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  • 1
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    Stochastic earthquake source model: the omega-square hypothesis and the directivity effect (2015)
    Oxford University Press
    Details
    Publication Date: 2015-05-16
    Description: Recently A. Gusev suggested and numerically investigated the doubly stochastic earthquake source model. The model is supposed to demonstrate the following features in the far-field body waves: (1) the omega-square high-frequency (HF) behaviour of displacement spectra; (2) lack of the directivity effect in HF radiation; and (3) a stochastic nature of the HF signal component. The model involves two stochastic elements: the local stress drop (SD) on a fault and the rupture time function (RT) with a linear dominant component. The goal of the present study is to investigate the Gusev model theoretically and to find conditions for (1, 2) to be valid and stable relative to receiver site. The models with smooth elements SD, RT are insufficient for these purposes. Therefore, SD and RT are treated as realizations of stochastic fields of the fractal type. The local smoothness of such fields is characterized by the fractional (Hurst) exponent H , 0 〈 H 〈 1. This allows us to consider a wide class of stochastic functions without regard to their global spectral properties. We show that the omega-square behavior of the model is achieved approximately if the rupture time function is almost regular ( H ~1) while the stress drop is rough function of any index H . However, if the rupture front is linear, the local stress drop has to be function of minimal smoothness ( H ~0). The situation with the directivity effect is more complicated: for different RT models with the same fractal index, the effect may or may not occur. The nature of the phenomenon is purely analytical. The main controlling factor for the directivity is the degree of smoothness of the 2-D distributions of RT random function. For this reason the directivity effect is unstable. This means that in practice the opposite conclusions relative to the statistical significance of the directivity effect are possible.
    Keywords: Seismology
    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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  • 2
    Electronic Resource
    Electronic Resource
    Turbulent cascades: Limitations and a statistical test of the lognormal hypothesis (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 2387-2396 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Multiplicative random cascade models were introduced in the 1970s to explain the intermittency of turbulent energy dissipation. The rigorous results in the multifractality of cascade measures recently derived by this author are used in two ways. (1) The statistical test for the Kolmogorov–Obukhov lognormal hypothesis (K62) is revised. Contrary to what is generally believed, we show that the K62 theoretical prediction is in good agreement with experimental data in the range (1,18) of the parameter p (the order of velocity structure functions). This revised conclusion was necessitated by violations in previous comparisons of the "ergodic hypothesis" for large p. (2) Physical limitations on cascade models are analyzed. We show that cascade measures demonstrate a strict dependence on the scaling parameter. This circumstance affects interpretations of statistics of multipliers, shows that the models used in practice are not really superior to others, and indicates the necessity to study cascades with a random scaling parameter. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869358
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  • 3
    Electronic Resource
    Electronic Resource
    Aftershock identification: methods and new approaches (1992)
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 109 (1992), S. 0 
    Details
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: The problem of aftershock identification in earthquake catalogues is studied. Some empirical methods are considered and quantitavely analysed.Game theory approach is applied to formulate the problem allowing a whole class of optimal methods of aftershock identification. Each method is optimal depending on the goals and gives the best trade-off between the number of missed aftershocks and the number of incorrectly identified ones. Some illustrations of the new approach to the aftershock identification problem are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1365-246X.1992.tb00113.x
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Earthquake prediction as a decision-making problem (1997)
    Springer
    Pure and applied geophysics 149 (1997), S. 233-247 
    Details
    ISSN: 1420-9136
    Keywords: Earthquake prediction ; prediction objective ; prediction error diagram ; hazard function ; Bellman equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract In this review we consider an interdisciplinary problem of earthquake prediction involving economics. This joint research aids in understanding the prediction problem as a whole and reveals additional requirements for seismostatistics. We formulate the problem as an optimal control problem: Prossessing the possibility to declare several types of alerts, it is necessary to find an optimal changing alert types; each successful prediction prevents a certain amount of losses; total expected losses are integrated over the semi-infinite time interval. The discount factor is included in the model. Algorithmic and exact solutions are indicated. This paper is based on the recent results byMolchan (1990, 1991, 1992).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945169
