For a spherical layered Earth model, by assuming that the medium parameters in each layer follow specific variation laws and introducing earth flattening transformation, the ordinary differential equations (ODEs) with variable coefficients in the spherical model are transformed into ODEs with constant coefficients that can be solved using the generalized reflection-transmission coefficient method (GRTCM), and the theoretical seismograms are calculated. Numerical results show that the generalized reflection-transmission coefficient method is accurate and efficient for computing theoretical seismograms at epicentral distances within 100 degrees. The error of the method will be significantly reduced as the layer thickness of spherical model is reduced. 

Synthetic theoretical seismograms, Generalized reflection-transmission coefficient method (GRTCM); earth flattening transformation

针对球状分层地球模型, 通过假设每层中的介质参数具有特定的变化规律并引入展平变换, 将球状模型中变系数的常微分方程组转化为可以使用广义反射–透射系数法(GRTCM)求解的常系数的常微分方程组, 并计算理论地震图。计算结果表明, 对于计算震中距在100°以内的理论地震图, 广义反射–透射系数法是正确且高效的。随着球状模型中层厚减小, 该方法的误差得到明显改善。