TY - JOUR A1 - Holschneider, Matthias A1 - Zöller, Gert A1 - Hainzl, Sebastian T1 - Estimation of the maximum possible magnitude in the framework of a doubly truncated Gutenberg-Richter Model JF - Bulletin of the Seismological Society of America N2 - 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. Y1 - 2011 U6 - https://doi.org/10.1785/0120100289 SN - 0037-1106 VL - 101 IS - 4 SP - 1649 EP - 1659 PB - Seismological Society of America CY - El Cerrito ER - TY - THES A1 - Hainzl, Sebastian T1 - Earthquake triggering and interaction T1 - Erdbebenentstehung und Wechselwirkungen N2 - Earthquake faults interact with each other in many different ways and hence earthquakes cannot be treated as individual independent events. Although earthquake interactions generally lead to a complex evolution of the crustal stress field, it does not necessarily mean that the earthquake occurrence becomes random and completely unpredictable. In particular, the interplay between earthquakes can rather explain the occurrence of pronounced characteristics such as periods of accelerated and depressed seismicity (seismic quiescence) as well as spatiotemporal earthquake clustering (swarms and aftershock sequences). Ignoring the time-dependence of the process by looking at time-averaged values – as largely done in standard procedures of seismic hazard assessment – can thus lead to erroneous estimations not only of the activity level of future earthquakes but also of their spatial distribution. Therefore, it exists an urgent need for applicable time-dependent models. In my work, I aimed at better understanding and characterization of the earthquake interactions in order to improve seismic hazard estimations. For this purpose, I studied seismicity patterns on spatial scales ranging from hydraulic fracture experiments (meter to kilometer) to fault system size (hundreds of kilometers), while the temporal scale of interest varied from the immediate aftershock activity (minutes to months) to seismic cycles (tens to thousands of years). My studies revealed a number of new characteristics of fluid-induced and stress-triggered earthquake clustering as well as precursory phenomena in earthquake cycles. Data analysis of earthquake and deformation data were accompanied by statistical and physics-based model simulations which allow a better understanding of the role of structural heterogeneities, stress changes, afterslip and fluid flow. Finally, new strategies and methods have been developed and tested which help to improve seismic hazard estimations by taking the time-dependence of the earthquake process appropriately into account. N2 - Erdbeben interagieren in vielfältiger Weise miteinander, weshalb sie nicht als einzelne, unabhängige Ereignisse behandelt werden können. Obwohl diese Erdbebenwechselwirkungen in der Regel zu einer komplexen Entwicklung des Spannungsfelds führen, bedeutet dies nicht zwangsläufig, dass Erdbeben rein zufällig und völlig unberechenbar auftreten. Insbesondere kann das Zusammenspiel zwischen Erdbeben zu ausgeprägten Charakteristiken wie Phasen beschleunigter Aktivität, seismischer Ruhe sowie raumzeitlichen Erdbebenanhäufungen (Schwärme und Nachbebensequenzen) führen. Die Vernachlässigung der Zeitabhängigkeit des Erdbebenprozesses kann somit zu fehlerhaften Einschätzungen nicht nur des zukünftigen Aktivitätsniveaus, sondern auch der räumlichen Verteilung führen. Daher besteht ein dringender Bedarf an geeigneten zeitabhängigen Seismizitätsmodellen. Meine Arbeit zielt auf ein verbessertes Verständnis und Charakterisierung der Interaktionen von Erdbeben ab, um Abschätzungen der Erdbebengefährdung zu verbessern. Zu diesem Zweck untersuche ich Seismizitätsmuster auf den räumlichen Skalen von hydraulisch induzierten Öffnungsbrüchen (Meter bis Kilometer) bis zu Verwerfungssystemen (Hunderte von Kilometern), während die zeitlichen Skalen von Nachbebenaktivität (Minuten bis Monate) bis zu seismischen Zyklen (bis zu mehrere tausendend Jahre) reichen. Meine Studien ergeben eine Reihe neuer Merkmale von Fluid- und Spannungs-induzierten Erdbeben. Ergänzend zur reinen Datenanalyse der Erdbeben- und Deformationsdaten liefern statistische und Physik-basierte Modellsimulationen ein besseres Verständnis der Rolle von strukturellen Heterogenitäten, Spannungsänderungen und postseismischen Prozessen. Schließlich konnten neue Strategien und Methoden entwickelt und getestet werden, mit denen die Erdbebengefährdung besser eingeschätzt werden kann, indem die Zeitabhängigkeit des Erdbebens Prozess angemessen berücksichtigt wird. KW - Erdbebeninteraktion KW - Erdbebengefährdung KW - earthquake interaction KW - seismic hazard Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-50095 ER - TY - JOUR A1 - Daniel, G. A1 - Prono, E. A1 - Renard, F. A1 - Thouvenot, F. A1 - Hainzl, Sebastian A1 - Marsan, D. A1 - Helmstetter, A. A1 - Traversa, P. A1 - Got, J. L. A1 - Jenatton, L. A1 - Guiguet, R. T1 - Changes in effective stress during the 2003-2004 Ubaye seismic swarm, France JF - Journal of geophysical research : Solid earth N2 - We study changes in effective stress (normal stress minus pore pressure) that occurred in the French Alps during the 2003-2004 Ubaye earthquake swarm. Two complementary data sets are used. First, a set of 974 relocated events allows us to finely characterize the shape of the seismogenic area and the spatial migration of seismicity during the crisis. Relocations are performed by a double-difference algorithm. We compute differences in travel times at stations both from absolute picking times and from cross-correlation delays of multiplets. The resulting catalog reveals a swarm alignment along a single planar structure striking N130 degrees E and dipping 80 degrees W. This relocated activity displays migration properties consistent with a triggering by a diffusive fluid overpressure front. This observation argues in favor of a deep-seated fluid circulation responsible for a significant part of the seismic activity in Ubaye. Second, we analyze time series of earthquake detections at a single seismological station located just above the swarm. This time series forms a dense chronicle of +16,000 events. We use it to estimate the history of effective stress changes during this sequence. For this purpose we model the rate of events by a stochastic epidemic-type aftershock sequence model with a nonstationary background seismic rate lambda(0)(t). This background rate is estimated in discrete time windows. Window lengths are determined optimally according to a new change-point method on the basis of the interevent times distribution. We propose that background events are triggered directly by a transient fluid circulation at depth. Then, using rate-and-state constitutive friction laws, we estimate changes in effective stress for the observed rate of background events. We assume that changes in effective stress occurred under constant shear stressing rate conditions. We finally obtain a maximum change in effective stress close to -8 MPa, which corresponds to a maximum fluid overpressure of about 8 MPa under constant normal stress conditions. This estimate is in good agreement with values obtained from numerical modeling of fluid flow at depth, or with direct measurements reported from fluid injection experiments. Y1 - 2011 U6 - https://doi.org/10.1029/2010JB007551 SN - 2169-9313 SN - 2169-9356 VL - 116 IS - 4 PB - American Geophysical Union CY - Washington ER -