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We show that realistic aftershock sequences with space-time characteristics compatible with observations are generated by a model consisting of brittle fault segments separated by creeping zones. The dynamics of the brittle regions is governed by static/kinetic friction, 3D elastic stress transfer and small creep deformation. The creeping parts are characterized by high ongoing creep velocities. These regions store stress during earthquake failures and then release it in the interseismic periods. The resulting postseismic deformation leads to aftershock sequences following the modified Omori law. The ratio of creep coefficients in the brittle and creeping sections determines the duration of the postseismic transients and the exponent p of the modified Omori law
Due to large uncertainties and non-uniqueness in fault slip inversion, the investigation of stress coupling based on the direct comparison of independent slip inversions, for example, between the coseismic slip distribution and the interseismic slip deficit, may lead to ambiguous conclusions. In this study, we therefore adopt the stress-constrained joint inversion in the Bayesian approach of Wang et al., and implement the physical hypothesis of stress coupling as a prior. We test the hypothesis that interseismic locking is coupled with the coseismic rupture, and the early post-seismic deformation is a stress relaxation process in response to the coseismic stress perturbation. We characterize the role of stress coupling in the seismic cycle by evaluating the efficiency of the model to explain the available data. Taking the 2004 M6 Parkfield earthquake as a study case, we find that the stress coupling hypothesis is in agreement with the data. The coseismic rupture zone is found to be strongly locked during the interseismic phase and the post-seismic slip zone is indicated to be weakly creeping. The post-seismic deformation plays an important role to rebuild stress in the coseismic rupture zone. Based on our results for the stress accumulation during both inter- and post-seismic phase in the coseismic rupture zone, together with the coseismic stress drop, we estimate a recurrence time of M6 earthquake in Parkfield around 23-41 yr, suggesting that the duration of 38 yr between the two recent M6 events in Parkfield is not a surprise.
Based on an analysis of continuous monitoring of farm animal behavior in the region of the 2016 M6.6 Norcia earthquake in Italy, Wikelski et al., 2020; (Seismol Res Lett, 89, 2020, 1238) conclude that animal activity can be anticipated with subsequent seismic activity and that this finding might help to design a "short-term earthquake forecasting method." We show that this result is based on an incomplete analysis and misleading interpretations. Applying state-of-the-art methods of statistics, we demonstrate that the proposed anticipatory patterns cannot be distinguished from random patterns, and consequently, the observed anomalies in animal activity do not have any forecasting power.
Time-dependent probabilistic seismic hazard assessment requires a stochastic description of earthquake occurrences. While short-term seismicity models are well-constrained by observations, the recurrences of characteristic on-fault earthquakes are only derived from theoretical considerations, uncertain palaeo-events or proxy data. Despite the involved uncertainties and complexity, simple statistical models for a quasi-period recurrence of on-fault events are implemented in seismic hazard assessments. To test the applicability of statistical models, such as the Brownian relaxation oscillator or the stress release model, we perform a systematic comparison with deterministic simulations based on rate- and state-dependent friction, high-resolution representations of fault systems and quasi-dynamic rupture propagation. For the specific fault network of the Lower Rhine Embayment, Germany, we run both stochastic and deterministic model simulations based on the same fault geometries and stress interactions. Our results indicate that the stochastic simulators are able to reproduce the first-order characteristics of the major earthquakes on isolated faults as well as for coupled faults with moderate stress interactions. However, we find that all tested statistical models fail to reproduce the characteristics of strongly coupled faults, because multisegment rupturing resulting from a spatiotemporally correlated stress field is underestimated in the stochastic simulators. Our results suggest that stochastic models have to be extended by multirupture probability distributions to provide more reliable results.
