A detailed study of the duality relation for the least squares adjustment in euclidean spaces

The Euclidean spaces with their inner products are used to describe methods of least squares adjustment as orthogonal projections on finite-dimensional subspaces. A unified Euclidean space approach to the least squares adjustment methods “observation equations” and “condition equations” is suggested. Hence not only the two adjustment solutions are treated from the view-point of Euclidean space theory in a unified frame but also the existing duality relation between the methods of “observation equations” and “condition equations” is discussed in full detail. Another purpose of this paper is to contribute to the development of some familiarity with Euclidean and Hilbert space concepts. We are convinced that Euclidean and Hilbert space techniques in least squares adjustment are elegant and powerful geodetic methods.     

Metamorphic gradients in burial metamorphosed vesicular lavas: Comparison of basalt and spilite in Cretaceous basic flows from central Chile

Partial spilitization of a 9 km thick pile of flood basalts with highly vesicular flow tops gave rise to patterns of secondary mineralogy at different scales: (a) a local pattern of mineralogical variation from the almost unaltered bottom towards the altered top of each flow, and (b) an overall pattern, comparing flow tops throughout the pile, with changes in mineralogical composition within a sequence of metamorphic zones and facies. The local patterns mimic the trend of the overall pattern, but are of opposite direction and telescoped. Thus, a gradual ordering and Andepletion of the secondary albite and increases in the Fe^*/Al ratio of epidote and pumpellyite upwards within individual flows are comparable in range to corresponding overall changes downwards throughout several kilometres. The mineralogical changes within the flows diminish in range towards the more altered deeper part of the pile.The local and overall patterns cannot be interpreted in terms of grade. They represent trends from metastable towards stable equilibrium, this latter only approached in the flow tops of the lower part of the pile. The patterns of secondary mineralogy were formed by an interplay of metamorphic gradients at different scales at any given time, and as burial proceeded. The overall pattern was caused by depth-controlled gradients: increasing P _fluid, temperature and temperature-induced increase of reaction rates, and decreasing fO₂ (downwards in the pile). The local patterns resulted from permeability-controlled gradients: increasing reaction rates, fO₂ and contrast in chemical activity between different domains, and decreasing P _fluid (upwards in each flow). The mineralogical observations reported in this paper fall into line if the overall temperature-induced increase of reaction rates and the local permeability-controlled rate factors played the leading role during burial metamorphism of the pile.     

Post-Svecokarelian andinotype evolution in central Sweden

Granitoids and associated volcanics, postorogenic in relation to the Svecokarelian orogeny, constitute a belt in central Sweden. Evidence presented in this paper suggest that the belt originated in an Andinotype orogenic environment. The inferred development of the belt was characterized by fracture-controlled high-level emplacement of batholiths in an ensialic setting. Voluminous venting of ignimbrites and formation of grabens through cauldron subsidence accompanied the recurrent intrusive activity. Block movements and episodes of burial metamorphism appear to have been prominent features throughout the history of the post-Svecokarelian belt.

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Zusammenfassung Granitoide Plutonite und verwandte Vulkanite, post-orogen im Verhältnis zur Svekokarelischen Orogenese, bilden einen Gürtel in Mittelschweden. Es wird gezeigt, daß der Gürtel in einer andinotypen Orogenese gebildet wurde. Die vorgeschlagene Entwicklung des Gürtels ist geprägt durch spaltentektonisch kontrollierte Platznahme von Batholithen in einem seichten Niveau der Kruste in ensialischem Mileau. Umfangreiche Eruptionen von Ignimbriten sowie die Bildung von Grabenbrüchen durch Kalderen-Einstürzungen begleiten die erneute intrusive Tätigkeit. Blockbewegungen und episodische Versenkungsmetamorphosen sind charakteristisch während der gesamten Entwicklungsgeschichte des post-svekokarelischen Gürtels.

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Résumé Des granitoïdes et des volcanites associées, postorogéniques par rapport à l'orogénese svécokarélienne, forment une ceinture en Suède centrale. La présente étude suggère que la mise en place de ces roches s'est effectuée dans un environment orogénique Andinotype. L'évolution de la ceinture c'est caractérisée par la mise en place; contrée par des fractures, de batholites peu profonds, en milieu ensialique. Des volumineuses éruptions d'ignimbrites et la formation de grabens par «cauldron subsidence» ont accompagné la mise en place des batholites. Des mouvements verticaux de blocs, ainsi que des épisodes de métamorphisme d'enfouissement («burial metamorphism») semblent être des faits dominants du développement historique de la ceinture post-svécokarélienne.

