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   

Paleo- and Neoproterozoic magmatic and tectonometamorphic evolution of the Isla Cristalina de Rivera (Nico Pérez Terrane, Uruguay)   总被引：1，自引：0，他引：1  

Pedro Oyhant?abal  Martin Wagner-Eimer  Klaus Wemmer  Bernhard Schulz  Robert Frei  Siegfried Siegesmund 《International Journal of Earth Sciences》2012,101(7):1745-1762

The Isla Cristalina de Rivera crystalline complex in northeastern Uruguay underwent a multistage magmatic and metamorphic evolution. Based on SHRIMP U–Pb zircon, Th–U–Pb monazite (CHIME-EPMA method) and K–Ar age data from key units several events can be recognized: (1) multistage magmatism at 2,171–2,114?Ma, recorded on zircon of the granulitic orthogneisses and their 2,093–2,077?Ma overgrowths; (2) a distinct amphibolite facies metamorphism at ~1,980?Ma, recorded by monazite; (3) greenschist facies reworking and shearing at ca. 606?Ma (monazite and K–Ar on muscovite) along the Rivera Shear Zone, and finally (4) intrusion of the post-tectonic Sobresaliente and Las Flores granites at around 585?Ma. Lithological similarities, geographic proximity and coeval magmatic and metamorphic events indicate a similar tectonometamorphic evolution for the Isla Cristalina de Rivera, the Valentines Block in Uruguay and the Santa María Chico Granulitic Complex in southern Brazil, since at least 2.1?Ga.  相似文献   

The influence of recultivation technique and seed mixture on erosion stability after restoration in mountain environment     

Bernhard Krautzer  Wilhelm Graiss  Giovanni Peratoner  Christian Partl  Sonia Venerus  Brigitte Klug 《Natural Hazards》2011,56(2):547-557

Control of erosion, and all of its after effects, from increased surface drainage and erosion to the formation of karst, is one of the essential problems when undertaking recultivation following necessary interventions in the sub-alpine and alpine vegetation stage (high zones). Average slope inclinations of 30–45% in the vicinity of ski runs, and far above in areas of natural erosion and avalanche zones, make restoration processes with sufficient erosion protection the prerequisite for success. Only a sufficient vegetation development of more than 70% ground cover stabilises the topsoil in the long term and reduces soil erosion to an acceptable degree. From 1999 to 2002, an international EU project with the participation of research groups and private firms from Austria, Italy and Germany was carried out under the direction of the Agricultural Research and Education Centre Raumberg-Gumpenstein (AREC) on five different Alpine sites at altitudes from 1,245 to 2,350 m above sea level. The aim of the work was the formulation of practice-relevant requirements for recultivation following intervention in high zones, especially following constructional measures in the vicinity of ski runs and lifts, torrent- and avalanche barriers. In a statistical comparison, the relationship between restoration techniques, seed mixtures of differing ecological value and vegetation cover was observed. The influence of application technique on erosion processes after restoration was obvious for the first two vegetation periods. Only with the additional use of mulch covers could increase surface drainage and noticeable soil loss be avoided. At high altitudes, the choice of seed mixture, irrespective of whether rapid or slow growing and independent of the extent of accompanying fertilisation, had no significance in the first two vegetation periods following sowing. In the following growing seasons, however, higher cover values were obtained with site-specific seed mixtures at three of the five experimental sites. While few species of the commercial seed mixture showed satisfactory persistency, most of the grasses and in particular the alpine leguminosae of site-specific seed mixtures increased their share during the observation period. In the long-term, sufficient protection against erosion is only guaranteed by the use of stable, enduring and ecologically adapted species.  相似文献   

Monazite CHIME/EPMA dating of Erinpura granitoid deformation: Implications for Neoproterozoic tectono-thermal evolution of NW India     

Jana Just  Bernhard Schulz  Helga de Wall  Fred Jourdan  Manoj K. Pandit 《Gondwana Research》2011,19(2):402-412

