Optimized formulas for the gravitational field of a tesseroid   总被引：7，自引：3，他引：4  

Thomas Grombein  Kurt Seitz  Bernhard Heck 《Journal of Geodesy》2013,87(7):645-660

Various tasks in geodesy, geophysics, and related geosciences require precise information on the impact of mass distributions on gravity field-related quantities, such as the gravitational potential and its partial derivatives. Using forward modeling based on Newton’s integral, mass distributions are generally decomposed into regular elementary bodies. In classical approaches, prisms or point mass approximations are mostly utilized. Considering the effect of the sphericity of the Earth, alternative mass modeling methods based on tesseroid bodies (spherical prisms) should be taken into account, particularly in regional and global applications. Expressions for the gravitational field of a point mass are relatively simple when formulated in Cartesian coordinates. In the case of integrating over a tesseroid volume bounded by geocentric spherical coordinates, it will be shown that it is also beneficial to represent the integral kernel in terms of Cartesian coordinates. This considerably simplifies the determination of the tesseroid’s potential derivatives in comparison with previously published methodologies that make use of integral kernels expressed in spherical coordinates. Based on this idea, optimized formulas for the gravitational potential of a homogeneous tesseroid and its derivatives up to second-order are elaborated in this paper. These new formulas do not suffer from the polar singularity of the spherical coordinate system and can, therefore, be evaluated for any position on the globe. Since integrals over tesseroid volumes cannot be solved analytically, the numerical evaluation is achieved by means of expanding the integral kernel in a Taylor series with fourth-order error in the spatial coordinates of the integration point. As the structure of the Cartesian integral kernel is substantially simplified, Taylor coefficients can be represented in a compact and computationally attractive form. Thus, the use of the optimized tesseroid formulas particularly benefits from a significant decrease in computation time by about 45 % compared to previously used algorithms. In order to show the computational efficiency and to validate the mathematical derivations, the new tesseroid formulas are applied to two realistic numerical experiments and are compared to previously published tesseroid methods and the conventional prism approach.  相似文献   

Wide-band multi-spectral space for color representation     

Kong Lingwang  Zhu Yuanhong  Kurt Muenger  Zhang Xuliang 《地球空间信息科学学报》2013,16(2):69-74

This paper develops a wide-band multi-spectral space for color representation with Aitken PCA algorithm. This novel mathematical space using the broad-band spectra matching method aims at improving the accuracy of color representation as well as reducing costs for processing and storing multi-spectral images. The results show that the space can present our experimental original spectral spaces (i. e. Munsell color matt and DIN-6164 color chips) with high efficiency, and that the spanning space with three eigenvectors can present the original space at more than 98% CSCR, and when 5 eigenvectors are used it can cover almost the whole original spaces.  相似文献   

Groundwater Evolution and Mineral Alteration Reactions in the Basaltic Rock Sequence of Mt. Wasserkuppe, Germany: A Case Study     

Florian Ludwig  Ingrid Stober  Kurt Bucher 《Aquatic Geochemistry》2012,18(3):185-215

Groundwater sampling was accomplished in the basaltic sequence of the Rh?n mountain range, Germany, in order to investigate hydrochemical groundwater evolution and to delineate mineral alteration reactions involved in natural weathering. The hydrochemical compositions of near-surface groundwaters indicate a Ca/Mg–HCO₃ type with near-neutral pH and evolve to a Na–HCO₃ type with high pH at greater depth. Column experiments were performed with basaltic and phonolitic rock samples to determine individual mineral alteration reactions. The basic reactions could be related to the alteration of olivine, Ca-pyroxene, plagioclase, pyrrhotite, and feldspathoids under formation of secondary clay minerals (smectites, illite) and goethite. The mineral alteration reactions deduced from the leaching experiments by inverse modelling were found to be consistent with the mineral reactions associated with the natural groundwaters. The reactions calculated for groundwater evolution involve the alteration of primary and secondary minerals to produce low-T mineral phase. The conversion of secondary Na-beidellite to illite occurs at a later stage of groundwater evolution, reducing the concentrations of K⁺ and Mg²⁺. Near-surface groundwaters do not indicate significant cation exchange. Initial cation exchange requires elevated pH values, with Mg²⁺ removed from solution preferred to Ca²⁺. Na-alkalisation of the groundwaters at greater depth suggests the exchange of Na⁺ for Mg²⁺ and Ca²⁺ on Na-beidellite, supported by cation exchange on coatings of iron hydroxides as alteration products. Among the mature high-pH groundwater at greater depth, the dissolution of anorthite and albite has significant effect on groundwater composition.  相似文献   

