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