Nach oben pdf Regional gravity field recovery using the point mass method

Regional gravity field recovery using the point mass method

Regional gravity field recovery using the point mass method

The applicability of this regional approach was demonstrated by analyzing the results of five nu- merical tests with synthetic and real data. The first numerical test aimed at investigating the effect of different choices of model factors on the solutions. As a result, a computation procedure of PM-FIX was proposed for practical applications. Regarding PM-FRE, an empirical rule was developed for choosing the initial depth and depth limits and the radial-direction optimization was preferred in the search process. In the second step, the reduced RBFs are highly recommended for the readjust- ment of the magnitudes, leading to an unconstrained solution. Alternatively, the use of full RBFs for constructing the linear equation system and the adding of the constraints in the adjustment are also able to provide good solutions, resulting in a constrained solution. The unconstrained solution performed slightly better than the constrained one, and also was easier to calculate. Therefore, the former was preferred. By means of numerical comparisons between PM-FIX and PM-FRE, the lat- ter outperformed the former. Therefore, only PM-FRE was used in the remaining numerical tests. Through the second and the third tests, it was shown that PM-FRE can recover the gravity anoma- lies from the observed geoid heights, providing better solutions than LSC. We also found that the use of full RBFs works fine for computing the unconstrained solution, indicating that the choice of spectral bandwidths of the RBFs depends on the type of modeled gravity field quantities. If they were in the short-wavelength domain, the use of reduced RBFs is not necessary. In addition, an iterative procedure based on VCE was developed for dealing with the case of several data groups with the same data type but different accuracies. The numerical results confirmed the advantage of the iterative procedure. On the basis of the three numerical tests, the “optimal” strategy for PM- FRE was obtained. In the fourth numerical test, a set of synthetic terrestrial and airborne gravity disturbances were used for the regional modeling. When using terrestrial data only, the solution of PM-FRE was compared to the LSC solution, showing a smaller RMS error of the modeled disturbing potential at ground. When considering both terrestrial and airborne data, the solutions obtained by using different schemes for finding the point mass RBFs were compared and validated, exhibiting a good agreement between each other. In the last numerical test in the Auvergne area using a large number of real gravity observations, both gravity and height anomaly solutions were calculated with small RMS (or STD) errors by PM-FRE. Two combination approaches were successfully applied to eliminate the discrepancies between the gravimetric and GPS/leveling-derived height anomalies.
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Quantum corpuscular approach to solutions in gravity and field theory

Quantum corpuscular approach to solutions in gravity and field theory

respect to small x), where the gluon distribution becomes maximally packed. Since this point corresponds to a critical point in the flow equation, the phenomenon is universal for arbitrary hadrons. Remembering our discussion about the scale dependence of the Fock space representation of a hadron, this result tells us that at that point all hadrons basically look like a dense state of gluons. As such the hadron could be represented as a coherent state of longitudinal gluons which at the classical level of the description is replaced by a classical field configuration, i.e. a classical color background [66]. Notice that the coherent state can be represented as some kind of condensate from the QFT’s persective. Since there is a large number of quanta of characteristic wavelength given by the inverse typical mass scale of the kinematic regime one considers, the classical background simply corresponds to a high flux of particles of the underlying microscopic theory in a given momentum mode, i.e. a condensate. Taking this analogy seriously we might be tempted to interpret gravi- tational backgrounds in a similar way. There is, however, one more input that we need. While Duff’s computation of the Schwarzschild metric in terms of tree level processes [67] seems to be somewhat analogous to the BFKL resummation, there is still an important difference. While in QCD the internal structure of a hadron in terms of quarks and gluons is taken into account explicitly, this is not the case in Duff’s computation. Instead, he considers the scattering on a classical external source with no internal dynamics. It is exactly this type of internal dynamics which we need in order to postulate the existence of condensates in gravity. In particular, we saw that an interpretation of a hadron in terms of a condensate of gluons heavily relies on the distribution function of gluons inside the hadron. Using additional input from the Black Hole Quantum N portrait, the analogy to QCD in the small-x regime becomes more appropriate. In particular, since black holes are maximally packed systems of N gravitons of typical wavelength set by the Schwarzschild radius there is a high graviton flux concentrated in the black hole which we interprete as condensation process with respect to flat space-time.
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Sampling the Earth`s Time-Variable Gravity Field from Satellite Orbit  --  Design of Future Gravity Satellite Missions

