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41.
42.
Methodology and use of tensor invariants for satellite gravity gradiometry   总被引:2,自引:1,他引:1  
Although its use is widespread in several other scientific disciplines, the theory of tensor invariants is only marginally adopted in gravity field modeling. We aim to close this gap by developing and applying the invariants approach for geopotential recovery. Gravitational tensor invariants are deduced from products of second-order derivatives of the gravitational potential. The benefit of the method presented arises from its independence of the gradiometer instrument’s orientation in space. Thus, we refrain from the classical methods for satellite gravity gradiometry analysis, i.e., in terms of individual gravity gradients, in favor of the alternative invariants approach. The invariants approach requires a tailored processing strategy. Firstly, the non-linear functionals with regard to the potential series expansion in spherical harmonics necessitates the linearization and iterative solution of the resulting least-squares problem. From the computational point of view, efficient linearization by means of perturbation theory has been adopted. It only requires the computation of reference gravity gradients. Secondly, the deduced pseudo-observations are composed of all the gravitational tensor elements, all of which require a comparable level of accuracy. Additionally, implementation of the invariants method for large data sets is a challenging task. We show the fundamentals of tensor invariants theory adapted to satellite gradiometry. With regard to the GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite gradiometry mission, we demonstrate that the iterative parameter estimation process converges within only two iterations. Additionally, for the GOCE configuration, we show the invariants approach to be insensitive to the synthesis of unobserved gravity gradients.  相似文献   
43.
Large-scale ancient landslides of the area of more than 5 km2 and volume exceeding 200 × 106 m3 are characteristic features of the valleys incised in the northern periphery of the Crimean Mountains (Ukraine). The largely affected area is located in the outermost cuesta range of the Crimean Mountains which consists of rigid Sarmatian limestones overlying weak Middle Miocene and Upper Palaeogene deposits. A giant landslide arose in the Alma water gap as a reflection of several coincident preparatory factors such as suitable bedrock stratification, smectite-rich bedrock exposed to swelling activity, presence of faults parallel to the valley trend, and river capture event which preceded the landslide event. The occurrence of such ancient megaslides is particularly interesting in the area which is characterized by low precipitation (<500 mm/year) and weak contemporary seismicity. It probably reflects a more dynamic environment in humid phases of the Holocene; however, seismic triggering along the Mesozoic suture zone cannot be rejected. Compressional features such as gravitational folds in the central and distal parts of the landslide, which probably correlate with the whole landslide genesis or its significant reactivation, arose, according to the radiocarbon dating, during the Holocene climatic optimum in the Atlantic period. The slope deformation has been relatively quiescent since that time, except minor historic reactivization which took place in the frontal part of the landslide. We suppose that the studied landslide could be classified as a transitional type of slope deformation with some signs of spreading and translational block slides.  相似文献   
44.
We introduce and propose zircon M257 as a future reference material for the determination of zircon U‐Pb ages by means of secondary ion mass spectrometry. This light brownish, flawless, cut gemstone specimen from Sri Lanka weighed 5.14 g (25.7 carats). Zircon M257 has TIMS‐determined, mean isotopic ratios (2s uncertainties) of 0.09100 ± 0.00003 for 206pb/238U and 0.7392 ± 0.0003 for 207pb/235U. Its 206pb/238U age is 561.3 ± 0.3 Ma (unweighted mean, uncertainty quoted at the 95% confidence level); the U‐Pb system is concordant within uncertainty of decay constants. Zircon M257 contains ~ 840 μg g?1 U (Th/U ~ 0.27). The material exhibits remarkably low heterogeneity, with a virtual absence of any internal textures even in cathodoluminescence images. The uniform, moderate degree of radiation damage (estimated from the expansion of unit‐cell parameters, broadening of Raman spectral parameters and density) corresponds well, within the “Sri Lankan trends”, with actinide concentrations, U‐Pb age, and the calculated alpha fluence of 1.66 × 1018 g?1. This, and a (U+Th)/He age of 419 ± 9 Ma (2s), enables us to exclude any unusual thermal history or heat treatment, which could potentially have affected the retention of radiogenic Pb. The oxygen isotope ratio of this zircon is 13.9%o VSMOW suggesting a metamorphic genesis in a marble or calc‐silicate skarn.  相似文献   
45.
Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.  相似文献   
46.
The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.  相似文献   
47.
Let there be given a twodimensional symmetric rank two tensor of random type (examples:strain, stress) which is either directly observed or indirectly estimated from observations by an adjustment procedure. Under the assumption of normalityof tensor components we compute the joint probability density functionas well as the marginal probability density functionsof its eigenspectra (eigenvalues) and eigendirections (orientation parameters). Due to the nonlinearity of the relation between eigenspectra-eigendirections and the random tensor components, via the inverse nonlinear error propagationbiases and aliases of their first and centralized second moments (mean value, variance-covariance) are expressed in terms of Jacobianand Hessianmatrices. The joint probability density function and the first and second moments thus form the fundamental of hypothesis testing and qualify control of eigenspectra (eigenvalues, principal components) and eigendirections (orientation parameters, eigenvectors, principial direction) of a twodimensional, symmetric rank two random tensor.  相似文献   
48.
Summary A coalification data set from the first seam of the Rosice-Oslavany coal district in the Boskovice furrow was used to estimate the temperature gradient prevailing within the furrow during Autunian sedimentation. An appreciable scatter of the data reflects the complicated history of the sedimentary region. The northern part of the district displays a higher degree of coalification. The results of the evaluation suggest that the region ceased to subside in the upper Autunian, and that the extent of the post-Autunian erosion does not exceed 500 metres. This version of the burial history, which is consistent with geological data, yields a temperature paleogradient of 76 mK/m for the northern part and of 72 mK/m for the southern part of the district. The gradients estimated are higher than those prevailing during the Carboniferous sedimentation in the Central Bohemian Basin (45 – 53 mK/m), lower than values found for the Ostrava Formation in the Upper Silesian Basin during its Namurian A sedimentation (about 95 mK/m), but comparable with values evaluated for the Karviná Formation of the same basin deposited during the Namurian B - C and Westphalian A (60 – 77 mK/m).Dedicated to the Memory of Professor Karel P  相似文献   
49.
The hitherto longest found lake sediment sequence on Byers Peninsula, Livingston Island, South Shetland Islands, was analysed with respect to lithology, chronology, diatoms, Pediastrum, pollen and spores, mosses, mineralogy, and sediment chemistry. During the ca. 5000 year long development the sediments were influenced by frequent tephra fall-outs. This volcanic impact played a major role in the lake's history during two periods, 4700–4600 and 2800–2500 BP, but was of importance during the lake's entire history with considerable influence on many of the palaeoenvironmentally significant indicators. The large and complex data set was analysed and zonated with different types of multivariate analysis. This resulted in a subdivision of the sequence into 8 time periods and 21 variables. Redundancy analysis (RDA) of this data set, both without and with the tephra periods, and with 4–6 of the variables as explanatory environmental variables, reveal that climatic/environmental signals are detectable. The palaeoclimatic picture that emerged out of the tephra noise suggests that the first 100 years were characterized by mild, humid conditions. This was followed by a less mild and humid climate until ca. 4000 BP when a gradual warming seems to have started, coupled with increased humidity. These mild and humid conditions seem to have reached an optimum slightly after 3000 BP. At ca. 2500 BP a distinct climatic deterioration occurred with colder and drier conditions and long seasons with ice cover. This arid, cold phase probably reached its optimum conditions at ca. 1500 BP, when slightly warmer conditions might have prevailed for a while. Except for the modern sample with rather mild climate, the last 1400 years seem to have been fairly arid and cold, and the effects of the frequent volcanic activity during this period is only vaguely seen in the records.  相似文献   
50.
Summary The Banach theorem is applied to the Lagrange planetary equation for the semimajor axis of a geostationary satellite orbit to estimate the stability of near-geostationary satellite orbits. To achieve a graveyard (disposal) orbit, which will not interfere (=cross) the initial geostationary orbit, the geostationary semi-major axis ag have to be increased at least by 50 km. Numerical results for a variety of graveyard orbits show that the increase of ag by about 100 km will yield sufficiently stable orbits (accounting for the Earth's gravitational perturbations only) during the next 150 years.Dedicated to the 75th Birthday of Professor Academician Tibor Kolbenheyer  相似文献   
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