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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   
74.
This paper deals with the problem of detecting and correcting cycle-slips in Global Navigation Satellite System (GNSS) phase data by exploiting the Bayesian theory. The method is here applied to undifferenced observations, because repairing cycle-slips already at this stage could be a useful pre-processing tool, especially for a network of permanent GNSS stations. If a dual frequency receiver is available, the cycle-slips can be easily detected by combining two phase observations or phase and range observations from a single satellite to a single receiver. These combinations, expressed in a distance unit form, are completely free from the geometry and depend only on the ionospheric effect, on the electronic biases and on the initial integer ambiguities; since these terms are expected to be smooth in time, at least in a short period, a cycle-slip in one or both the two carriers can be modelled as a discontinuity in a polynomial regression. The proposed method consists in applying the Bayesian theory to compute the marginal posterior distribution of the discontinuity epoch and to detect it as a maximum a posteriori (MAP) in a very accurate way. Concerning the cycle-slip correction, a couple of simultaneous integer slips in the two carriers is chosen by maximazing the conditional posterior distribution of the discontinuity amplitude given the detected epoch. Numerical experiments on simulated and real data show that the discontinuities with an amplitude 2 or 3 times larger than the noise standard deviation are successfully identified. This means that the Bayesian approach is able to detect and correct cycle-slips using undifferenced GNSS observations even if the slip occurs by one cycle. A comparison with the scientific software BERNESE 5.0 confirms the good performance of the proposed method, especially when data sampled at high frequency (e.g. every 1 s or every 5 s) are available.  相似文献   
75.
The assessment of positional uncertainty in line and area features is often based on uncertainty in the coordinates of their elementary vertices which are assumed to be connected by straight lines. Such an approach disregards uncertainty caused by sampling and approximation of a curvilinear feature by a sequence of straight line segments. In this article, a method is proposed that also allows for the latter type of uncertainty by modelling random rectangular deviations from the conventional straight line segments. Using the model on a dense network of sub‐vertices, the contribution of uncertainty due to approximation is emphasised; the sampling effect can be assessed by applying it on a small set of randomly inserted sub‐vertices. A case study demonstrates a feasible way of parameterisation based on assumptions of joint normal distributions for positional errors of the vertices and the rectangular deviations and a uniform distribution of missed sub‐vertices along line segments. Depending on the magnitudes of the different sources of uncertainty, not accounting for potential deviations from straight line segments may drastically underestimate the positional uncertainty of line features.  相似文献   
76.
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   
77.
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   
78.
Contents of 13C in kerogens and carbonates in 21 samples from a core of the MAX borehole, Mulhouse Evaporite Basin, range from -27.3 to -23.5 and -3.7 to -1.8% vs PDB, respectively. Organic nitrogen in the same samples is enriched in 15N relative to atmospheric N2 by 12.2-15.7%. Hydrogen indices and delta values for kerogens vary systematically with facies, averaging 493 mg HC/g Corg and -25.7% in the most saline facies (dominated by inputs from aquatic sources) and 267 mg HC/g Corg and -23.7% in the least saline facies (50/50 aquatic/terrigenous). Values of delta were measured for individual aliphatic hydrocarbons from three samples representing three different organic facies. For all samples, terrigenous inputs were unusually rich in 13C, the estimated delta value for bulk terrigenous debris, apparently derived partly from CAM plants, being -22.5%. In the most saline facies, isotopic evidence indicates the mixing of 13C-depleted products of photosynthetic bacteria with 13C-enriched products of halotolerant eukaryotic algae. At lower salinities, a change in the producer community is marked by a decrease in the 13C content of algal lipids. The content of 13C in algal lipids increases in the least saline facies, due either to succession of different organisms or to decreased concentrations of dissolved CO2.  相似文献   
79.
