Abstract: The use of observational methods to investigate great earthquake rupture processes has been one of the most important tools to study earthquake rupture physics. This review article gave a fairly detailed description about the compressive sensing technique, a method based on sparse inverse theory, and its application in studying the spatial and temporal distribution of seismic radiation at different frequencies during great earthquake ruptures. In particular, the main results about the frequency- and depth-dependent seismic radiation during rupture processes of subduction zone megathrust earthquakes that were revealed by the compressive sensing technique were reviewed as well as its correlation with depth-dependent co-seismic slip and early aftershocks distribution. These may provide important observational results for understanding the frictional properties of the subducting slab interface and rupture mechanisms of subduction zone great earthquakes. Finally, the current status and future directions on studying earthquake rupture process using observational methods were discussed. Some perspective researches about the use of the compressive sensing technique for studying seismic radiation during earthquake ruptures were also discussed as well as its application in some other fields in seismology and geophysics.

Key words: earthquake rupture process, compressive sensing, seismic radiation, subduction zone megathrust earthquake