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  • 1
    Monograph available for loan
    Monograph available for loan
    Oxford : Clarendon Press
    Call number: M 96.0280
    Type of Medium: Monograph available for loan
    Pages: XIII, 423 S.
    ISBN: 0198534817
    Series Statement: Oxford mathematical monographs
    Classification:
    C.1.6.
    Language: English
    Location: Upper compact magazine
    Branch Library: GFZ Library
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  • 2
    Electronic Resource
    Electronic Resource
    PO Box 1354, 9600 Garsington Road , Oxford OX4 2XG , UK . : Blackwell Science Ltd
    Geophysical prospecting 53 (2005), S. 0 
    ISSN: 1365-2478
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences , Physics
    Notes: We introduce a method of wavefield separation from multicomponent data sets based on the use of the continuous wavelet transform. Our method is a further generalization of the approach proposed by Morozov and Smithson, in that by using the continuous wavelet transform, we can achieve a better separation of wave types by designing the filter in the time–frequency domain. Furthermore, using the instantaneous polarization attributes defined in the wavelet domain, we show how to construct filters tailored to separate different wave types (elliptically or linearly polarized), followed by an inverse wavelet transform to obtain the desired wave type in the time domain. Using synthetic and experimental data, we show how the present method can be used for wavefield separation.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Inventiones mathematicae 105 (1991), S. 157-175 
    ISSN: 1432-1297
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We will show how to analyse the local regularity of functions with the help of the wavelet transform. These results will be applied to the function of Riemann, where we show the existence of a dense set of points where this function is differentiable. On another dense set we show the existence of local singularities of cusp type. On a third set we show differentiability to the right (left). On the remaining set the functions will be shown to be not differentiable.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 50 (1988), S. 995-1020 
    ISSN: 1572-9613
    Keywords: Fractal dimensions ; spectrum of singularities ; invariant measures ; homeomorphic conjugacies ; critical circle maps
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the behavior of the spectrum of singularities associated with the invariant measure of some dynamical systems under nonsmooth coordinate changes. When the homeomorphic conjugacy is not Lipschitz continuous, we discuss how its singularities can affect the whole set of generalized fractal dimensions. We give applications to homeomorphisms that conjugate critical circle maps with irrational (golden mean) winding numbers. We present numerical studies corroborating the theoretical predictions.
    Type of Medium: Electronic Resource
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  • 5
    Publication Date: 1988-11-14
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
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  • 6
    Publication Date: 2020-07-13
    Description: SUMMARY For the time stationary global geomagnetic field, a new modelling concept is presented. A Bayesian non-parametric approach provides realistic location dependent uncertainty estimates. Modelling related variabilities are dealt with systematically by making little subjective a priori assumptions. Rather than parametrizing the model by Gauss coefficients, a functional analytic approach is applied. The geomagnetic potential is assumed a Gaussian process to describe a distribution over functions. A priori correlations are given by an explicit kernel function with non-informative dipole contribution. A refined modelling strategy is proposed that accommodates non-linearities of archeomagnetic observables: First, a rough field estimate is obtained considering only sites that provide full field vector records. Subsequently, this estimate supports the linearization that incorporates the remaining incomplete records. The comparison of results for the archeomagnetic field over the past 1000 yr is in general agreement with previous models while improved model uncertainty estimates are provided.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
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  • 7
    Publication Date: 2007-09-01
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
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  • 8
    Publication Date: 2013-03-22
    Description: 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 α . 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 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.
    Print ISSN: 0037-1106
    Electronic ISSN: 1943-3573
    Topics: Geosciences , Physics
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  • 9
    Publication Date: 2016-01-08
    Description: In the present study, we summarize and evaluate the endeavors from recent years to estimate the maximum possible earthquake magnitude m max from observed data. In particular, we use basic and physically motivated assumptions to identify best cases and worst cases in terms of lowest and highest degree of uncertainty of m max . In a general framework, we demonstrate that earthquake data and earthquake proxy data recorded in a fault zone provide almost no information about m max unless reliable and homogeneous data of a long time interval, including several earthquakes with magnitude close to m max , are available. Even if detailed earthquake information from some centuries including historic and paleoearthquakes are given, only very few, namely the largest events, will contribute at all to the estimation of m max , and this results in unacceptably high uncertainties. As a consequence, estimators of m max in a fault zone, which are based solely on earthquake-related information from this region, have to be dismissed.
    Print ISSN: 0895-0695
    Electronic ISSN: 1938-2057
    Topics: Geosciences
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  • 10
    Publication Date: 2012-04-20
    Description: SUMMARY In the eighties, the analysis of satellite altimetry data leads to the major discovery of gravity lineations in the oceans, with wavelengths between 200 and 1400 km. While the existence of the 200 km scale undulations is widely accepted, undulations at scales larger than 400 km are still a matter of debate. In this paper, we revisit the topic of the large-scale geoid undulations over the oceans in the light of the satellite gravity data provided by the GRACE mission, considerably more precise than the altimetry data at wavelengths larger than 400 km. First, we develop a dedicated method of directional Poisson wavelet analysis on the sphere with significance testing, in order to detect and characterize directional structures in geophysical data on the sphere at different spatial scales. This method is particularly well suited for potential field analysis. We validate it on a series of synthetic tests, and then apply it to analyze recent gravity models, as well as a bathymetry data set independent from gravity. Our analysis confirms the existence of gravity undulations at large scale in the oceans, with characteristic scales between 600 and 2000 km. Their direction correlates well with present-day plate motion over the Pacific ocean, where they are particularly clear, and associated with a conjugate direction at 1500 km scale. A major finding is that the 2000 km scale geoid undulations dominate and had never been so clearly observed previously. This is due to the great precision of GRACE data at those wavelengths. Given the large scale of these undulations, they are most likely related to mantle processes. Taking into account observations and models from other geophysical information, as seismological tomography, convection and geochemical models and electrical conductivity in the mantle, we conceive that all these inputs indicate a directional fabric of the mantle flows at depth, reflecting how the history of subduction influences the organization of lower mantle upwellings.
    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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