CLEAN: project overview on CO2 large-scale enhanced gas recovery in the Altmark natural gas field (Germany)     

Michael Kühn  Maja Tesmer  Peter Pilz  Robert Meyer  Kurt Reinicke  Andrea F?rster  Olaf Kolditz  Dirk Sch?fer 《Environmental Earth Sciences》2012,67(2):311-321

The joint research project CLEAN was conducted in the years 2008?C2011 by a German research and development (R&D) alliance of 16 partners from science and industry. The project was set-up as pilot project to investigate the processes relevant to enhanced gas recovery (EGR) by the injection of CO₂ into a subfield of the almost depleted Altmark natural gas field. Despite the setback that permission for active injection was not issued by the mining authority during the period of the project, important results fostering the understanding of processes linked with EGR were achieved. Work carried out led to a comprehensive evaluation of the EGR potential of the Altmark field and the Altensalzwedel subfield in particular. The calculated safety margins emphasize that technical well integrity of the 12 examined boreholes is given for EGR without a need for any further intervention. The laboratory and field tests confirm that the Altensalzwedel subfield is suitable for the injection of 100,000?t of CO₂. Numerical simulations provide sound predictions for the efficiency and safety of the EGR technology based on the CO₂ injection. The development and testing of different monitoring techniques facilitate an improved surveying of CO₂ storage sites in general. The CLEAN results provide the technological, logistic and conceptual prerequisites for implementing a CO₂-based EGR project in the Altmark and provide a benchmark for similar projects in the world.  相似文献   

Tracking transformation processes of organic micropollutants in aquatic environments using multi-element isotope fractionation analysis     

Thomas B. Hofstetter  Jakov Bolotin  Marita Skarpeli-Liati  Reto Wijker  Zohre Kurt  Shirley F. Nishino  Jim C. Spain 《Applied Geochemistry》2011

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Latitudinal variation in the aerial/aquatic ratio of oxygen consumption of a supratidal high rocky‐shore crab     

Marco A. Lardies  José Luis Muñoz  Kurt A. Paschke  Francisco Bozinovic 《Marine Ecology》2011,32(1):42-51

The colonisation of the terrestrial environment by crustaceans is more apparent in tropical latitudes because of the high diversity of semi‐terrestrial and terrestrial crabs. However, in temperate regions there are also great numbers of crustaceans that inhabit ecological niches at the water–air interface. Grapsidae crabs (Decopoda) are especially important in studies of water‐to‐land transition as the family contains species occupying the intertidal and adjacent regions. A way to evaluate the ability of intertidal invertebrates to breathe air is to measure the aerial/aquatic oxygen consumption ratio. The objective of this study was to test the effect of thermal variation on the aquatic and aerial metabolism. We selected as study model the decopoda crab Cyclograpsus cinereus Dana and utilised five populations of the species spread over 2000 km along the Chilean coast. To determine the compensation capacity in respiration with respect to latitude, we evaluated metabolic rate at the same temperature in a common garden design in the laboratory, to examine the extent to which variation in crab physiology is environmentally determined. Whereas in our study, m_b (body mass) varied significantly with latitude, the difference in mass‐independent metabolism both in air and water persisted, indicating that observed differences in MR (Metabolic Rate) were not an effect of differences in body size. We demonstrated that C. cinereus is able to breath oxygen from air and water as expected for an amphibious crab. Almost all the studied populations of C. cinereus show a aerial/aquatic metabolism ratio near 1. The pattern found indicates an increase in metabolic rate, both aerial and aquatic, in low latitudes and therefore does not support the latitudinal compensation hypothesis for temperate habitats. Finally, these kinds of studies are required to make the necessary link between ecological physiology and macroecology and to help develop a global understanding of organismal function in marine systems.  相似文献   

Eoalpine tectonics of the Eastern Alps: implications from the evolution of monometamorphic Austroalpine units (Schneeberg and Radenthein Complex)     

Kurt Krenn  Walter Kurz  Harald Fritz  Georg Hoinkes 《Swiss Journal of Geoscience》2011,104(3):471-491