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Anomalies in Multifractal Formalism for Local Time of Brownian Motion (1998)
    Springer
    Journal of statistical physics 91 (1998), S. 199-220 
    Details
    ISSN: 1572-9613
    Keywords: Multifractals ; generalized Rényi dimension ; fractal Brownian motion ; subordinators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Renyi function for the logical time measure μ of Brownian motion is found. It is shown that this function, the Legendre transform of the multifractal spectrum of μ and the τ-function derived by the reciprocal measure formalism are not identical. More examples of μ having similar anomalies are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023044221942
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  • 6
    Electronic Resource
    Electronic Resource
    Maximum of a Fractional Brownian Motion: Probabilities of Small Values (1999)
    Springer
    Communications in mathematical physics 205 (1999), S. 97-111 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: Let b γ (t), b γ(0)= 0 be a fractional Brownian motion, i.e., a Gaussian process with the structure function , 0 〈 γ 〈 2. We study the logarithmic asymptotics of P T = P{b γ (t) 〈 1,□t∈TΔ} as T→∞, where Δ is either the interval (0,1) or a bounded region that contains a vicinity of 0 for the case of multidimensional time. It is shown that ln P T = - D ln T(1 + o(1)), where D is the dimension of zeroes of b γ (t) in the former case and the dimension of time in the latter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050669
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  • 7
    Electronic Resource
    Electronic Resource
    Scaling exponents and multifractal dimensions for independent random cascades (1996)
    Springer
    Communications in mathematical physics 179 (1996), S. 681-702 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper is concerned with Mandelbrot's stochastic cascade measures. The problems of (i) scaling exponents of structure functions of the measure, τ(q), and (ii) multifractal dimensions are considered for cascades with a generator vector (w 1...w c) of the general type. These problems were previously studied for independent strongly bounded variablesw i: 0〈a〈w i≦c. Consequently, a broad class of models used in applications, including Kolmogorov's long-normal model in turbulence, long-stable “universal” cascades in atmospheric dynamics, has not been covered. Roughly speaking, problems (i), (ii) are here solved under the condition that the scaling exists; the τ-function is calculated for all arguments (previously this was done for positiveq) and a new effect emerges: the τ-function can generally involve discontinuities in the first derivative as well as in the second.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02100103
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  • 8
    Electronic Resource
    Electronic Resource
    Multifractal analysis of Brownian zero set (1995)
    Springer
    Journal of statistical physics 79 (1995), S. 701-730 
    Details
    ISSN: 1572-9613
    Keywords: Multifractals ; Brownian motion ; limit theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The multifractal structure of zerosZ of Brownian motion is considered. For different measures onZ we find typical characteristics: the τ-function and the multifractal spectrumf(α). A dimensional interpretation off(α) is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02184877
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  • 9
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    Seismic hazard assessment for the Caucasus test area (2006)
    Details
    Publication Date: 2021-04-07
    Description: The GSHAP CAUCAS test area was established under the INTAS Ct.94-1644 (Test Area for sismic Hazard Assessment in the Caucasus) and NATO ARW Ct.95-1521 (Historical and Prehistorical Earthquakes in the Caucasus), with the initial support of IASPEI, UNESCO and ILP. The high tectonic interest and seismicity rate of the whole area, the availability of abundant multi-disciplinary data and the long established tradition in hazard assessment provide a unique opportunity to test different methodologies in a common test area and attempt to establish some consensus in the scientific community. Starting from the same input data (historical and instrumental seismic catalogue, lineament and homogeneous seismic source models) six independent approaches to seismic hazard assessment have been used, ranging from pure historical deterministic to seismotectonic probabilistic and areal assessment methodologies. The results are here compared.
    Description: JCR Journal
    Description: open
    Keywords: Seismic hazard assessment ; Caucasus ; historical earthquake ; UN/IDNDR ; active faults ; 04. Solid Earth::04.06. Seismology::04.06.99. General or miscellaneous ; 04. Solid Earth::04.06. Seismology::04.06.11. Seismic risk
    Repository Name: Istituto Nazionale di Geofisica e Vulcanologia (INGV)
    Type: article
    Format: 3841063 bytes
    Format: application/pdf
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  • 10
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    Seismic hazard assessment for the Caucasus test area (1997)
    In:  Proceedings of the 29th IASPEI General Assembly Workshop 17
    Details
    Publication Date: 2020-02-12
    Keywords: 550 - Earth sciences
    Type: info:eu-repo/semantics/conferenceObject
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