Sebastian Hainzl

Observation of growing correlation length as an indicator for critical point behavior prior to large earthquakes

We test the critical point concept for earthquakes in terms of the spatial correlation length. A system near a critical point is associated with a diverging correlation length following a power law time-to-failure relation. We estimate the correlation length directly from an earthquake catalog using single-link cluster analysis. Therefore we assume that the distribution of moderate earthquakes reflects the state of the regional stress field. The parameters of the analysis are determined by an optimization procedure, and the results are tested against a Poisson process with realistic distributions of epicenters, magnitudes, and aftershocks. A systematic analysis of all earthquakes with M≥6.5 in California since 1952 is conducted. In fact, we observe growing correlation lengths in most cases. The null hypothesis that this behavior can be found in random data is rejected with a confidence level of more than 99%. Furthermore, we find a scaling relation log R∼0.7M (log〈ξmax〉 ∼ 0.5M), between the mainshock magnitude M and the critical region R (the correlation length 〈ξmax〉 before the mainshock), which is in good agreement with theoretical values.

Evidence for rainfall‐triggered earthquake activity

[1] Fluids are known to be of major importance for the earthquake generation because pore pressure variations alter the strength of faults. Thus they can initiate earthquakes if the crust is close enough to its critical state. Based on the observations of the isolated seismicity below the densely monitored Mt. Hochstaufen, SE Germany, we are now able to demonstrate that the crust can be so close-to-failure that even tiny pressure variations associated with precipitation can trigger earthquakes in a few kilometer depth. We find that the recorded seismicity is highly correlated with the calculated spatiotemporal pore pressure changes due to diffusing rain water and in good agreement with the response of faults described by the rate-state friction law.

Estimating Background Activity Based on Interevent-Time Distribution

The statistics of time delays between successive earthquakes has re- cently been claimed to be universal and to show the existence of clustering beyond the duration of aftershock bursts. We demonstrate that these claims are unjustified. Stochastic simulations with Poissonian background activity and triggered Omori- type aftershock sequences are shown to reproduce the interevent-time distributions observed on different spatial and magnitude scales in California. Thus the empirical distribution can be explained without any additional long-term clustering. Further- more, we find that the shape of the interevent-time distribution, which can be ap- proximated by the gamma distribution, is determined by the percentage of main- shocks in the catalog. This percentage can be calculated by the mean and variance of the interevent times and varies between 5% and 90% for different regions in California. Our investigation of stochastic simulations indicates that the interevent- time distribution provides a nonparametric reconstruction of the mainshock magnitude-frequency distribution that is superior to standard declustering algorithm.

Similar power laws for foreshock and aftershock sequences in a spring‐block model for earthquakes

We introduce a crust relaxation process in a continuous cellular automaton version of the Burridge and Knopoff [1967] model. The most important model parameters are the level of conservation and the ratio of the crust relaxation time to the tectonic reloading time. In correspondence with the original spring-block model, the modified model displays a robust power law distribution of event sizes. The principal new result obtained with our model is the spatiotemporal clustering of events exhibiting several characteristics of earthquakes in nature. Large events are followed by aftershock sequences obeying the Omori [1894] law and preceded by localized foreshocks, which are initiated after a time period of seismic quiescence. While we observe a considerable variability of precursory seismicity, we find that the rate of foreshocks increases on average, according to a power law with an exponent q, which is in good agreement with the exponent p of the Omori law. In contrast to other events, the distribution of foreshock sizes is characterized by a significantly smaller Richter B value. Our model reproduces simultaneously the empirically observed values of the power law exponents, the Richter B, p and q, and their variability.

Aftershock modeling based on uncertain stress calculations

[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 Asn � 0.017 MPa and a coefficient of stress variation CV = 0.95.

Seismic quiescence as an indicator for large earthquakes in a system of self‐organized criticality

Seismically active fault systems may be in a state of self-organized criticality (SOC). Investigations of simple SOC models have suggested that earthquakes might be inherently unpredictable. In this paper, we analyze the question of predictability in a more complex and realistic SOC model, which consists of a spring-block system with transient creep characteristics. Additionally to the power law distribution of earthquake sizes, this model reproduces also foreshock and aftershock sequences. Aside from a short-term increase of seismicity immediately prior to large model earthquakes, these events are preceded on average by an intermediate-term period of reduced seismicity. The stronger and the longer the duration of this period, the larger on average is the subsequent mainshock. We find that the detection of seismic quiescence can improve the time—independent hazard assessment. The improvement is most significant for the largest target events.

