Abstract: We develop a methodology that combines compressive sensing backprojection (CS-BP) and source spectral analysis of teleseismic P waves to provide metrics relevant to earthquake dynamics of large events. We improve the CS-BP method by an autoadaptive source grid refinement as well as a reference source adjustment technique to gain better spatial and temporal resolution of the locations of the radiated bursts. We also use a two-step source spectral analysis based on (i) simple theoretical Green's functions that include depth phases and water reverberations and on (ii) empirical P wave Green's functions. Furthermore, we propose a source spectrogram methodology that provides the temporal evolution of dynamic parameters such as radiated energy and falloff rates. Bridging backprojection and spectrogram analysis provides a spatial and temporal evolution of these dynamic source parameters. We apply our technique to the recent 2015 Mw 8.3 megathrust Illapel earthquake (Chile). The results from both techniques are consistent and reveal a depth-varying seismic radiation that is also found in other megathrust earthquakes. The low-frequency content of the seismic radiation is located in the shallow part of the megathrust, propagating unilaterally from the hypocenter toward the trench while most of the high-frequency content comes from the downdip part of the fault. Interpretation of multiple rupture stages in the radiation is also supported by the temporal variations of radiated energy and falloff rates. Finally, we discuss the possible mechanisms, either from prestress, fault geometry, and/or frictional properties to explain our observables. Our methodology is an attempt to bridge kinematic observations with earthquake dynamics.