High-resolution atmospheric angular momentum functions related to Earth rotation parameters during CONT08

Due to the temporal resolution of available numerical weather analyses, the effect of the atmosphere on Earth rotation at daily and sub-daily periods is usually investigated using 6-hourly atmospheric angular momentum (AAM) functions. During the period of CONT08, however, atmospheric analysis data were provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) also on an hourly basis. In this paper, we, therefore, determine two sets of AAM functions from ECMWF data—one for CONT08 with hourly resolution and one for the year 2008 with 6-hourly resolution. The comparisons of the AAM functions to high-resolution Earth rotation parameters (ERP) from VLBI and GPS observations are carried out in the frequency domain. Special attention is paid to the preparation of the high-resolution data sets for the geodetic purposes, as there are jump discontinuities at 12 h intervals. Hence, the hourly AAM functions need to be concatenated. The revised functions yield much smaller amplitudes than their 6-hourly counterparts, as can be seen from the equatorial and the axial frequency spectra of atmospheric excitation in Earth rotation. This decrease of spectral power in the hourly AAM functions is found to be associated with a strong counteraction of pressure and wind terms, which originates from atmospheric circulation on short time scales. The results are compared to previous findings published by Brzeziński and Petrov (IERS Tech Note 28:53–60, 2000) based on the data from the U.S. National Centers for Environmental Prediction (NCEP).     

GOCE gravitational gradients along the orbit

GOCE is ESA’s gravity field mission and the first satellite ever that measures gravitational gradients in space, that is, the second spatial derivatives of the Earth’s gravitational potential. The goal is to determine the Earth’s mean gravitational field with unprecedented accuracy at spatial resolutions down to 100 km. GOCE carries a gravity gradiometer that allows deriving the gravitational gradients with very high precision to achieve this goal. There are two types of GOCE Level 2 gravitational gradients (GGs) along the orbit: the gravitational gradients in the gradiometer reference frame (GRF) and the gravitational gradients in the local north oriented frame (LNOF) derived from the GGs in the GRF by point-wise rotation. Because the V _XX , V _YY , V _ZZ and V _XZ are much more accurate than V _XY and V _YZ , and because the error of the accurate GGs increases for low frequencies, the rotation requires that part of the measured GG signal is replaced by model signal. However, the actual quality of the gradients in GRF and LNOF needs to be assessed. We analysed the outliers in the GGs, validated the GGs in the GRF using independent gravity field information and compared their assessed error with the requirements. In addition, we compared the GGs in the LNOF with state-of-the-art global gravity field models and determined the model contribution to the rotated GGs. We found that the percentage of detected outliers is below 0.1% for all GGs, and external gravity data confirm that the GG scale factors do not differ from one down to the 10⁻³ level. Furthermore, we found that the error of V _XX and V _YY is approximately at the level of the requirement on the gravitational gradient trace, whereas the V _ZZ error is a factor of 2–3 above the requirement for higher frequencies. We show that the model contribution in the rotated GGs is 2–35% dependent on the gravitational gradient. Finally, we found that GOCE gravitational gradients and gradients derived from EIGEN-5C and EGM2008 are consistent over the oceans, but that over the continents the consistency may be less, especially in areas with poor terrestrial gravity data. All in all, our analyses show that the quality of the GOCE gravitational gradients is good and that with this type of data valuable new gravity field information is obtained.     

A High Order Perturbation Analysis of the Sitnikov Problem

The Sitnikov problem is one of the most simple cases of the elliptic restricted three body system. A massless body oscillates along a line (z) perpendicular to a plane (x,y) in which two equally massive bodies, called primary masses, perform Keplerian orbits around their common barycentre with a given eccentricity e. The crossing point of the line of motion of the third mass with the plane is equal to the centre of gravity of the entire system. In spite of its simple geometrical structure, the system is nonlinear and explicitly time dependent. It is globally non integrable and therefore represents an interesting application for advanced perturbative methods. In the present work a high order perturbation approach to the problem was performed, by using symbolic algorithms written in Mathematica. Floquet theory was used to derive solutions of the linearized equation up to 17th order in e. In this way precise analytical expressions for the stability of the system were obtained. Then, applying the Courant and Snyder transformation to the nonlinear equation, algebraic solutions of seventh order in z and e were derived using the method of Poincaré–Lindstedt. The enormous amount of necessary computations were performed by extensive use of symbolic programming. We developed automated and highly modularized algorithms in order to master the problem of ordering an increasing number of algebraic terms originating from high order perturbation theory.     

Upscaling of fractured oil reservoirs using homogenization including non-equilibrium capillary pressure and relative permeability

Recovery from incompletely water-wet fractured reservoirs can be extremely low. A reason for the low recovery is related to wetting issues, whereas the reason for slow recovery can be the non-equilibrium behavior of capillary pressure. One of the non-equilibrium theories is developed by Barenblatt et al. and it modifies both capillary pressure and relative permeabilities. The other theory is developed by Hassanizadeh et al. and it only deals with non-equilibrium effects for capillary pressure. To incorporate non-equilibrium in larger-scale problems, we apply homogenization to derive an upscaled model for fractured reservoirs in which the non-equilibrium effects are included. We formulate a fully implicit three-dimensional upscaled numerical model. Furthermore, we develop a computationally efficient numerical approach to solve the upscaled model. We use simulations to determine the range of delay times and capillary-damping coefficients for which discernable effects occur in terms of oil recovery. It is shown that at low Peclet numbers, i.e., when the residence time of the fluids in the fracture is long with respect to the imbibition time, incorporation of delay times of the order of few months have no significant effect on the oil recovery. However, when the Peclet number is large, the delay times reduce the rate of oil recovery. We discuss for which values of the delay time (Barenblatt) and capillary-damping coefficient (Hassanizadeh), significant delays in oil production occur.     

