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  • 1
    Digitale Medien
    Digitale Medien
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 58 (1995), S. 2131-2135 
    ISSN: 0021-8995
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Publikationsdatum: 2016-05-05
    Beschreibung: We review the theory of the Earth's elastic and gravitational response to a surface disk load. The solutions for displacement of the surface and the geoid are developed using expansions of Legendre polynomials, their derivatives and the load Love numbers. We provide a matlab  function called diskload that computes the solutions for both uncompensated and compensated disk loads. In order to numerically implement the Legendre expansions, it is necessary to choose a harmonic degree, n max , at which to truncate the series used to construct the solutions. We present a rule of thumb (ROT) for choosing an appropriate value of n max , describe the consequences of truncating the expansions prematurely and provide a means to judiciously violate the ROT when that becomes a practical necessity.
    Schlagwort(e): Gravity, Geodesy and Tides
    Print ISSN: 0956-540X
    Digitale ISSN: 1365-246X
    Thema: Geologie und Paläontologie
    Publiziert von Oxford University Press im Namen von The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    Publikationsdatum: 2014-09-07
    Beschreibung: We focus on the relation between seismic and total postseismic afterslip following the Maule M w 8.8 earthquake on 2010 February 27 in central Chile. First, we calculate the cumulative slip released by aftershock seismicity. We do this by summing up the aftershock regions and slip estimated from scaling relations. Comparing the cumulative seismic slip with afterslip models we show that seismic slip of individual aftershocks exceeds locally the inverted afterslip model from geodetic constraints. As the afterslip model implicitly contains the displacements from the aftershocks, this reflects the tendency of afterslip models to smear out the actual slip pattern. However, it also suggests that locally slip for a number of the larger aftershocks exceeds the aseismic slip in spite of the fact that the total equivalent moment of the afterslip exceeds the cumulative moment of aftershocks by a large factor. This effect, seen weakly for the Maule 2010 and also for the Tohoku 2011 earthquake, can be explained by taking into account the uncertainties of the seismicity and afterslip models. In spite of uncertainties, the hypocentral region of the Nias 2005 earthquake is suggested to release a large fraction of moment almost purely seismically. Therefore, these aftershocks are not driven solely by the afterslip but instead their slip areas have probably been stressed by interseismic loading and the mainshock rupture. In a second step, we divide the megathrust of the Maule 2010 rupture into discrete cells and count the number of aftershocks that occur within 50 km of the centre of each cell as a function of time. We then compare this number to a time-dependent afterslip model by defining the ‘afterslip to aftershock ratio’ (ASAR) for each cell as the slope of the best fitting line when the afterslip at time t is plotted against aftershock count. Although we find a linear relation between afterslip and aftershocks for most cells, there is significant variability in ASAR in both the downdip and along-strike directions of the megathrust. We compare the spatial distribution of ASAR with the spatial distribution of seismic coupling, coseismic slip and Bouguer gravity anomaly, and in each case we find no significant correlation.
    Schlagwort(e): Seismology
    Print ISSN: 0956-540X
    Digitale ISSN: 1365-246X
    Thema: Geologie und Paläontologie
    Publiziert von Oxford University Press im Namen von The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
    Standort Signatur Erwartet Verfügbarkeit
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  • 4
    Publikationsdatum: 2019
    Beschreibung: 〈span〉〈div〉Summary〈/div〉We present an accurate approach for calculating the point-dislocation Green's functions (GFs) for a layered, spherical, transversely-isotropic and self-gravitating Earth. The formalism is based on the approach recently used to find analytical solutions for the dislocation Love numbers (DLNs). However, in order to make use of the DLNs, we first analyze their asymptotic behavior, and then the behavior of the GFs computed from the DLNs. We note that the summations used for different GF components evolve at different rates towards asymptotic convergence, requiring us to use two new and different truncation values for the harmonic degree (i.e. the index of summation). We exploit this knowledge to design a Kummer's transformation that allows us to reduce the computation required to evaluate the GFs at the desired level of accuracy. Numerical examples are presented to clarify these issues and demonstrate the advantages of our approach. Even with the Kummer's transformation, DLNs of high degree are still needed when the Earth model contains very fine layers, so computational efficiency is important. The effect of anisotropy is assessed by comparing GFs for isotropic and transversely isotropic media. It is shown that this effect, though normally modest, can be significant in certain contexts, even in the far field.〈/span〉
    Print ISSN: 2051-1965
    Digitale ISSN: 1365-246X
    Thema: Geologie und Paläontologie
    Publiziert von Oxford University Press im Namen von The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
    Standort Signatur Erwartet Verfügbarkeit
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  • 5
    Publikationsdatum: 2019
    Beschreibung: 〈span〉〈div〉SUMMARY〈/div〉We present an accurate approach for calculating the point-dislocation Green's functions (GFs) for a layered, spherical, transversely-isotropic and self-gravitating Earth. The formalism is based on the approach recently used to find analytical solutions for the dislocation Love numbers (DLNs). However, in order to make use of the DLNs, we first analyse their asymptotic behaviour, and then the behaviour of the GFs computed from the DLNs. We note that the summations used for different GF components evolve at different rates towards asymptotic convergence, requiring us to use two new and different truncation values for the harmonic degree (i.e. the index of summation). We exploit this knowledge to design a Kummer transformation that allows us to reduce the computation required to evaluate the GFs at the desired level of accuracy. Numerical examples are presented to clarify these issues and demonstrate the advantages of our approach. Even with the Kummer transformation, DLNs of high degree are still needed when the earth model contains very fine layers, so computational efficiency is important. The effect of anisotropy is assessed by comparing GFs for isotropic and transversely isotropic media. It is shown that this effect, though normally modest, can be significant in certain contexts, even in the far field.〈/span〉
    Print ISSN: 2051-1965
    Digitale ISSN: 1365-246X
    Thema: Geologie und Paläontologie
    Publiziert von Oxford University Press im Namen von The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
    Standort Signatur Erwartet Verfügbarkeit
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  • 6
    Publikationsdatum: 2015-11-07
    Beschreibung: We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/ r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.
