We calculate regional synthetic seismograms for a realistic structure model beneath Greenland, including surface topography and ice sheet thickness, for observations of the multinational GreenLand Ice Sheet monitoring Network (GLISN). The thick and heterogeneous Greenland ice sheet can cause distortion of the seismic waveforms observed at the GLISN stations on ice. We developed a numerical technique that calculates accurate regional seismic wavefields with low computational requirements. Here, we calculate the elastic wave propagation up to 2 Hz for four structural models of the Greenland ice sheet from a seismic source at various depths and with different mechanisms. Our computations for a realistic ice sheet model, the near-surface seismic source produced a very characteristic wave train with a group velocity smaller than the S-wavespeed in the ice, considered to be an ice-sheet guided S wave, developed by the superposition of post-critical reflections between the free surface and the ice bed. We named this wave "Le", analogous to the Lg wave, a crustally guided S wave. Furthermore, computation for a deeper seismic source resulted in reinforcement of the crustal Sg-coda wave with a group velocity range of similar to 3.1-2.6 km/s, which agrees with the characteristic waveform observed on the Greenland ice sheet. (C) 2014 Elsevier B.V. and NIPR. All rights reserved.