TY - JOUR A1 - Engbert, Ralf A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Testing for unstable periodic orbits to characterize spatiotemporal dynamics Y1 - 1998 ER - TY - JOUR A1 - Fiedler, Bernhard A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Holschneider, Matthias T1 - Detection of Gutenberg-Richter b-Value Changes in Earthquake Time Series JF - Bulletin of the Seismological Society of America N2 - 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. Y1 - 2018 U6 - https://doi.org/10.1785/0120180091 SN - 0037-1106 SN - 1943-3573 VL - 108 IS - 5A SP - 2778 EP - 2787 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Fiedler, Bernhard A1 - Zöller, Gert A1 - Holschneider, Matthias A1 - Hainzl, Sebastian T1 - Multiple Change-Point Detection in Spatiotemporal Seismicity Data JF - Bulletin of the Seismological Society of America N2 - Earthquake rates are driven by tectonic stress buildup, earthquake-induced stress changes, and transient aseismic processes. Although the origin of the first two sources is known, transient aseismic processes are more difficult to detect. However, the knowledge of the associated changes of the earthquake activity is of great interest, because it might help identify natural aseismic deformation patterns such as slow-slip events, as well as the occurrence of induced seismicity related to human activities. For this goal, we develop a Bayesian approach to identify change-points in seismicity data automatically. Using the Bayes factor, we select a suitable model, estimate possible change-points, and we additionally use a likelihood ratio test to calculate the significance of the change of the intensity. The approach is extended to spatiotemporal data to detect the area in which the changes occur. The method is first applied to synthetic data showing its capability to detect real change-points. Finally, we apply this approach to observational data from Oklahoma and observe statistical significant changes of seismicity in space and time. Y1 - 2018 U6 - https://doi.org/10.1785/0120170236 SN - 0037-1106 SN - 1943-3573 VL - 108 IS - 3A SP - 1147 EP - 1159 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Brietzke, Gilbert B. A1 - Zöller, Gert T1 - Quantitative earthquake forecasts resulting from static stress triggering N2 - In recent years, the triggering of earthquakes has been discussed controversially with respect to the underlying mechanisms and the capability to evaluate the resulting seismic hazard. Apart from static stress interactions, other mechanisms including dynamic stress transfer have been proposed to be part of a complex triggering process. Exploiting the theoretical relation between long-term earthquake rates and stressing rate, we demonstrate that static stress changes resulting from an earthquake rupture allow us to predict quantitatively the aftershock activity without tuning specific model parameters. These forecasts are found to be in excellent agreement with all first-order characteristics of aftershocks, in particular, (1) the total number, (2) the power law distance decay, (3) the scaling of the productivity with the main shock magnitude, (4) the foreshock probability, and (5) the empirical Bath law providing the maximum aftershock magnitude, which supports the conclusion that static stress transfer is the major mechanism of earthquake triggering. Y1 - 2010 UR - http://www.agu.org/journals/jb/ U6 - https://doi.org/10.1029/2010jb007473 SN - 0148-0227 ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Brietzke, Gilbert B. A1 - Hinzen, Klaus-G. T1 - Comparison of deterministic and stochastic earthquake simulators for fault interactions in the Lower Rhine Embayment, Germany JF - Geophysical journal international N2 - 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. KW - Earthquake interaction KW - forecasting KW - and prediction KW - Seismicity and tectonics KW - Statistical seismology Y1 - 2013 U6 - https://doi.org/10.1093/gji/ggt271 SN - 0956-540X SN - 1365-246X VL - 195 IS - 1 SP - 684 EP - 694 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Self-organization of spatio-temporal earthquake clusters Y1 - 2000 ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Self-organized criticality model for earthquakes : Quiescence, foreshocks and aftershocks Y1 - 1999 ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen T1 - Similar power laws for foreshock and aftershock sequences in a spring block model for earthquakes Y1 - 1999 ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Kurths, Jürgen A1 - Zschau, Jochen T1 - Seismic quiescence as an indicator for large earthquakes in a system of self-organized criticality Y1 - 2000 ER - TY - JOUR A1 - Hainzl, Sebastian A1 - Zöller, Gert A1 - Main, Ian T1 - Introduction to special issue: Dynamics of seismicity patterns and earthquake triggering - Preface JF - Tectonophysics : international journal of geotectonics and the geology and physics of the interior of the earth Y1 - 2006 U6 - https://doi.org/10.1016/j.tecto.2006.03.034 SN - 0040-1951 SN - 1879-3266 VL - 424 IS - Special issue SP - 135 EP - 138 PB - Elsevier CY - Amsterdam ER -