Directly estimating earthquake rupture area using second moments to reduce the uncertainty in stress drop

The key kinematic earthquake source parameters: rupture velocity, duration and area, shed light on earthquake dynamics, provide direct constraints on stress drop, and have implications for seismic hazard. However, for moderate and small earthquakes, these parameters are usually poorly constrained due to limitations of the standard analysis methods. Numerical experiments by Kaneko and Shearer demonstrated that standard spectral fitting techniques can lead to roughly one order of magnitude variation in stress-drop estimates that do not reflect the actual rupture properties even for simple crack models. We utilize these models to explore an alternative approach where we estimate the rupture area directly. For the suite of models, the area averaged static stress drop is nearly constant for models with the same underlying friction law, yet corner-frequency-based stress-drop estimates vary by a factor of 5-10 even for noise-free data. Alternatively, we simulated inversions for the rupture area as parametrized by the second moments of the slip distribution. A natural estimate for the rupture area derived from the second moments is A = pi LcWc, where L-c and W-c are the characteristic rupture length and width. This definition yields estimates of stress drop that vary by only 10 per cent between the models but are slightly larger than the true area averaged values. We simulate inversions for the second moments for the various models and find that the area can be estimated well when there are at least 15 available measurements of apparent duration at a variety of take-off angles. The improvement compared to azimuthally averaged corner-frequency-based approaches results from the second moments accounting for directivity and removing the assumption of a circular rupture area, both of which bias the standard approach. We also develop a new method that determines the minimum and maximum values of rupture area that are consistent with a particular data set at the 95 per cent confidence level. For the Kaneko and Shearer models with 20+ randomly distributed observations and similar to 10 per cent noise levels, we find that the maximum and minimum bounds on rupture area typically vary by a factor of two and that the minimum stress drop is often more tightly constrained than the maximum.