In this thesis, we studied the earthquake process from a dual perspective: i.e. modeling the complex Earth medium and the earthquake dislocations at the source. These two fundamental aspects define the ground motion. Existing kinematic source models are essentially based on the low frequencies contained in the seismic signals (< 1 Hz). Due to our limited knowledge of the Earth medium, the high frequencies in the seismic signals are difficult to be modeled properly. In order to optimize our understanding of the complex earthquake rupture process, a synthesis of both the Earth medium and source model is required.

For modeling the complex Earth medium, we developed a tomographic method that exploits the ellipticity of the fundamental Rayleigh wave (ZH ratio). This method enables us to constrain the shear-wave velocity in a narrower target depth range than conventional methods. The ZH ratio method has been applied to the crust and upper mantle beneath the GEOSCOPE stations. The results show that low-velocity zones exist beneath some stations near hotspots.

The ZH ratio was applied to the L'Aquila basin area to constrain the shallow velocity structure prior to a kinematic source inversion of the 2009 L'Aquila earthquake. Because of differences in the slip models derived from seismological or geodetic data, we introduced a new strategy to differentiate between slip that occurs co-seismically and that occurs as early post-seismic afterslip. The results suggest that the co-seismic rupture was followed by a slow-slip event with significant moment release in the first day.

Lastly, we discussed the development of a back-propagation method to map high-frequency spatial-temporal seismic wave radiation sources onto the fault plane. The new approach considers the free surface reverberations and the fault geometry while existing methods doesn't. Based on results from a synthetic test, we demonstrate that the new back-propagation method is better than existing back-projection method because it not only can locate the spatial-temporal locations of the target sources but also can fairly well recover their amplitudes.