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Turbulent characteristics of a shallow convective internal boundary layer

Turbulent characteristics of a 50 to 100 m deep convective internal boundary layer (I.B.L.) have been studied. The data were gathered at a flat coastal site (Näsudden on the island of Gotland, Sweden) during three consecutive days in May 1980 which were characterized by a steady, very stable stratified marine approach flow. The site is situated on a flat area ca. 1500 m from the shoreline. Only daytime runs have been analysed in the present paper. The sensible heat flux at the ground was typically 200 W m^-2 and was found to decrease more or less linearly with height throughout the I.B.L., being slightly negative at greater heights. The momentum flux was also found to decrease with height, but nevertheless shear production of turbulent kinetic energy was found to be large throughout the entire I.B.L. The analysis shows that the turbulent regime has a mixed character. Certain characteristics, such as the rate of growth of the I.B.L., appear to be almost entirely controlled by mechanical turbulence, while others, notably temperature variance and the spectrum of vertical velocity, scale remarkably well with w _* and z _i, in accordance with the results found in fully convective conditions during the experiments at Minnesota and Aschurch. Other turbulent characteristics, such as spectra of the horizontal wind components measured near the top of the I.B.L. tend to adhere to mixed-layer scaling in the high frequency range, exhibiting much increased energy in the lower (reduced) frequency range. Spectra of the velocity components from 10 m are shown to be in general agreement with findings from ‘ideal’, homogeneous sites (Kansas) when properly normalized, although the low frequency part of u- and v-spectra are slightly reduced compared to the case with deep convection.     

Spectra of the earthquake sequence February-March, 1981, in south-central Sweden

On February 13, 1981 a relatively strong earthquake occurred in the Lake Vänern region in south-central Sweden. The shock had a magnitude ofM_L = 3.3 and was followed within three weeks by three aftershocks, with magnitudes 0.5 ≤ M_L ≤ 1.0. The focal mechanism solution of the main shock indicates reverse faulting with a strike in the N-S or NE-SW direction and a nearly horizontal compressional stress. The aftershocks were too small to yield data for a full mechanism solution, but first motions of P-waves, recorded at two stations, are consistent for the aftershocks. Dynamic source parameters, derived from Pg- and Sg-wave spectra, show similar stress drops for the main shock (2 bar) and the aftershocks (1 bar), while the differences in seismic moment (1.5·10²⁰ resp. 4·10¹⁸dyne cm), fault length (0.7 resp. 0.2 km) and relative displacement (0.15 resp. 0.03 cm) are significant.     

Global high resolution versus Limited Area Model climate change projections over Europe: quantifying confidence level from PRUDENCE results

Four high resolution atmospheric general circulation models (GCMs) have been integrated with the standard forcings of the PRUDENCE experiment: IPCC-SRES A2 radiative forcing and Hadley Centre sea surface temperature and sea-ice extent. The response over Europe, calculated as the difference between the 2071–2100 and the 1961–1990 means is compared with the same diagnostic obtained with nine Regional Climate Models (RCM) all driven by the Hadley Centre atmospheric GCM. The seasonal mean response for 2m temperature and precipitation is investigated. For temperature, GCMs and RCMs behave similarly, except that GCMs exhibit a larger spread. However, during summer, the spread of the RCMs—in particular in terms of precipitation—is larger than that of the GCMs. This indicates that the European summer climate is strongly controlled by parameterized physics and/or high-resolution processes. The temperature response is larger than the systematic error. The situation is different for precipitation. The model bias is twice as large as the climate response. The confidence in PRUDENCE results comes from the fact that the models have a similar response to the IPCC-SRES A2 forcing, whereas their systematic errors are more spread. In addition, GCM precipitation response is slightly but significantly different from that of the RCMs.     

Cumulating processes at the crust-mantle transition zone inferred from Permian mafic-ultramafic xenoliths (Puy Beaunit,France)

Ultramafic and mafic xenoliths of magmatic origin, sampled in the Beaunit vent (northern French Massif Central), derive from the Permian (257 Ma) Beaunit layered complex (BLC) that was emplaced at the crust-mantle transition zone (∼1 GPa). These plutonic xenoliths are linked to a single fractional crystallisation process in four steps: peridotitic cumulates; websteritic cumulates; Al-rich mafic cumulates (plagioclase, pyroxenes, garnet, amphibole and spinel) and finally low-Al mafic cumulates. This sequence of cumulates can be related to the compositional evolution of hydrous Mg basaltic magma that evolved to high-Al basalt and finally to andesitic basalt. Sr and Nd isotopic compositions confirm the co-genetic character of the various magmatic xenoliths and argue for an enriched upper mantle source comparable to present mantle wedges above subduction zones. LILE, LREE and Pb enrichment are a common feature of all xenoliths and argue for an enriched sub-alkaline transitional parental magma. The existence of a Permian magma chamber at 30 km depth suggests that the low-velocity zone observed locally beneath the Moho probably does not represent an anomalous mantle but rather a sequence of mafic/ultramafic cumulates with densities close to those of mantle rocks.     

Hydrogeologic studies for nuclear-waste disposal in Sweden

Safety Report 1997 (SR 97) of the Swedish Nuclear Fuel and Waste Management Company is a comprehensive performance assessment of three hypothetical radioactive waste repositories in Sweden. It includes hydrogeologic studies (data compilation, parameter synthesis, and groundwater flow modeling) to determine groundwater flow and the associated uncertainties for the three sites. This report reviews and compares the hydrogeologic characterization programs, the site characteristics, and the groundwater flow models used in the SR 97 performance assessment. Although differences in site-characterization programs tend to mask differences in site characteristics, the sites do have notable differences that affect the results of the performance assessment. The effects of model uncertainties evaluated by the variant cases appear to be smaller than the variability of results for the base case (best estimate of site conditions) of each site. Electronic Publication