Despite recent advances in High Performance Computing (HPC), numerical simulation of high frequency (e.g. 1 Hz or higher) seismic wave propagation at the global scale is still prohibitive. To overcome this difficulty, we propose a hybrid method to efficiently compute teleseismic waveforms with 3-D source-side structures. By coupling the Spectral Element Method (SEM) with the Direct Solution Method (DSM) based on the representation theorem, we are able to limit the costly SEM simulation to a small source-side region and avoid computation over the entire space of the Earth. Our hybrid method is benchmarked against 1-D DSM synthetics and 3-D SEM synthetics. We also discuss numerical difficulties in the implementation, including slow DSM convergence near source depth, discretization error, Green’s function interpolation and local 3-D wavefield approximations. As a case study, we apply our hybrid method to two subduction earthquakes and show its advantage in understanding 3-D source-side effects on teleseismic P-waves. Our hybrid method reduces computational cost by more than two orders of magnitude when only source-side 3-D complexities are of concern. Thus our hybrid method is useful for a series of problems in seismology, such as imaging 3-D structures of a subducting slab or a mid-ocean ridge and studying source parameters with 3-D source-side complexities using teleseismic waveforms