Summary Olivine-plagioclase and phlogopite-plagioclase coronas have been identified from olivine melanorites of the Mid- to Late Proterozoic Equeefa Suite in southern Natal, South Africa. Olivine, in contact with plagioclase, is mantled by a shell of clear orthopyroxene, in turn rimmed by pale green (pargasitic) clinoamphibole. Locally a third rim, composed of a fine pargasite-spinel symplectite is developed adjacent to the plagioclase. The second corona reaction has produced greenish-brown pargasite at phlogopite-plagioclase interfaces. A third, less obvious reaction, between olivine and phlogopite is also noted. Analytical data of all the mineral phases present, along with the coronas, are given. Two-pyroxene thermometry yields magmatic core temperatures ( 1120°C), with rim compositions indicating equilibration at 850°C. Consistent with this, the modelled olivine-plagioclase reaction occurs between 830–1050°C with awaterbetween 0.1 and 1.0 at 7 kbar. The three reactions took place during a prolonged history of cooling and partial hydration of the magmatic olivine melanorites from over 1000°C down to 600°C. The P-T conditions indicated by the reactions suggest this cooling process was essentially isobaric, indicating that the area was not subjected to rapid uplift or burial throughout this entire period.
Korona-Texturen in proterozoischen Olivin-Melanoriten der Equeefa Suite, Natal Metamorphic Province, Südafrika
Zusammenfassung Aus Olivin-Melanoriten der mittel- bis spätproterozoischen Equeefa Suite im südlichen Natal, Südafrika, wurden Olivin-Plagioklas und Phlogopit-Plagioklas-Koronartexturen beobachtet. Olivin, der mit Plagioklas im Kontakt steht, wird von einem klaren Saum vom Orthopyroxen ummantelt, der seinerseits von blaßgrünem (pargasitischem) Klinoamphibol umsäumt wird. Stellenweise ist ein dritter Saum, bestehend aus feinkörnigem symplektitischem Pargasit-Spinell im Kontakt mit Plagioklas ausgebildet. Die zweite koronabildende Reaktion resultiert in Bildung eines grünbraunen Pargasites an Phlogopit-Plagioklas Kornkontakten. Eine dritte, weniger auffällige Reaktion zwischen Olivin und Phlogopit wurde ebenfalls beobachtet. Zwei-Pyroxen-Thermometrie ergab magmatische Temperaturen der Kernbereiche ( 1120°C) und belegt eine Gleichgewichtseinstellung in den Randzonen bei ca. 850°C. Olivin-Plagioklas-Modellreaktionen liegen ebenfalls in einem Temperaturbereich von 830–1050°C bei Wasseraktivitäten von 0.1 bis 1.0 und einem Druck von 7 kbar. Die drei Reaktionen liefen im Zuge einer länger andauernden Abkühlung unter teilweiser Hydratisierung der magmatischen Melanorite in einem Temperaturbereich von 1000°C bis ca. 600°C ab. Die aus den Reaktionen ableitbaren P-T-Bedingungen sprechen für eine im wesentlichen isobare Abkhlungsgeschichte und zeigen, daß dieses Gebiet wáhrend dieser gesamten Periode keiner raschen Hebung bzw. keiner Versenkung unterworfen worden ist.
  相似文献   
80.
Nearshore sandbars are important features in the surf zone of many beaches because they strongly influence the mean circulation and evolving morphology. Due to variations in wave conditions, sandbars can experience cross-shore migration and vary in shape from alongshore uniform (shore-parallel) to alongshore rhythmic (crescentic). Sandbar dynamics have been studied extensively, but existing observational studies usually do not quantify the processes leading to crescentic bar formation and straightening. This study analyses the dynamics of crescentic bar events at the fetch-limited beach of Castelldefels (northwestern Mediterranean Sea, Spain) using 7.5 years of hourly time-exposure video images and detailed wave conditions. The results show that, despite the generally calm wave conditions, the sandbars were very dynamic in the cross-shore and longshore directions. They often migrated rapidly offshore during storms (up to 70 m in one day) and more slowly onshore during post-storm conditions. Crescentic bars were often present at the study site (48% of the time), but only when the sandbar was at least 10 m from the shoreline. They displayed a large variability in wavelengths (100–700 m), alongshore migration speeds (0–50 m/day) and cross-shore amplitudes (5–20 m). Wavelengths increased for larger bar–shoreline distances and the alongshore migration speeds were strongly correlated with the alongshore component of the radiation stresses. Crescentic patterns typically developed during low–medium energetic waves with limited obliquity ( θ20° at 10 m depth), while bar straightening occurred during medium–high energetic waves with strong oblique angles of incidence ( θ15°). Overall, this study provides further proof for the important role of wave direction in crescentic bar dynamics and highlights the strong dependence of crescentic bar development on the initial bathymetric configuration.  相似文献   
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