The in-situ “chemical” Th–U–Pb dating of monazite with the electron microprobe is used to unravel the Neoproterozoic tectono-thermal history of the “Erinpura Granite” terrane in the foreland of the Delhi Fold Belt (DFB) in the NW Indian craton. These granitoids are variably deformed and show effects of shearing activity. Monazites from the Erinpura granitoids recorded two main events; (1) protolith crystallization at 863 ± 23 Ma and (2) recrystallization and formation of new Th-poor monazite at 775 ± 26 Ma during shear overprint. Some components of the Erinpura granitoids, such as the Siyawa Granite and granites exposed near Sirohi town, show evidence of migmatization. This migmatization event is documented by anatexis and associated monazite crystallization at 779 ± 16 Ma. The age data indicate an overlap in timing between anatectic event and ductile shear deformation. The end of the tectono-thermal event in the Sirohi area is constrained by a 736 ± 6 Ma Ar–Ar muscovite age data from the ductile shear zone.  相似文献   

Discovery of Ordovician–Silurian metamorphic monazite in garnet metapelites of the Alpine External Aiguilles Rouges Massif     

Bernhard Schulz  Jürgen F. von Raumer 《Swiss Journal of Geoscience》2011,104(1):67-79

The pre-Mesozoic, mainly Variscan metamorphic basement of the Col de Bérard area (Aiguilles Rouges Massif, External domain) consists of paragneisses and micaschists together with various orthogneisses and metabasites. Monazite in metapelites was analysed by the electron microprobe (EMPA-CHIME) age dating method. The monazites in garnet micaschists are dominantly of Variscan age (330–300 Ma). Garnet in these rocks displays well developed growth zonations in Fe–Mg–Ca–Mn and crystallized at maximal temperatures of 670°C/7 kbar to the west and 600°C/7–8 kbar to the east. In consequence the monazite is interpreted to date a slightly pressure-dominated Variscan amphibolite-facies evolution. In mylonitic garnet gneisses, large metamorphic monazite grains of Ordovician–Silurian (~440 Ma) age but also small monazite grains of Variscan (~300 Ma) age were discovered. Garnets in the mylonitic garnet gneisses display high-temperature homogenized Mg-rich profiles in their cores and crystallized near to ~800°C/6 kbar. The Ordovician–Silurian-age monazites can be assigned to a pre-Variscan high-temperature event recorded by the homogenised garnets. These monazite age data confirm Ordovician–Silurian and Devonian–Carboniferous metamorphic cycles which were already reported from other Alpine domains and further regions in the internal Variscides.  相似文献   

Lateral fold growth and linkage in the Zagros fold and thrust belt (Kurdistan,NE Iraq)   总被引：1，自引：0，他引：1  

Bernhard Bretis  Nikolaus Bartl  Bernhard Grasemann 《Basin Research》2011,23(6):615-630

The Zagros fold and thrust belt is a seismically active orogen that has accommodated the N–S shortening between the Arabian and Eurasian plates since the Miocene. Whereas the southeast parts of the belt have been studied in detail, the northwest extent has received considerably less attention, being part of the Republic of Iraq. In this study, we investigate fold growth in the area NE of Erbil (Kurdistan, Iraq). In particular, we focus on the interaction of the transient development of drainage patterns along growing antiforms, as this directly reflects the kinematics of progressive fold growth. Detailed geomorphological studies of the Bana Bawi‐, Permam‐ and Safeen‐fold trains show that these anticlines did not develop from a single embryonic fold but by lateral linkage of several different fold segments. These segments, with length between 5 and 25 km, have been detected by mapping ancient and modern river courses; these initially cut the nose of growing folds until eventually defeated, leaving curved wind gaps behind. Depending on the alignment of the initial embryonic folds, the segments can either record a linear‐ or an en‐echelon linkage. Comparison of natural examples from the Zagros fold and thrust belt in Iraq with published numerically modelled fold growth suggests that both linear‐linkage and en‐echelon linkage are mechanically feasible and are common processes during progressive shortening and fold growth.  相似文献   

Mesozoic (Late Jurassic) palynomorphs and charcoal from a sandstone pebble from Quaternary glacial deposits of the North Sea     

Haytham El Atfy  Dieter Uhl  Bernhard Stribrny 《Geological Journal》2013,48(4):376-384

The palynological contents as well as macroscopic charcoal fragments from a calcareous sandstone pebble from Quaternary glacial deposits of the North Sea (80 km SW of the Dogger Bank) are described. The taxonomic composition of the palynoflora points to a Late Jurassic (or Late Jurassic/Early Cretaceous) age of the sandstone. The charcoal is interpreted as direct evidence of palaeo‐wildfire occurring during this period in the source area of the sediments of this particular sandstone. This finding, together with already published data on Mesozoic deposits, allows to conclude that wildfires were obviously widespread during this period in the area of the modern day North Sea and adjacent areas. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献