Sampling the Earth`s Time-Variable Gravity Field from Satellite Orbit -- Design of Future Gravity Satellite Missions

Another limit of GRACE mission performance is the use of accelerometers to measure the non-gravitational forces. In contrast, the GOCE mission takes advantage of single-axis drag- free control by using a shielded proof mass as a reference point which can be employed for the inter-satellite measurements. The mission accelerometry senses drag forces and compensates them by employing electric propulsion. The proof mass acceleration noise of GOCE is lower than the noise level of an accelerometer. That is because the uncertainty associated with ac- celerometer scale factor is avoided. The GOCE mission successfully implemented single-axis drag-free control (Drinkwater et al., 2007). Further developments in drag-free system may allow us to benefit from better sensitivity of short wavelength features of the gravity field by flying the spacecraft in lower altitudes (Aguirre-Martinez and Sneeuw, 2002). However, flying at lower altitudes causes drag forces to increase exponentially which limits the lifetime of the mission. This fact should also be considered when formation flights for future missions are designed. As an example, the GRACE mission was originally designed for 5 years in oper- ation at an altitude of 480 km, while GOCE is expected to be in operation for approximately 2 years at its orbit around 255 km.
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Regional Gravity Field Modeling with Adjusted Spherical Cap Harmonics in an Integrated Approach

Regional Gravity Field Modeling with Adjusted Spherical Cap Harmonics in an Integrated Approach

The calculation of the SH coefficients can only be solved by means of global data coverage. This could only be achieved after the first geodetic satellite missions (like the LAGEOS, GRACE, GOCE and CHAMP missions). The satellite missions are utilizing different types of measurement principles. The LAGEOS satellites apply the principle of Satellite Laser Ranging (SLR), while the CHAMP mission uses the principle of Satellite-to-Satellite tracking in high- low mode, where the residual gravity accelerations are additionally measured by means of an accelerometer. The GRACE Satellite mission uses the principle of Satellite-to-Satellite tracking in low-low mode, where the gravity differences between two satellites separated by hundreds of kilometers are observed. The most modern GOCE mission uses the principle of gravity gradiometry using a group of accelerometers fixed on the three axes of the satellite. The combination of satellite observations with terrestrial measurements led to the combined gravity models (e.g. EGM98A, EGM96, EIGEN06c and EGM2008). The SH can be calculated by two methods: the first is the integration method that keeps the orthogonality conditions of the SH, and second is the least squares estimation (Fan, 2004).
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Sampling the earth's time-variable gravity field from satellite orbit : design of future gravity satellite missions

Sampling the earth's time-variable gravity field from satellite orbit : design of future gravity satellite missions

Another limit of GRACE mission performance is the use of accelerometers to measure the non-gravitational forces. In contrast, the GOCE mission takes advantage of single-axis drag- free control by using a shielded proof mass as a reference point which can be employed for the inter-satellite measurements. The mission accelerometry senses drag forces and compensates them by employing electric propulsion. The proof mass acceleration noise of GOCE is lower than the noise level of an accelerometer. That is because the uncertainty associated with ac- celerometer scale factor is avoided. The GOCE mission successfully implemented single-axis drag-free control (Drinkwater et al., 2007). Further developments in drag-free system may allow us to benefit from better sensitivity of short wavelength features of the gravity field by flying the spacecraft in lower altitudes (Aguirre-Martinez and Sneeuw, 2002). However, flying at lower altitudes causes drag forces to increase exponentially which limits the lifetime of the mission. This fact should also be considered when formation flights for future missions are designed. As an example, the GRACE mission was originally designed for 5 years in oper- ation at an altitude of 480 km, while GOCE is expected to be in operation for approximately 2 years at its orbit around 255 km.
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Global and regional gravity field recovery by combining satellite, air-shipborne and terrestrial gravimetry data