Comparison of polynomial models for land surface curvature calculation

Curvature is a fundamental surface property whose application, for example in geomorphology and hydrology, has long been recognised. Its measurement from Digital Terrain Models (DTMs) has received less attention than that of slope, and there is even disagreement about which definitions of curvature are most applicable. Here these problems are related to semantic problems in the definition of the land surface, and three distinct algorithms for the three main gravity-related components of curvature are compared for both artificial and real surfaces. Quadratic-based algorithms are shown to give more stable results. Higher-order local surfaces (e.g. partial quartic) can fit more complex landform features, but are reliable only for very accurate data.     

Rough classification and accuracy assessment

In search for methods to handle imprecision in geographical information this paper explores the use of rough classification to represent uncertainty. Rough classification is based on rough set theory, where an uncertain set is specified by giving an upper and a lower approximation. Novel measures are presented to assess a single rough classification, to compare a rough classification to a crisp one and to compare two rough classifications. An extension to the error matrix paradigm is also presented, both for the rough-crisp and the roughrough cases. An experiment on vegetation and soil data demonstrates the viability of rough classification, comparing two incompatible vegetation classifications covering the same area. The potential uses of rough sets and rough classification are discussed and it is suggested that this approach should be further investigated as it can be used in a range of applications within geographic information science from data acquisition and analysis to metadata organization.     

Age and kinematics of ductile deformation in the Cerro Durazno area, NW Argentina: Significance for orogenic processes operating at the western margin of Gondwana during Ordovician – Silurian times

The Cerro Durazno Pluton belongs to a suite of Paleozoic granitoid intrusions in NW-Argentina, that are central for understanding the tectonic setting of the western margin of Gondwana in Ordovician and Silurian times. The pluton and its host rocks were tectonically overprinted by metamorphic mineral shape fabrics formed under middle greenschist-facies metamorphic conditions and associated with the nearby Agua Rosada Shear Zone. Kinematic analysis of the shear zone based on the geometric relationship between individual segments of the shear plane and principal axes of mineral fabric ellipsoids indicates reverse-sense of shear with a minor component of left-lateral displacement. This is compatible with the kinematics of other ductile deformation zones in this area, collectively forming a network, which accomplished orogen-parallel extension in addition to vertical thickening. Using the Rb–Sr isotopic system, an undeformed pegmatite dike of the Cerro Durazno Pluton was dated at 455.8 ± 3.6 Ma and mineral fabrics of the Agua Rosada Shear Zone formed at middle greenschist-facies metamorphism gave deformation ages of 437.0 ± 3.8 Ma and 428.4 ± 4.5 Ma. Thus, tectonic overprint at low metamorphic grade occurred about 20–30 Ma after terminal magmatism in the Cerro Durazno area. Our data from the Cerro Durazno area and regional considerations suggest that the western margin of Gondwana was characterized by orogen-parallel extension in addition to crustal thickening as well as episodes of magmatism and ductile deformation that varied greatly in time and space.     

Geochronology of fluid-induced eclogite and amphibolite facies metamorphic reactions in a subduction–collision system,Bergen Arcs,Norway

Rb–Sr multimineral isochron data for metamorphic veins allow to date separate increments of the mineral reaction history of polymetamorphic terranes. Granulite facies rocks of the Lindås nappe, Bergen Arcs, Norway, were subducted and exhumed during the Caledonian orogeny. The rocks show petrographic evidence for two distinct events of local fluid infiltration and vein formation, along fractures and shear zones. The first occurred at eclogite facies (15–21 kbar, 650–750°C) and a later one at amphibolite facies conditions (8–10 kbar, 600°C). The presence of fluids enabled local metamorphic equilibration only near fluid pathways. In fluid-absent domains, preexisting assemblages were metastably preserved. This resulted in a heterogeneity of metamorphic signatures on meter to μm-scales. Well-preserved granulite facies rocks preserve their Proterozoic Rb–Sr mineral ages, as does the U–Pb system of zircon in most lithologies. Six Rb/Sr multimineral isochron ages for eclogite facies veins and their immediate wallrocks date the fluid-induced eclogitization at 429.9 ± 3.5 Ma (2σ, weighted average, MSWD = 0.39). An eclogite facies vein has yielded metamorphic zircon with concordant U–Pb ages of 429 ± 3 Ma, identical to the U–Pb age of 427.4 ± 0.9 Ma for zircon xenocrysts in an amphibolite facies vein. Seven Rb/Sr mineral isochron ages date amphibolite-facies fluid infiltration at 414.2 ± 2.8 Ma (MSWD = 1.5), an age value testifying to residence of the rocks in the deep orogenic crust at temperatures >600°C for nearly 15 Ma. The new data show that Rb–Sr mineral isochron ages effectively date fluid-induced (re)crystallization events rather than stages of cooling. The direct link between isotopic ages and distinct petrographic equilibrium assemblages aids to constrain the evolution of rocks in the P–T-reaction-time space, which is essential for understanding exhumation histories and the internal dynamics of orogens in general.