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  • 2010-2014  (13)
  • 1
    Monograph available for loan
    Monograph available for loan
    [Washington, D.C.] : AGU, American Geophysical Union
    Call number: 8/M 14.0116
    Description / Table of Contents: A comprehensive and methodologically rigorous analysis of earthquake occurrence. Models based on the theory of the stochastic multidimensional point processes are employed to approximate the earthquake occurrence pattern and evaluate its parameters. The Author shows that most of these parameters have universal values. These results help explain the classical earthquake distributions: Omori's law and the Gutenberg-Richter relation.The Author derives a new negative-binomial distribution for earthquake numbers, instead of the Poisson distribution, and then determines a fractal correlation dimension for spatial distributions of earthquake hypocenters. The book also investigates the disorientation of earthquake focal mechanisms and shows that it follows the rotational Cauchy distribution. These statistical and mathematical advances make it possible to produce quantitative forecasts of earthquake occurrence. In these forecasts earthquake rate in time, space, and focal mechanism orientation is evaluated.
    Type of Medium: Monograph available for loan
    Pages: XVIII, 283 S. , Ill., graph. Darst., Kt.
    ISBN: 9781118637920
    Series Statement: Statistical physics of fracture and breakdown
    Classification:
    Seismology
    Location: Reading room
    Branch Library: GFZ Library
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  • 2
    Publication Date: 2012-05-22
    Description: SUMMARY Since 1977 we have developed statistical short- and long-term earthquake forecasts to predict earthquake rate per unit area, time and magnitude. The forecasts are based on smoothed maps of past seismicity and assume spatial and temporal clustering. Our new program forecasts earthquakes on a 0.1° grid for a global region 90N–90S latitude. We use the PDE catalogue that reports many smaller quakes ( M ≥ 5.0). For the long-term forecast we test two types of smoothing kernels based on the power law and on the spherical Fisher distribution. The effective width of these kernels is much larger than the cell size, thus the map discretization effects are insignificant. We employ adaptive kernel smoothing which improves our forecast both in seismically quiet and active areas. Our forecasts can be tested within a relatively short-time period since smaller events occur with greater frequency. The forecast efficiency can be measured by likelihood scores expressed as the average probability gains per earthquake compared to spatially or temporally uniform Poisson distribution. Another method uses the error diagram to display the forecasted point density and the point events. Our short-term forecasts also assume temporal clustering described by a variant of Omori’s law. Like the long-term forecast, the short-term version is expressed as a rate density in location, magnitude and time. Any forecast with a given lower magnitude threshold can be recalculated, using the tapered Gutenberg–Richter relation, to larger earthquakes with the maximum (corner) magnitude determined for appropriate tectonic zones.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 3
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    Oxford University Press
    Publication Date: 2011-07-19
    Description: SUMMARY We consider two statistical regularities that were used to explain Omori's law of the aftershock rate decay: the Lévy and Inverse Gaussian (IGD) distributions. These distributions are thought to describe stress behaviour influenced by various random factors: post-earthquake stress time history is described by a Brownian motion. Both distributions decay to zero for time intervals close to zero. But this feature contradicts the high immediate aftershock level according to Omori's law. We propose that these statistical distributions are influenced by the power-law stress distribution near the earthquake focal zone and we derive new distributions as a mixture of power-law stress with the exponent ψ and Lévy as well as IGD distributions. Such new distributions describe the resulting inter-earthquake time intervals and closely resemble Omori's law. The new Lévy distribution has a pure power law form with the exponent −(1 +ψ/2) and the mixed IGD has two exponents: the same as Lévy for small time intervals and −(1 +ψ) for longer times. For even longer time intervals this power-law behaviour should be replaced by a uniform seismicity rate corresponding to the long-term tectonic deformation. We compute these background rates using our former analysis of earthquake size distribution and its connection to plate tectonics. We analyse several earthquake catalogues to confirm and illustrate our theoretical results. Finally, we discuss how the parameters of random stress dynamics can be determined through a more detailed statistical analysis of earthquake occurrence or by new laboratory experiments.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 4
    Publication Date: 2011-10-01
    Description: Branching point process models such as the epidemic-type aftershock sequence (ETAS) models introduced by Ogata (1988, 1998) are often used in the description, characterization, simulation, and declustering of modern earthquake catalogs. The present work investigates how the parameters in these models vary across different tectonic zones. After considering divisions of the surface of the Earth into several zones based on the plate-boundary model of Bird (2003), ETAS models are fit to the occurrence times and locations of shallow earthquakes within each zone. Computationally, the expectation-maximization (EM) type algorithm of Veen and Schoenberg (2008) is employed for the purpose of model fitting. The fits and variations in parameter estimates for distinct zones are compared, and seismological implications are discussed. In particular, we find that estimated background seismicity rates range by a factor of nearly 500 for interplate and trench events, respectively; the estimated productivity parameter, governing the relationship between the magnitude of an earthquake and its expected number of direct aftershocks, ranges by a factor of more than five from events in the slow-moving zone to events in active continental areas, suggesting a much higher rate of swarming in the ridges than in the trenches and active continental zones. Despite the pronounced differences between the seismicity patterns and parameter estimates in the different zones, the ETAS model with few parameters and with the same functional form seems to fit reasonably well to the seismicity in each zone.
