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