Monometamorphic metasediments of Paleozoic or Mesozoic age constituting Schneeberg and Radenthein Complex experienced coherent deformation and metamorphism during Late Cretaceous times. Both complexes are part of the Eoalpine high-pressure wedge that formed an intracontinental suture and occur between the polymetamorphosed Ötztal–Bundschuh nappe system on top and the Texel–Millstatt Complex below. During Eoalpine orogeny Schneeberg and Radenthein Complexes were south-dipping and they experienced a common tectonometamorphic history from ca. 115 Ma onwards until unroofing of the Tauern Window in Miocene times. This evolution is subdivided into four distinct tectonometamorphic phases. Deformation stage D1 is characterized by WNW-directed shearing at high temperature conditions (550–600°C) and related to the initial exhumation of the high-pressure wedge. D2 and D3 are largely coaxial and evolved during high- to medium-temperature conditions (ca. 450 to ≥550°C). These stages are related to advanced exhumation and associated with large-scale folding of the high-pressure wedge including the Ötztal-Bundschuh nappe system above and the Texel–Millstatt Complex below. For the area west of the Tauern Window, F2/F3 fold interference results in the formation of large-scale sheath-folds in the frontal part of the nappe stack (formerly called “Schlingentektonik” by previous authors). Earlier thrusts were reactivated during Late Cretaceous normal faulting at the base of the Ötztal–Bundschuh nappe system and its cover. Deformation stage D4 is of Oligo-Miocene age and accounted for tilting of individual basement blocks along large-scale strike-slip shear zones. This tilting phase resulted from indentation of the Southern Alps accompanied by the formation of the Tauern Window.  相似文献   

Beryllium-10 terrestrial cosmogenic nuclide surface exposure dating of Quaternary landforms in Death Valley     

Lewis A. Owen  Kurt L. Frankel  Jeffrey R. Knott  Scott Reynhout  Robert C. Finkel  James F. Dolan  Jeffrey Lee 《Geomorphology》2011,125(4):49

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Lunar atmospheric H₂ detections by the LAMP UV spectrograph on the Lunar Reconnaissance Orbiter     

S. Alan Stern  Jason C. Cook  Jean -Yves Chaufray  Paul D. Feldman  G. Randall Gladstone  Kurt D. Retherford 《Icarus》2013

We report on the detection of H₂ as seen in our analysis of twilight observations of the lunar atmosphere observed by the LAMP instrument aboard NASA’s Lunar Reconnaissance Orbiter. Using a large amount of data collected on the lunar atmosphere between September 2009 and March 2013, we have detected and identified, the presence of H₂ in the native lunar atmosphere, for the first time. We derive a surface density for H₂ of 1.2 ± 0.4 × 10³ cm⁻³ at 120 K. This is about 10 times smaller than originally predicted, and several times smaller than previous upper limits from the Apollo era data.  相似文献   

TiO2 exsolution from garnet by open-system precipitation: evidence from crystallographic and shape preferred orientation of rutile inclusions     

Alexander Proyer  Gerlinde Habler  Rainer Abart  Richard Wirth  Kurt Krenn  Georg Hoinkes 《Contributions to Mineralogy and Petrology》2013,166(1):211-234

We investigated rutile needles with a clear shape preferred orientation in garnet from (ultra) high-pressure metapelites from the Kimi Complex of the Greek Rhodope by electron microprobe, electron backscatter diffraction and TEM techniques. A definite though complex crystallographic orientation relationship between the garnet host and rutile was identified in that Rt[001] is either parallel to Grt<111> or describes cones with opening angle 27.6° around Grt<111>. Each Rt[001] small circle representing a cone on the pole figure displays six maxima in the density plots. This evidence together with microchemical observations in TEM, when compared to various possible mechanisms of formation, corroborates a precipitate origin. A review of exchange vectors for Ti substitution in garnet indicates that rutile formation from garnet cannot occur in a closed system. It requires that components are exchanged between the garnet interior and the rock matrix by solid-state diffusion, a process we refer to as “open-system precipitation” (OSP). The kinetically most feasible reaction of this type will dominate the overall process. The perhaps most efficient reaction involves internal oxidation of Fe²⁺ to Fe³⁺ and transfer from the dodecahedral to the octahedral site just vacated by $ {\text{Ti}}^{ 4+ }: 6\,{\text{M}}^{ 2+ }_{ 3} {\text{TiAl}}\left[ {{\text{AlSi}}_{ 2} } \right]{\text{O}}_{ 1 2} + 6\,{\text{M}}^{ 2+ }_{ 2, 5} {\text{TiAlSi}}_{ 3} {\text{O}}_{ 1 2} = 10\,{\text{M}}^{ 2+ }_{ 3.0} {\text{Al}}_{ 1. 8} {\text{Fe}}_{0. 2} {\text{Si}}_{ 3} {\text{O}}_{ 1 2} + {\text{M}}^{2+} + 2 {\text{e}}^{-} + 1 2\,{\text{TiO}}_{ 2} . $ OSP is likely to occur at conditions where the transition of natural systems to open-system behaviour becomes apparent, as in the granulite and high-temperature eclogite facies.  相似文献