Global and regional gravity field recovery by combining satellite, air-shipborne and terrestrial gravimetry data

The main contributions of this thesis, as well as outlooks, can be summarized as follows: The gravity field model IGGT_R1 has been generated using the GOCE IGGT by least squares method as described in this thesis. Due to the special characteristics of IGGT, this model avoids errors introduced by inaccurate measurement of the satellite’s attitude during the traditional coordinate transformations. Additionally, according to the principle of least squares, the direct solution method is theoretically strict and there are no grid or integral discretization errors introduced in the harmonic analysis. The linearization error can be neglected if the a-priori gravity field model is relatively accurate. In such a case the corresponding linearization error is smaller than the accuracy of the GOCE GGs. Using the SCRA in combination with Kaula’s rule of thumb is an effective way to reduce the ill-conditioned problem of the normal equation which primarily helps to improve the low-order coefficients. From numerical analyses of this gravity field model, it showed that the precision of the obtained gravity anomaly values over Antarctica, South America, Africa, west China and Indonesia are improved due to the GOCE GGs. The RMS differences between GNSS/Leveling data and the model-derived geoid heights show that IGGT_R1 is more precise than SPW_R1 and TIM_R1, and it performs similarly to DIR_R1 and DIR_R2. In comparison to the a-priori gravity field model EIGEN-5C, the overall accuracy of IGGT_R1 is improved according to the GNSS/Leveling checking results. This represents the contribution of the GOCE GGs, especially in Brazil and China. According to geostrophic velocity speeds in the Agulhas current area, IGGT_R1, which yields more details because of the GOCE GGs, might be an improvement over EIGEN-5C. Considering time-consuming of calculation by the least squares method, IGGT_R1 contains the same GOCE GGs as ESA’s gravity field models of the First Released . In the future, I plan to calculate a more precise gravity field model which contains all GGs data of GOCE mission. The conclusion is that high precision gravity field models can be obtained using the approach as outlined in this thesis. This provides a new direction for building gravity field models from the GOCE GGs as well as from future satellite GGs. Paper 1 (c.f. chapter 2) is my contribution to answer the reseach question 1 (c.f. chapter 1)
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The Valuation of Different Island Destinations Using Gravity Models

The Valuation of Different Island Destinations Using Gravity Models

The Gross domestic product (GDP) associated to the emitting countries, indicator of the dimension of the markets that compose the demand, was obtained from series published for the OECD. As a consequence of being expressed at current prices and American dollars (USD), we were forced to deflation this variable using the price index for the United States (2000 = 100), which means that we assume that the rate of relative inflation is implicit in the exchange rate. We work, in such a way, with the GDP at constant prices of 2000.
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EU2'S REGIONAL ECONOMIC RECOVERY SOLUTIONS UNDER THE GLOBAL CRISIS

EU2'S REGIONAL ECONOMIC RECOVERY SOLUTIONS UNDER THE GLOBAL CRISIS

sector. On the other hand, some EU member states from Central and Eastern Europe were particularly hard hit by this way to attract revenues to the public budget. The second category is connected to the economy dependence on exports and the current budget position. Those countries which had a powerful export demand and/or had current budgetary surplus were highly exposed to the world trade contraction. On the other hand, other countries which had high budgetary deficits faced to a flooding capital flows risk. Some Central and Eastern European member states can be included into the last category. Sometimes, the sudden stop of the foreign financing forces the governments to ask for technical assistance connected to the cash flow from the EU, IMF and World Bank.
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Method of Constructing Point Generalization Constraints Based on the Cloud Platform

Method of Constructing Point Generalization Constraints Based on the Cloud Platform

