Physical explanations on the observations

1. Relation between the backprojection images and earthquake source kinematics on the fault (see here)

Although the BP methods have been successful in studying large earthquakes, the physical interpretations of the BP results are still not clear. All those previous comparisons between independent methods are qualitative. The explanation of BP with respect to energy is probably not incorrect, but is limited by the perspective of seismic signal processing instead of source physics. Obviously, better understandings on the BP images and their relation to the physics of earthquake rupture is significant and highly needed. In this study, we start from the theoretical formulation of the BP images, which is linear in the frequency domain, and carry on a synthetic exercise in a homogeneous fullspace. We find that the fundamental linear formulation of the BP method is most correlated with the true kinematic source properties: the images \(\mathbf{U_{BP}}(\omega)\) from linear BP is a snapshot of the slip motion \(\mathbf{U}(\omega)\) on the fault plane after a spatial smoothing with a frequency-dependent resolution matrix \(\mathbf{F}(\omega)\):

\(\mathbf{U_{BP}}(\omega) =\mathbf{F(\omega)}\mathbf{U}(\omega)\)

This direct relation between BP image and source kinematics helps to better understand and interpret the BP observations of the real earthquake rupture. For more details, please see Yin and Denolle (2019 GJI).

BP results of kinematic source

 

2. Dynamics implied from the earthquake source time functions

We developed different methods to extract physical information from a large population of earthquake source time functions (mainly the SCARDEC source time function database). Decomposing (please see here) and clustering (please see here) source time functions provides us a lot of new observations. Comparing with the results from real STFs and those from dynamic simulations, we find that the population behaviors of source time functions are closely related to earthquake dynamics and might be helpful to constrain the source heterogeneity. We are currently working on the relavent papers and will be updated soon.

STF
Left: Clustering for the SCARDEC source time functions. G1-G4 corresponds to STF groups with increasing complexity. Right: Clustering for the STFs from dynamic simulations.