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Directly Estimating Rupture Area to Remove the Uncertainty in Stress Drop

Jeff J. McGuire, & Yoshihiro Kaneko

Published August 14, 2017, SCEC Contribution #7564, 2017 SCEC Annual Meeting Poster #052

The key kinematic earthquake source parameters: rupture velocity, duration and area, shed light on earthquake dynamics. They can 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 in the standard analysis methods. For instance, rupture velocity is typically assumed, and static stress-drop estimates often vary by 2-3 orders of magnitude in many datasets. Numerical experiments by Kaneko and Shearer [2014,2015] demonstrated that standard spectral fitting techniques can lead to roughly 1 order of magnitude variations in stress-drop estimates that result from variability in source geometry, rupture velocity, and rupture directivity but do not reflect the actual variability in stress drop.

We utilize these dynamic 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 (5% variation) because of identical dynamic stress drop values. Despite this underlying similarity, corner frequency based stress-drop estimates can vary by a factor of 5-10 even for noise free data. Instead, we simulated inversions for the rupture area as parameterized by the second moments of the slip distribution. A natural estimate for the rupture area derived from the second moments is A=LcWc, where Lc and Wc are the characteristic rupture length and width. This definition yields estimates of stress drop that vary by only 10% between the different models. The second moment based estimates are slightly larger than the true area-averaged values of the model (~6 MPa vs 5 MPa) owing to their weighted average nature. 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. The improvement compared to 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. Another advantage of the second moments approach is the ability to place limits on the acceptable range of rupture areas. We develop a new method that determines the minimum and maximum values of rupture area that are consistent with a particular earthquake at the 95% confidence level. For the Kaneko and Shearer models with 20+ randomly distributed observations and ~10% noise levels, we find that the maximum and minimum bounds on rupture area typically vary by a factor of two. Interestingly, the minimum stress drop is more tightly constrained than the maximum owing to the dependence of stress drop on rupture width.

Key Words
Stress Drop, Directivity

McGuire, J. J., & Kaneko, Y. (2017, 08). Directly Estimating Rupture Area to Remove the Uncertainty in Stress Drop. Poster Presentation at 2017 SCEC Annual Meeting.

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