Cartographic generalization is an indispensable technique for transferring or changing the scale of digital maps [ 4 ]. It is an important means of modelling and understanding geographical phenomena [ 5 ]. Map generalization provides many algorithms to retain the important feature points, or groups of statistics, topics, topological and geometric information [ 6 – 9 ], to improve the readability of the map [ 10 ]. When manually carried out, map generalization can be a very long task for a cartographer, so its automation has been studied by scholars and practitioners for years [ 11 ]. Automatic map generalization processes are computationally intensive, and usually they are unable to deal with the size of real region-wide or countrywide geographical datasets [ 12 ]. Meanwhile, in order to meet the needs of web maps, on-the-fly generalization, denotes the use of automated generalization techniques in real-time [ 13 ], has also become a research hotspot. But all demonstrations of fully automated generalization from a single large scale database are either quite limited in the range of generalization operations that can be performed or not performed in a time that is applicable to online applications [ 14 ]. Therefore, it is urgent to further study the real-time realization of map generalization. Some scholars have put forward the methods of establishing a spatial index [ 15 ], a progressive integrated strategy [ 16 , 17 ], and constructing a multi-scale spatial database [ 18 ] to improve the efficiency of map generalization. Although these methods improve the implementation efficiency of map generalization to some extent, the traditional stand-alone processing approach has reached a bottleneck [ 19 ].
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Phase field modeling of ferroelectrics with
point defects

Phase field modeling of ferroelectrics with point defects

Phase field methods are used widely for the study of domain structures in ferroelectrics re- cent years. Cao et al. first introduced a gradient energy in the order parameter to account for interphase boundaries energy of the tetragonal phase in perovskites [70]. Some works also extended the free energy to include dipole-dipole interaction in the phase field model. Li et al. raised a phenomenological model. They introduced remanent polarization and remanent strain as an internal variable which only consider the single-axial case [71]. Wang et al. simulated polarization switching in ferroelectrics using a phase field model based on the Ginzburg-Landau equation. The phase field model takes both multiple-dipole-dipole-elastic and multiple-dipole- dipole-electric interactions into account [72]. Zhang and Bhattacharya formulated a phase field model which can predict the macroscopic behavior and the microstructural evolution of ferro- electrics under electro-mechanical boundary conditions [73]. Soh et al. have also done phase field simulations and the results have shown that the coupled electro-mechanical loading change both the symmetry of hysteresis loops and the coercive field of ferroelectric materials [74]. Su and Landis devised a continuum thermodynamic framework to model the evolution of domain structures in ferroelectrics [75]. Schrade et al. established a continuum physics model which is descretized with finite element method. In contrast to other phase field models, the model takes the spontaneous polarization as primary order parameter [76, 77]. Size dependent domain configurations and dead layers in ferroelectrics have also been studied by phase field models [78, 79]. Phase transition induced by mechanical stress in ferroelectrics has also been studied by phase field models [80, 81].
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On the accuracy of gravity-RAS approaches used for inter-regional trade estimation: evidence using the 2005 inter-regional input–output table of Japan

On the accuracy of gravity-RAS approaches used for inter-regional trade estimation: evidence using the 2005 inter-regional input–output table of Japan

Julio Gustavo Fournier Gabela German Institute for Economic Research (DIW Berlin) and Humboldt University of Berlin, Berlin, Germany ABSTRACT In contrast to international trade, it is still difficult to find regional trade statistics within a nation. Given that the gravity model con- tinues to be very popular, we test two gravity-RAS approaches used for interregional trade estimation: a standard one and an extended version, which additionally estimates intra-regional flows. We assess the accuracy with the help of two measures and for different sec- toral aggregation levels. For that, we use the survey-based 2005 interregional input–output table of Japan as a benchmark. Results show high overall accuracy levels for the standard approach, bet- ter than when using international data, albeit with heterogeneous errors for sectors and regions. We further find that the results of a multiregional input-output model are highly sensitive to the trade estimation approach and that errors slightly increase for increasing sectoral disaggregation levels. Results from an experiment based on a random number generator show how RAS influences results.
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A Combined Entropy/Phase-Field Approach to Gravity

