Volcanological constraints of Archaean tectonics

Volcanological and trace element geochemical data can be integrated to place some constraints upon the size, character and evolutionary history of Archean volcanic plumbing, and hence indirectly, Archean tectonics. The earliest volcanism in any greenhouse belt is almost universally tholeitic basalt. Archean mafic magma chambers were usually the site of low pressure fractionation of olivine, plagioclase and later Cpx + or - an oxide phase during evolution of tholeitic liquids. Several models suggest basalt becoming more contaminated by sial with time. Data in the Uchi Subprovince shows early felsic volcanics to have fractionated REE patterns followed by flat REE pattern rhyolites. This is interpreted as initial felsic liquids produced by melting of a garnetiferous mafic source followed by large scale melting of LIL-rich sial. Rare andesites in the Uchi Subprovince are produced by basalt fractionation, direct mantle melts and mixing of basaltic and tonalitic liquids. Composite dikes in the Abitibi Subprovince have a basaltic edge with a chill margin, a rhyolitic interior with no basalt-rhyolite chill margin and partially melted sialic inclusions. Ignimbrites in the Uchi and Abitibi Subprovinces have mafic pumice toward the top. Integration of these data suggest initial mantle-derived basaltic liquids pond in a sialic crust, fractionate and melt sial. The inirial melts low in heavy REE are melts of mafic material, subsequently melting of adjacent sial produces a chamber with a felsic upper part underlain by mafic magma

Area Inequalities for Embedded Disks Spanning Unknotted Curves

We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bounds the area of an embedded disk spanning the curve in terms of two parameters: the length L of the curve and the thickness r (maximal radius of an embedded tubular neighborhood) of the curve. For fixed length, the expression giving the upper bound on the area grows exponentially in 1/r^2. In the direction of lower bounds, we give a sequence of length one curves with r approaching 0 for which the area of any spanning disk is bounded from below by a function that grows exponentially with 1/r. In particular, given any constant A, there is a smooth, unknotted length one curve for which the area of a smallest embedded spanning disk is greater than A.Comment: 31 pages, 5 figure

Solution of the symmetric eigenproblem AX=lambda BX by delayed division

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity

Igneous Rock Associations 19. Greenstone Belts and Granite−Greenstone Terranes: Constraints on the Nature of the Archean World

