Synthetic seismograms for seismic waves penetrating near the inneroutercore boundary are implemented using the generalized ray method.The model takes into account the detailed velocity jump near the inneroutercore boundary and the possible depth dependent attenuation of theinner core.The source-side surface reflections,considered as the later phasesof the observed seismograms,are included in the model.The program developedin this study is suitable for the modeling of shallow and intermediatedeep events along the major seismic zones and the mid-ocean ridges.These areas provide good global coverage of ray paths for studying thestructure of the earth's core in detail.Numerical modeling in this studyshows that the source-side surface reflections of the core phases make asignificant contribution to determining the core velocity structure for theobservations of the spatial-dense array with small aperture.Additionally,the possible depth dependent inner-core attenuation can be resolved fromregional array seismograms.The results of this study show that the newlydeveloped generalized ray code displays a high potential for further elucidatingthe earth's core structure using the available data.