A Combined Entropy/Phase-Field Approach to Gravity

4. Lagrange Formalism Similar to entropy, the Lagrange formalism also plays a significant role in many areas of physics. In addition to the derivation of the Boltzmann factor depicted above, the Lagrange formalism is a major foundation for quantum mechanics and, in particular, has been used to derive relations between symmetries and conservation laws. The Noether theorems, which were derived using the Lagrange formalism, showed that invariance of physical laws subject to a translation implies the conservation of momentum and invariance subject to translation in time implies the conservation of energy. A further striking observation is that major physical laws all contain a Laplacian operator (that is, are a Poisson-type equation) somehow suggesting a common ground of all these models, which comprise all different length scales like gravitation, electrostatics, thermal conductivity, diffusion, flow, phase-field, Schrödinger equations, density functional equations and many others. Some operators present in the Lagrange scheme have the property of generating Laplacian operators. The basic concept of the Lagrange formalism is based on a functional being a scalar function F of a variable Φ i which, itself, is a function of space and time Φ i = Φ i ( r, t ) , and being an integral of a density function f.
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Electric Field Gradients Around Point Defects in Metals 

Electric Field Gradients Around Point Defects in Metals 

Note that the displacements at the next-nearest neigh- bour atoms, while still small (3.6 • 10" 3 a 0 ), are much larger than those of the nearest neighbours of the vacant site. [r]

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Statistical properties of the cosmic density field beyond 2-point statistics

Statistical properties of the cosmic density field beyond 2-point statistics

To explain the amplitude of density fluctuations today compared to those observed in the CMB (but also to explain other observations such as galaxy rotation curves) gravity must be stronger on the scales of galaxies and galaxy clusters than would be expected from GR and the amount of Baryonic matter (i.e. ordinary matter that interacts with the electromagnetic field). This could either be caused by the exis- tence of a dark matter component or by deviations of gravity from Einstein’s theory (see Plehn 2017 for a review about dark matter; see Milgrom 2001 for alternative considerations). In any case, this would represent a shortcoming of either GR or the standard model of particle physics. Recent hypotheses that link this excess gravity to the thermodynamics of quantum degrees of freedom of spacetime might even signify that this problem is directly relevant to the problem of a combined description of quantum and gravitational physics (Verlinde, 2016, see also chapter 21 of this thesis for a brief review).
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Using field experiments in the economics of charity

Using field experiments in the economics of charity

Economists have long known the importance of focusing on “real” as opposed to “nominal” variables in order to understand a wide range of economic outcomes including growth, productiv- ity, and welfare. While the distinction between real and nominal variables is simple in theory, in practice it is very difficult for statistical agencies to mea- sure prices accurately. One of the main problems is that the set of goods in the economy is constantly changing because of the creation of new goods and quality upgrading. How can we measure price changes when the set of goods consumed in two periods is different? Much of our research over the last few years has focused on estimating the impact of new goods on our understanding of the U.S. and world economies.
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Supporting IT Service Fault Recovery with an Automated Planning Method

Supporting IT Service Fault Recovery with an Automated Planning Method

for the purpose of storage provisioning and disaster recovery. The archi- tecture has two separated planners: a provisioning planner and a recovery planner. The provisioning planner resolves the storage requirements from users and finds a set of configurations and corresponding implementation details, whereas the recovery planner is responsible for finding application- level recovery actions in cases of service failure. As the recovery planner is directly related to our research, in this section we will discuss the recov- ery planner instead of investigating the whole architecture. The recovery planner consists of several components collaborating together to fulfill the functionality: the discovery engine is designed to gather static information from the servers, storages, networks and so on that are associated with the storage service. Furthermore, it collects data on the software applications and their configuration from those associated devices that are involved in the service. The knowledge base is a repository which persistently stores the best recovery practices and suggestions from operators and the sys- tem designer. The knowledge is in the form of a recipe template, which describes best-practices such as configuration options and replication tech- niques that could be applied in cases of storage failure. The match maker component finds a set of replication technologies to fulfill the requirements of recovery. The match maker module computes the solution based on the pre-determined requirements or profiles from the administrators for the spe- cific services. It takes such information as input and searches the knowledge base for the qualified solutions. There are two types of searches involved in the operations: searching in the solution templates for the popular strategies that could match the requirements or searching in the technology category. Finally, the search results are consolidated and combined as solutions by the optimisation and orchestration modules.
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Approximate Approximations and a Boundary Point Method for the Linearized Stokes System