    Schlagwort(e): Gravity, Geodesy and Tides
    Print ISSN: 0956-540X
    Digitale ISSN: 1365-246X
    Thema: Geologie und Paläontologie
    Publiziert von Oxford University Press im Namen von The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
    Standort Signatur Erwartet Verfügbarkeit
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  • 7
    Publikationsdatum: 2019
    Beschreibung: 〈span〉〈div〉Abstract〈/div〉In this paper, we derive analytical expressions for the dislocation Love numbers (DLNs) for a layered, spherical, transversely isotropic and self-gravitating Earth. This solution is based on the spherical system of vector functions (or the vector spherical harmonics) and a new propagating matrix method called the dual variable and position method. The DLNs can be obtained with high accuracy to an arbitrarily high degree, thereby allowing a wide range of applications based on high resolution Earth models. Compared to the traditional numerical integration approach, the present analytical solution is at least 3 orders of magnitude faster. Our calculation also indicates that, compared to the isotropic PREM model, the effect of anisotropy is small, with a relative error about 5 per cent for DLN 〈span〉h〈/span〉〈sup〉12〈/sup〉 at degree 〈span〉n 〈/span〉= 69 with source located at depth 100 km. We provide MATLAB code for computing the analytical DLNs in the supplementary materials section, along with a user manual.〈/span〉
    Print ISSN: 2051-1965
    Digitale ISSN: 1365-246X
    Thema: Geologie und Paläontologie
    Publiziert von Oxford University Press im Namen von The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
    Standort Signatur Erwartet Verfügbarkeit
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  • 8
    Publikationsdatum: 2017-10-16
    Beschreibung: Pan et al. presented a new analytical approach to compute the elastic load Love numbers (ELLNs) for an elastic, transversely isotropic, spherical, layered and self-gravitating Earth with a layered fluid core. Any layer or shell can be compressible or incompressible. Here, we enhance this formulation by replacing the direct propagator matrix with the stiffness matrix, which allows us to calculate the ELLNs out to any high degree n. This allows users of the ELLNs to compute point- and disc-load Green's functions without relying on untested assumptions about the onset of asymptotic behaviour. The new method also allows us to compute the ELLNs for Earth models containing fine layers, and enables ELLN users to correctly compute the near-field response to very small disc loads. We demonstrate, using a modified preliminary reference Earth model (PREM) Earth model incorporating refined crustal structure, that the degree n associated with the onset of asymptotic convergence of the ELLNs is very strongly influenced by the fine details of shallow elastic structure, and that this onset degree can exceed 100 000 for plausible Earth models in which the outermost layer has a thickness of 1 km or less. We further demonstrate the excellent numerical stability attainable using the stiffness matrix rather than the direct propagator matrix. We implement our algorithms in a MATLAB library called ELLN, and provide the software in two versions (with and without a graphical user interface), the user guides, and example input files in the Supporting Information.
    Print ISSN: 0956-540X
    Digitale ISSN: 1365-246X
    Thema: Geologie und Paläontologie
    Standort Signatur Erwartet Verfügbarkeit
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  • 9
    Publikationsdatum: 2020-06-27
    Beschreibung: SUMMARY In this paper, we derive analytical solutions for the dislocation Love numbers (DLNs) and the corresponding Green's functions (GFs) within a layered, spherical, transversely isotropic and self-gravitating Earth. These solutions are based on the spherical system of vector functions (or the vector spherical harmonics) and the dual variable and position matrix method. The GFs for displacements, strains, potential and its derivatives are formulated in terms of the DLNs and the vector spherical harmonics. The vertical displacement due to a vertical strike-slip dislocation and the potential change (nΦ) due to a vertical dip-slip dislocation are found to be special, with an order O(1/n) on the source level and O(n) elsewhere. Numerical results are presented to illustrate how the internal fields depend on the particular type of dislocation. It is further shown that the effect of Earth anisotropy on the strain field can be significant, about 10 per cent in a layered PREM model and 30 per cent in a homogeneous earth model.
    Print ISSN: 0956-540X
    Digitale ISSN: 1365-246X
    Thema: Geologie und Paläontologie
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  • 10
    Publikationsdatum: 2019-02-28
    Print ISSN: 0956-540X
    Digitale ISSN: 1365-246X
    Thema: Geologie und Paläontologie
    Standort Signatur Erwartet Verfügbarkeit
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