Impact of Earthquake Rupture Extensions on Parameter Estimations of Point-Process Models

Online Material: Sensitivity to scaling of the d-parameter and to inhomogeneous background activity, and possible correlation between the largest magnitude and es- timated α-value. Abstract Stochastic point processes are widely applied to model spatiotemporal earthquake occurrence. In particular, the epidemic type aftershock sequence (ETAS) model has been shown to successfully reproduce the short-term clustering of earth- quakes. An important parameter of the model is the α-value describing the scaling of the aftershock productivity with magnitude of the triggering earthquake according to 10 αM . Fitting of the space-dependent ETAS model to empirical data yields α-values that are typically much smaller than the scaling inverted from more simple stacking of aftershock sequences. We show by means of synthetic simulations that this is likely to result from assuming spatial isotropy of aftershock occurrence that in fact aligns along the mainshock rupture. We fit the space-dependent and space-independent ETAS mod- els to simulations where each earthquake is a line source with an empirical magnitude- length relation. Although the space-time model describes past activity quite well, it overestimates the forecasted earthquake rate. On the other hand, the application of the space-independent ETAS model predicts future seismicity well and can therefore be applied for forecasting purposes. Our test for the observed aftershock sequence fol- lowing the 1992 M 7.3 Landers earthquake supports these results.

Estimation of the Maximum Possible Magnitude in the Framework of a Doubly Truncated Gutenberg–Richter Model

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 α 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 ![Graphic][1] 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 ![Graphic][2] , the resulting confidence intervals are essentially meaningless. The use of an informative prior distribution accounting for preknowledge 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. [1]: /embed/inline-graphic-1.gif [2]: /embed/inline-graphic-2.gif

Impact of Aseismic Transients on the Estimation of Aftershock Productivity Parameters

Abstract The epidemic‐type aftershock sequence (ETAS) model has been shown to describe successfully the statistical seismicity properties, if earthquake triggering is related to tectonic forcing and earthquake‐induced stress changes. However, seismicity is locally often dominated by stress changes related to transient aseismic processes. To avoid erroneous parameter estimations leading to biased forecasts, it is important to account for those transients. We apply a recently developed iterative algorithm based on the ETAS model to identify the time‐dependent background and ETAS parameters simultaneously. We find that this procedure works well for synthetic data sets if catalog errors are appropriately considered. However, ignoring the time dependence leads to significantly biased parameter estimations. In particular, the α ‐value describing the magnitude dependence of the triggering kernel can be strongly underestimated if transients are ignored. Low α ‐values have been previously found for swarm activity, for which transient aseismic processes are expected to play a major role. These observed anomalously low α ‐values might thus indicate the importance of transient forcing, rather than being due to differences in the earthquake–earthquake trigger mechanism. To explore this, we apply the procedure systematically to earthquake clusters detected in southern California and to earthquake swarm activity in Vogtland/Western Bohemia. While low α ‐values are mostly shown to be a consequence of catalog errors and time‐dependent forcing but not related to different earthquake–earthquake interaction mechanisms, some significant low values are observed in high heat‐flow areas in California, confirming the existence of thermal control on earthquake triggering.

Correlations of Seismicity Patterns in Southern California with Surface Heat Flow Data

We investigate the relations between properties of seismicity patterns in Southern California and the surface heat flow using a relocated earthquake catalog. We first search for earthquake sequences that are well separated in time and space from other seismicity and then determine the epidemic type aftershock sequence (ETAS) model parameters for the sequences with a sufficient number of events. We focus on the productivity parameter α of the ETAS model that quantifies the relative efficiency of an earthquake with magnitude M to produce aftershocks. By stacking sequences with relatively small and relatively large α values separately, we observed clear differences between the two groups. Sequences with a smaller α have a relatively large number of foreshocks and relatively small number of after- shocks. In contrast, more typical sequences with larger α have relatively few fore- shocks and larger number of aftershocks. The stacked premainshock activity for the more typical latter sequences has a clear increase in the day before the occurrence of the main event. The spatial distribution of the α values correlates well with the surface heat flow: areas of high heat flow are characterized by relatively small α, indicating that in such regions the swarm-type earthquake activity is more common. Our results are compatible with a damage rheology model that predicts swarm-type seismic activity in areas with relatively high heat flow and more typical foreshock- mainshock-aftershock sequences in regions with normal or low surface heat flow. The high variability of α in regions with either high or low heat flow values indicates that at local scales additional factors (e.g., fluid content and rock type) may influence the seismicity generation process.