Approximate Approximations and a Boundary Point Method for the Linearized Stokes System

Abstract The method of approximate approximations, introduced by Maz’ya [1], can also be used for the numerical solution of boundary integral equations. In this case, the matrix of the resulting algebraic system to compute an approximate source density depends only on the position of a finite number of boundary points and on the direction of the normal vector in these points (Boundary Point Method). We investigate this approach for the Sto- kes problem in the whole space and for the Stokes boundary value problem in a bounded convex domain G ⊂ R 2 , where the second part consists of three steps: In a first step the
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Orbital evolution of the BepiColombo Mercury Planetary Orbiter (MPO) in the gravity field of Mercury

Orbital evolution of the BepiColombo Mercury Planetary Orbiter (MPO) in the gravity field of Mercury

The simulations of the orbital evolution of MPO were performed using the generated gravity fields of Mercury with the scale factors 1, 3, 5 and 10. The results of the simulations were analyzed and compared with each other. The evolution of the orbit of MPO is expressed in the orbital elements. The analysis is mainly focused on the periherm as the minimal distance to the surface of Mercury is critical for the mission. The results show that the geopotential of Mercury causes an increase in the eccentricity and a decrease in the periherm altitude. The semi-major axis and the inclination have a periodic character but remain almost constant. The longitude of ascending node decreases slowly with periodic fluctuations. The argument of periapsis falls almost linear. The standard deviations, as well as the difference between the minimal and maximal values get larger with a growing scale factor and over time. The values of the elements are still in an acceptable range after the first year. The change in the periherm after 2 years could already be considered as critical in some cases for the scale factor 1 because the periherm falls below critical value of 200 km. Moreover, the likelihood that the periherm is below 200 km after 2 years increases with the rising scale factor. Furthermore, there is a possibility that the satellite collides with the planet in the simulations for the scale factor 5 and 10.
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The Gravity Model of Migration: The Successful Comeback of an Ageing Superstar in Regional Science

The Gravity Model of Migration: The Successful Comeback of an Ageing Superstar in Regional Science

ABSTRACT The Gravity Model of Migration: The Successful Comeback of an Ageing Superstar in Regional Science * For at least half a century, and building on observations first made a century earlier, the gravity model has been the most commonly‐used paradigm for understanding gross migration flows between regions. This model owes its success to, firstly, its intuitive consistency with migration theories; secondly, ease of estimation in its simplest form; and, thirdly, goodness of fit in most applications. While fitting gravity models of aggregate migration flows started taking backstage to microdata analysis in the 1980s, a recent comeback has resulted from increasing applications to international migration and from the emergence of statistical theories appropriate for studying spatial interaction. In this paper we review the status quo and argue for greater integration of internal and international migration modelling. Additionally we revisit the issues of parameter stability and distance deterrence measurement by means of a New Zealand case study. We argue that gravity modelling of migration has a promising future in a multi‐regional stochastic population projection system – an area in which the model has been to date surprisingly underutilised. We conclude with outlining current challenges and opportunities in this field.
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Novel sensor concepts for future gravity field satellite missions

Novel sensor concepts for future gravity field satellite missions

• Geodetic applications and reference systems > Novel sensor concepts for future gravity field satellite missions > M.. Schilling > 19.11.2020 DLR.de • Chart 2.[r]

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