Aftershock modeling based on uncertain stress calculations

Abstract

[1] We discuss the impact of uncertainties in computed coseismic stress perturbations on the seismicity rate changes forecasted through a rate-and state-dependent frictional model. We aim to understand how the variability of Coulomb stress changes affects the correlation between predicted and observed changes in the rate of earthquake production. We use the aftershock activity following the 1992 M7.3 Landers (California) earthquake as a case study. To accomplish these tasks, we first analyze the variability of stress changes resulting from the use of different published slip distributions. We find that the standard deviation of the uncertainty is of the same size as the absolute stress change and that their ratio, the coefficient of variation (CV), is approximately constant in space. This uncertainty has a strong impact on the forecasted aftershock activity if a rate-and-state frictional model is considered. We use the early aftershocks to invert for friction parameters and the coefficient of variation by means of the maximum likelihood method. We show that, when the uncertainties are properly taken into account, the inversion yields stable results, which fit the spatiotemporal aftershock sequence. The analysis of the 1992 Landers sequence demonstrates that accounting for realistic uncertainties in stress changes strongly improves the correlation between modeled and observed seismicity rate changes. For this sequence, we measure a friction parameter As n % 0.017 MPa and a coefficient of stress variation CV = 0.95.

A new estimation of the decay of aftershock density with distance to the mainshock

“…On the basis of a similar model, the same conclusion is reached by Hainzl et al [2009Hainzl et al [ , 2010, in the particular case of the Landers earthquake (also studied by Richards-Dinger et al, unpublished): the distance distribution for the direct aftershocks of Landers is well fitted by a static stress and rate-andstate friction model, assuming that the receiver faults have, at any location, all possible orientations [Hainzl et al, 2010].…”

A search for evidence of secondary static stress triggering during the 1992 Mw7.3 Landers, California, earthquake sequence

“…We choose the Landers sequence because the predominantly vertical fault orientations of the area make stress change estimates less susceptible to vertical location uncertainties and because the many previous studies of this sequence provide comparisons. Hainzl et al [2009], Cocco et al [2010], and Woessner et al [2011] tested multiple retrospective seismicity forecasting models during the sequence and speculated that modeling secondary stress transfer might improve Coulomb-based models. Here we investigate directly whether aftershocks were predominantly encouraged by secondary static stress transfer.…”

Earthquake forecasting based on data assimilation: sequential Monte Carlo methods for renewal point processes

“…Ogata, 2002) or present-day small repeating earthquakes (Nadeau and Johnson, 1998). Furthermore, formulating and implementing data-assimilation-based schemes for spatiotemporal short-term models of clustered seismicity could reduce their sensitivity to magnitude uncertainties (Werner and Sornette, 2008), errors in locating quakes or uncertain stress calculations (Hainzl et al, 2009). Finally, physics-based seismicity models, such as models based on static stress transfer or other earthquake simulators that require estimates of otherwise unobservable quantities, are particularly likely to benefit from methods of data assimilation.…”

“…Data assimilation provides a vehicle for correcting an existing forecast without having to re-calibrate and re-initialize the model on the entire data set. In its general formulation as a state and parameter estimation problem, data assimilation may also be viewed as a method for estimating physical quantities ("states") and model parameters, directly related to physics-based models, such as rate-and-state friction and Coulomb stress-change models (see, e.g., Hainzl et al, 2009). In the future, the coupled integration of several types of different data to constrain estimates of physical states is highly desirable.…”