The Gutenberg-Richter relation for earthquake magnitudes is the most famous empirical law in seismology. It states that the frequency of earthquake magnitudes follows an exponential distribution; this has been found to be a robust feature of seismicity above the completeness magnitude, and it is independent of whether global, regional, or local seismicity is analyzed. However, the exponent b of the distribution varies significantly in space and time, which is important for process understanding and seismic hazard assessment; this is particularly true because of the fact that the Gutenberg-Richter b-value acts as a proxy for the stress state and quantifies the ratio of large-to-small earthquakes. In our work, we focus on the automatic detection of statistically significant temporal changes of the b-value in seismicity data. In our approach, we use Bayes factors for model selection and estimate multiple change-points of the frequency-magnitude distribution in time. The method is first applied to synthetic data, showing its capability to detect change-points as function of the size of the sample and the b-value contrast. Finally, we apply this approach to examples of observational data sets for which b-value changes have previously been stated. Our analysis of foreshock and after-shock sequences related to mainshocks, as well as earthquake swarms, shows that only a portion of the b-value changes is statistically significant.
We discuss to what extent a given earthquake catalog and the assumption of a doubly truncated Gutenberg-Richter distribution for the earthquake magnitudes allow for the calculation of confidence intervals for the maximum possible magnitude M. We show that, without further assumptions such as the existence of an upper bound of M, only very limited information may be obtained. In a frequentist formulation, for each confidence level alpha the confidence interval diverges with finite probability. In a Bayesian formulation, the posterior distribution of the upper magnitude is not normalizable. We conclude that the common approach to derive confidence intervals from the variance of a point estimator fails. Technically, this problem can be overcome by introducing an upper bound (M) over tilde for the maximum magnitude. Then the Bayesian posterior distribution can be normalized, and its variance decreases with the number of observed events. However, because the posterior depends significantly on the choice of the unknown value of (M) over tilde, the resulting confidence intervals are essentially meaningless. The use of an informative prior distribution accounting for pre-knowledge of M is also of little use, because the prior is only modified in the case of the occurrence of an extreme event. Our results suggest that the maximum possible magnitude M should be better replaced by M(T), the maximum expected magnitude in a given time interval T, for which the calculation of exact confidence intervals becomes straightforward. From a physical point of view, numerical models of the earthquake process adjusted to specific fault regions may be a powerful alternative to overcome the shortcomings of purely statistical inference.
Aftershock models are usually based either on purely empirical relations ignoring the physical mechanism or on deterministic calculations of stress changes on a predefined receiver fault orientation. Here we investigate the effect of considering more realistic fault systems in models based on static Coulomb stress changes. For that purpose, we perform earthquake simulations with elastic half-space stress interactions, rate-and-state dependent frictional earthquake nucleation, and extended ruptures with heterogeneous (fractal) slip distributions. We find that the consideration of earthquake nucleation on multiple receiver fault orientations does not influence the shape of the temporal Omori-type aftershock decay, but changes significantly the predicted spatial patterns and the total number of triggered events. So-called stress shadows with decreased activity almost vanish, and activation decays continuously with increasing distance from the main shock rupture. The total aftershock productivity, which is shown to be almost independent of the assumed background rate, increases significantly if multiple receiver fault planes exist. The application to the 1992 M7.3 Landers, California, aftershock sequence indicates a good agreement with the locations and the total productivity of the observed directly triggered aftershocks.
Introduction to special issue: Dynamics of seismicity patterns and earthquake triggering - Preface
(2006)
The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model.
Stress drop is a key factor in earthquake mechanics and engineering seismology. However, stress drop calculations based on fault slip can be significantly biased, particularly due to subjectively determined smoothing conditions in the traditional least-square slip inversion. In this study, we introduce a mechanically constrained Bayesian approach to simultaneously invert for fault slip and stress drop based on geodetic measurements. A Gaussian distribution for stress drop is implemented in the inversion as a prior. We have done several synthetic tests to evaluate the stability and reliability of the inversion approach, considering different fault discretization, fault geometries, utilized datasets, and variability of the slip direction, respectively. We finally apply the approach to the 2010 M8.8 Maule earthquake and invert for the coseismic slip and stress drop simultaneously. Two fault geometries from the literature are tested. Our results indicate that the derived slip models based on both fault geometries are similar, showing major slip north of the hypocenter and relatively weak slip in the south, as indicated in the slip models of other studies. The derived mean stress drop is 5-6 MPa, which is close to the stress drop of similar to 7 MPa that was independently determined according to force balance in this region Luttrell et al. (J Geophys Res, 2011). These findings indicate that stress drop values can be consistently extracted from geodetic data.