Exploring the uncertainty range of coseismic stress drop estimations of large earthquakes using finite fault inversions

A new finite fault inversion strategy is developed to explore the uncertainty range for the energy based average coseismic stress drop ((Delta tau(E)) over bar) of large earthquakes. For a given earthquake, we conduct a modified finite fault inversion to find a solution that not only matches seismic and geodetic data but also has a (Delta tau(E)) over bar matching a specified value. We do the inversions for a wide range of stress drops. These results produce a trade-off curve between the misfit to the observations and (Delta tau(E)) over bar, which allows one to define the range of (Delta tau(E)) over bar that will produce an acceptable misfit. The study of the 2014 Rat Islands M-w 7.9 earthquake reveals an unexpected result: when using only teleseismic waveforms as data, the lower bound of (Delta tau(E)) over bar (5-10 MPa) for this earthquake is successfully constrained. However, the same data set exhibits no sensitivity to its upper bound of (Delta tau(E)) over bar because there is limited resolution to the fine scale roughness of fault slip. Given that the spatial resolution of all seismic or geodetic data is limited, we can speculate that the upper bound of (Delta tau(E)) over bar cannot be constrained with them. This has consequences for the earthquake energy budget. Failing to constrain the upper bound of (Delta tau(E)) over bar leads to the conclusions that (1) the seismic radiation efficiency determined from the inverted model might be significantly overestimated and (2) the upper bound of the average fracture energy EG cannot be constrained by seismic or geodetic data. Thus, caution must be taken when investigating the characteristics of large earthquakes using the energy budget approach. Finally, searching for the lower bound of (Delta tau(E)) over bar can be used as an energy-based smoothing scheme during finite fault inversions.