developed by Pei （2008）, for the homogeneous horizontal multilayered model and present an analytic solution for the inverse of the 4 ×4 layer matrix E in the traditional generalized R/T coefficient method of Chen（1993）. Dispersion curves of two typical models are computed by numerical experiments, whose results are compared with the compound matrix method. It demonstrates that our method is feasible. Compared with the Generalized R/T coefficient method（Chen 1993）, our research enhances the calculation efficiency greatly, especially in the cases of the high-frequency, thicker layers and more layers conditions.