Greenstone belts are long, curvilinear accumulations of mainly volcanic rocks within Archean granite−greenstone terranes, and are subdivided into two geochemical types: komatiite−tholeiite sequences and bimodal sequences. In rare instances where basement is preserved, the basement is unconformably overlain by platform to rift sequences consisting of quartzite, carbonate, komatiite and/or tholeiite. The komatiite−tholeiite sequences consist of km-scale thicknesses of tholeiites, minor intercalated komatiites, and smaller volumes of felsic volcanic rocks. The bimodal sequences consist of basal tholeiitic flows succeeded upward by lesser volumes of felsic volcanic rocks. The two geochemical types are unconformably overlain by successor basin sequences containing alluvial–fluvial clastic metasedimentary rocks and associated calc-alkaline to alkaline volcanic rocks.   Stratigraphically controlled geochemical sampling in the bimodal sequences has shown the presence of Fe-enrichment cycles in the tholeiites, as well as monotonous thicknesses of tholeiitic flows having nearly constant MgO, which is explained by fractionation and replenishment of the magma chamber with fresh mantle-derived material. Geochemical studies reveal the presence of boninites associated with the komatiites, in part a result of alteration or contamination of the komatiites. Within the bimodal sequences there are rare occurrences of adakites, Nb-enriched basalts and magnesian andesites.    The greenstone belts are engulfed by granitoid batholiths ranging from soda-rich tonalite−trondhjemite−granodiorite to later, more potassic granitoid rocks. Archean greenstone belts exhibit a unique structural style not found in younger orogens, consisting of alternating granitoid-cored domes and volcanic-dominated keels. The synclinal keels are cut by major transcurrent shear zones.   Metamorphic patterns indicate that low pressure metamorphism of the greenstones is centred on the granitoid batholiths, suggesting a central role for the granitoid rocks in metamorphosing the greenstones. Metamorphic patterns also show that the proportion of greenstones in granite−greenstone terranes diminishes with deeper levels of exposure.   Evidence is presented on both sides of the intense controversy as to whether greenstone belts are the product of modern plate tectonic processes complete with subduction, or else the product of other, lateral tectonic processes driven by the ‘mantle wind.’ Given that numerous indicators of plate tectonic processes – structural style, rock types, and geochemical features − are unique to the Archean, it is concluded that the evidence is marginally in favour of non-actualistic tectonic processes in Archean granite−greenstone terranes.RÉSUMÉLes ceintures de roches vertes sont des accumulations longiformes et curvilinéaires, principalement composées de roches volcaniques au sein de terranes granitique archéennes,  et étant subdivisées en deux types géochimiques: des séquences à komatiite–tholéite et des séquences bimodales. En de rares occasions, lorsque le socle est préservé, ce dernier est recouvert en discordance par des séquences de plateforme ou de rift, constituées de quartzite, carbonate, komatiite et/ou de tholéiite. Les séquences de komatiite-tholéiite forment des épaisseurs kilométriques de tholéiite, des horizons mineurs de komatiites, et des volumes de moindre importance de roches volcaniques felsiques. Les séquences bimodales sont constituées à la base, de coulées tholéiitiques surmontées par des volumes mineurs de roches volcaniques felsiques. Ces deux types géochimiques sont recouverts en discordance par des séquences de bassins en succession contenant des roches métasédimentaires clastiques fluvio-alluvionnaires associées à des roches volcaniques calco-alcalines à alcalines.   Un échantillonnage à contrôle stratigraphique des séquences bimodales a révélé la présence de cycles d’enrichissement en Fe dans les tholéiites, ainsi que des épaisseurs continues d’épanchements tholéiitiques ayant des valeurs presque constante en  MgO, qui s’explique par la cristallisation fractionnée et le réapprovisionnement de la chambre magmatique par du matériel mantélique. Les études géochimiques montrent la présence de boninites associées aux komatiites, résultant en partie de l’altération ou de la contamination des komatiites. Au sein des séquences bimodales, on retrouve en de rares occasions des adakites, des basaltes enrichis en Nb et des andésites magnésiennes.   Les ceintures de roches vertes sont englouties dans des batholites granitoïdes de composition passant des tonalites−trondhjémites−granodiorites enrichies en sodium, à des roches granitoïdes tardives plus potassiques. Les ceintures de roches vertes archéennes montrent un style structural unique que l’on ne retrouve pas dans des orogènes plus jeunes, et qui est constitué d’alternances de dômes à cœur granitoïdes et d`affaissements principalement composés de roches volcaniques. Les synclinaux formant les affaissements sont recoupés par de grandes zones de cisaillement.   Les profils métamorphiques indiquent que le métamorphisme de basse pression des roches vertes est centré sur les batholites, indiquant un rôle central des roches granitoïdes durant le métamorphisme des roches vertes. Les profils métamorphiques montrent également que la proportion de roches vertes dans les terranes granitiques diminue avec l’exposition des niveaux plus profonds.   On présente les arguments des deux côtés de l’intense controverse voulant que les ceintures de roches vertes soient le produit de processus moderne de la tectonique des plaques incluant la subduction, ou alors le produit d’autres processus tectoniques découlant du « flux mantélique ». Étant donné la présence des indicateurs des processus de tectonique des plaques – style structural, les types de roches, et les caractéristiques géochimiques – ne se retrouvent qu’à l’Archéen, nous concluons que les indices favorisent légèrement l’option de processus tectoniques non-actuels dans les terranes granitiques de roches vertes à l’Archéen

EAC: A program for the error analysis of STAGS results for plates

A computer code is now available for estimating the error in results from the STAGS finite element code for a shell unit consisting of a rectangular orthotropic plate. This memorandum contains basic information about the computer code EAC (Error Analysis and Correction) and describes the connection between the input data for the STAGS shell units and the input data necessary to run the error analysis code. The STAGS code returns a set of nodal displacements and a discrete set of stress resultants; the EAC code returns a continuous solution for displacements and stress resultants. The continuous solution is defined by a set of generalized coordinates computed in EAC. The theory and the assumptions that determine the continuous solution are also outlined in this memorandum. An example of application of the code is presented and instructions on its usage on the Cyber and the VAX machines have been provided

Cooperative program for design, fabrication, and testing of graphite/epoxy composite helicopter shafting

The fabrication of UH-1 helicopter tail rotor drive shafts from graphite/epoxy composite materials is discussed. Procedures for eliminating wrinkles caused by lack of precure compaction are described. The development of the adhesive bond between aluminum end couplings and the composite tube is analyzed. Performance tests to validate the superiority of the composite materials are reported

Geometry and observables in (2+1)-gravity

We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover by holonomies. We explain how this description can be used to clarify the geometrical interpretation of the fundamental physical variables of the theory, holonomies and Wilson loops. In particular, we discuss the role of Wilson loop observables as the generators of the two fundamental transformations that change the geometry of (2+1)-spacetimes, grafting and earthquake. We explain how these variables can be determined from realistic measurements by an observer in the spacetime.Comment: Talk given at 2nd School and Workshop on Quantum Gravity and Quantum Geometry (Corfu, September 13-20 2009); 10 pages, 13 eps figure