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We show how the maximum magnitude within a predefined future time horizon may be estimated from an earthquake catalog within the context of Gutenberg-Richter statistics. The aim is to carry out a rigorous uncertainty assessment, and calculate precise confidence intervals based on an imposed level of confidence a. In detail, we present a model for the estimation of the maximum magnitude to occur in a time interval T-f in the future, given a complete earthquake catalog for a time period T in the past and, if available, paleoseismic events. For this goal, we solely assume that earthquakes follow a stationary Poisson process in time with unknown productivity Lambda and obey the Gutenberg-Richter law in magnitude domain with unknown b-value. The random variables. and b are estimated by means of Bayes theorem with noninformative prior distributions. Results based on synthetic catalogs and on retrospective calculations of historic catalogs from the highly active area of Japan and the low-seismicity, but high-risk region lower Rhine embayment (LRE) in Germany indicate that the estimated magnitudes are close to the true values. Finally, we discuss whether the techniques can be extended to meet the safety requirements for critical facilities such as nuclear power plants. For this aim, the maximum magnitude for all times has to be considered. In agreement with earlier work, we find that this parameter is not a useful quantity from the viewpoint of statistical inference.

Both aftershocks and geodetically measured postseismic displacements are important markers of the stress relaxation process following large earthquakes. Postseismic displacements can be related to creep-like relaxation in the vicinity of the coseismic rupture by means of inversion methods. However, the results of slip inversions are typically non-unique and subject to large uncertainties. Therefore, we explore the possibility to improve inversions by mechanical constraints. In particular, we take into account the physical understanding that postseismic deformation is stress-driven, and occurs in the coseismically stressed zone. We do joint inversions for coseismic and postseismic slip in a Bayesian framework in the case of the 2004 M6.0 Parkfield earthquake. We perform a number of inversions with different constraints, and calculate their statistical significance. According to information criteria, the best result is preferably related to a physically reasonable model constrained by the stress-condition (namely postseismic creep is driven by coseismic stress) and the condition that coseismic slip and large aftershocks are disjunct. This model explains 97% of the coseismic displacements and 91% of the postseismic displacements during day 1-5 following the Parkfield event, respectively. It indicates that the major postseismic deformation can be generally explained by a stress relaxation process for the Parkfield case. This result also indicates that the data to constrain the coseismic slip model could be enriched postseismically. For the 2004 Parkfield event, we additionally observe asymmetric relaxation process at the two sides of the fault, which can be explained by material contrast ratio across the fault of similar to 1.15 in seismic velocity.

Interdisziplinäres Zentrum für Musterdynamik und Angewandte Fernerkundung Workshop vom 9. - 10. Februar 2006

Similar power laws for foreshock and aftershock sequences in a spring block model for earthquakes
(1999)

Seismic quiescence as an indicator for large earthquakes in a system of self-organized criticality
(2000)

In this study, we analyze acoustic emission (AE) data recorded at the Morsleben salt mine, Germany, to assess the catalog completeness, which plays an important role in any seismicity analysis. We introduce the new concept of a magnitude completeness interval consisting of a maximum magnitude of completeness (M-c(max)) in addition to the well-known minimum magnitude of completeness. This is required to describe the completeness of the catalog, both for the smallest events (for which the detection performance may be low) and for the largest ones (which may be missed because of sensors saturation). We suggest a method to compute the maximum magnitude of completeness and calculate it for a spatial grid based on (1) the prior estimation of saturation magnitude at each sensor, (2) the correction of the detection probability function at each sensor, including a drop in the detection performance when it saturates, and (3) the combination of detection probabilities of all sensors to obtain the network detection performance. The method is tested using about 130,000 AE events recorded in a period of five weeks, with sources confined within a small depth interval, and an example of the spatial distribution of M-c(max) is derived. The comparison between the spatial distribution of M-c(max) and of the maximum possible magnitude (M-max), which is here derived using a recently introduced Bayesian approach, indicates that M-max exceeds M-c(max) in some parts of the mine. This suggests that some large and important events may be missed in the catalog, which could lead to a bias in the hazard evaluation.