    Print ISSN: 0037-1106
    Electronic ISSN: 1943-3573
    Topics: Geosciences , Physics
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  • 5
    Publication Date: 2011-06-01
    Description: We constructed 5- and 10-yr smoothed-seismicity forecasts of moderate-to-large California earthquakes, and we examined the importance of several assumptions and choices. To do this, we divided the available catalog into learning and testing periods and optimized parameters to best predict earthquakes in the testing period. Fourteen different 5-yr testing periods were considered, in which the number of earthquakes varies from 18 to 63. We then compared the likelihood gain per target earthquake for the various choices. In this study, we assumed that the spatial, temporal, and magnitude distributions were independent of one another, so that the joint probability distribution could be factored into those three components. We compared several disjoint test periods of the same length to determine the variability of the likelihood gain. The variability is large enough to mask the effects of some modeling choices. Stochastic declustering of the learning catalog produced a significantly better forecast, and representing larger earthquakes by their rupture surfaces provided a slightly better result, all other choices being equal. Inclusion of historical earthquakes and the use of an anisotropic smoothing kernel based on focal mechanisms failed to improve the forecast consistently. We chose a lower threshold magnitude of 4.7 for our learning catalog so that our results could be compared in the future to other forecasts relying on shorter catalogs with a smaller magnitude threshold.
    Print ISSN: 0037-1106
    Electronic ISSN: 1943-3573
    Topics: Geosciences , Physics
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  • 6
    Publication Date: 2011-08-01
    Description: We present two models for estimating the probabilities of future earthquakes in California, to be tested in the Collaboratory for the Study of Earthquake Predictability (CSEP). The first is a time-independent model of adaptively smoothed seismicity that we modified from Helmstetter et al. (2007). The model provides five-year forecasts for earthquakes with magnitudes M[≥]4.95. We show that large earthquakes tend to occur near the locations of small M[≥]2 events, so that a high-resolution estimate of the spatial distribution of future large quakes is obtained from the locations of the numerous small events. We further assume a universal Gutenberg-Richter magnitude distribution. In retrospective tests, we show that a Poisson distribution does not fit the observed rate variability, in contrast to assumptions in current earthquake predictability experiments. We therefore issued forecasts using a better-fitting negative binomial distribution for the number of events. The second model is a time-dependent epidemic-type aftershock sequence (ETAS) model that we modified from Helmstetter et al. (2006) and that provides next-day forecasts for M[≥]3.95. In this model, the forecasted rate is the sum of a background rate (proportional to the time-independent model rate) and of the expected rate of triggered events due to all prior earthquakes. Each earthquake triggers events with a rate that increases exponentially with its magnitude and decays in time according to the Omori-Utsu law. An isotropic kernel models the spatial density of aftershocks for small (M[≤]5.5) events, while for larger quakes, we smooth early aftershocks to forecast later events. We estimate parameter values by optimizing retrospective forecasts and find that the short-term model realizes a probability gain of about 6.0 per earthquake over the time-independent model.
    Print ISSN: 0037-1106
    Electronic ISSN: 1943-3573
    Topics: Geosciences , Physics
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  • 7
    Publication Date: 2011-07-18
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
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  • 8
    Publication Date: 2013-05-16
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
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  • 9
    Publication Date: 2014-02-11
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
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  • 10
    Publication Date: 2010-12-01
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
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