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DTD 5ARTICLE IN PRESS22L. Baratoux et al. / Journal of Structural Geology xx (xxxx) 1–24isogon patterns (Fig. 12) we propose an explanation ofalternations of hinge zones thickened by this mechanism ofmicrofolding with those without any thickening and distinctmicrostructural changes.The staurolite grade region. In the limbs of foldsgenerated in the staurolite zone, the pre-folding fabric ismarked by fairly well developed, alternating elongateaggregates of plagioclase and amphibole. The intensity ofmineral preferred orientation is very strong, as documentedby the high aspect ratio and strong GBPO and SPO values.Inspection of the fabric in thin sections (Fig. 3c and d)suggests that this structure approximates to the so-called‘interconnected weak layer structure’ (IWL of Handy(1990)) characterized by an alternation of relatively strongamphibole rich domains and relatively weak domains rich inplagioclase. Because the alternating domains differ only insmall modal differences in amphiboles and plagioclase thisstructure represents an IWL structure with a low viscositycontrast as defined by Handy (1994). Such a systempossesses the geometrical characteristics of a bilaminatewith diffuse boundaries between the layers. In the hingezones the microfabric shows areas of distributed deformation.During fold development these zones of distributeddeformation (granular flow in the hinge zones) wouldcontribute to strain softening in this region leading tocontinuous amplification of the folds. We note that even ifthe deformation of the amphiboles is by brittle failure, itresults in distributed ductile flow in the highly deformedhinges. Unlike the folds in the garnet zone where probablyno slip on the limbs occurred, in the staurolite zone the slipis distributed through the relatively weak plagioclase richzones increasing the tendency for active amplification of thefold. In addition, on the limbs, because of the presence ofrelatively weak ‘layers’, fold amplification can be furtherassisted by flattening. This is well documented by the dipisogons pattern and the b 1 vs. F graph of Fig. 12.The sillimanite grade zone. In the sillimanite zone theamphibole and plagioclase show a relatively high aspectratio connected with a low degree of GBPO of like–like andunlike boundaries. In this zone, unlike the staurolite zonewhere the plagioclase was interconnected, isolated elongategrains or aggregates of plagioclase surrounded by highlyelongate and well-oriented crystals of amphibole occur(Figs. 3e and f and 8). This structure and the flattening ofboth minerals can be interpreted in terms of a stresssupportingnetwork with a low viscosity contrast betweenweaker plagioclase and stronger amphibole (Handy, 1990).Thus, in the sillimanite zone, it was the strength of ‘weaker’plagioclase that dominated the rheological properties of thesystem, which therefore acted as a relatively weak,homogeneous material.In contrast to the garnet zone, where buckling wascontrolled by localized microfolding and to the staurolitezone where it was controlled by ductile shearing alongweak, plagioclase rich zones, no such zones of weakness,which facilitate the active amplification of the folds, areobserved in the sillimanite zone. Instead the fold shapeanalysis shows an importance of post-buckle flattening overactive fold amplification. The micro structural analysis ofboth the limb and hinge areas shows features consistent withhomogeneous flattening (i.e. higher aspect ratio and smallergrain size in the hinge domains than in the limbs) anobservation entirely consistent with passive amplification ofa material with a low mechanical anisotropy.The contact metamorphic aureole. The deformation inthe contact aureole (Figs. 3g and h and 8) is an extremeexample of flattening dominated deformation as shown bydifferences in grain size and grain shapes in the hinge andlimb areas. The lack of macroscopic folds in theamphibolites within the aureole is taken as further evidencethat the amplification was almost entirely passive.AcknowledgementsThe project was funded by grants of Czech NationalGrant Agency No. 42-201-204 to K.S. and 42-201-318 to P.Štípská, by Czech Geological Service assignment No. 6327to P. Mixa, and by a Ph.D. financial support attributed by theFrench Government to L.B. We thank R. Vernon and D.Grujic for constructive reviews and J. Hippertt for editorialhelp.Appendix AA polar graph aimed to represent the variation oforthogonal thickness t around folded layers was first utilizedby Lisle (1997). A fold can be represented by a series ofpoints with polar coordinates (1/t 0 , a), where 1/t 0 is thereciprocal normalized thickness (t 0 Zt/t h , where t h is theextreme value of t, which is generally situated in the foldhinge), and a is the orientation of the layer tangent. Usingthis technique, Ramsay’s (1967) fold types give rise tovarious conic sections (ellipses, hyperbolas) in the polargraph with horizontal semiaxis equal to unity (see Lisle,1997).Flattening index F, or axial ratio of strain ellipse, expressthe amount of post-buckle flattening superimposed on theparallel fold. We used a numerically stable direct leastsquaremethod (Halír` and Flusser, 1998) to fit either ellipsesor hyperbolas onto points in a polar graph of normalizedthickness. This technique of evaluation of the flatteningindex F poses a robust estimate and is preferred in this work.The method of analysing fold shapes in terms of theharmonic coefficients of a Fourier series was originallydevised by Stabler (1968) and subsequently elaborated byHudleston (1973).The most basic and suitable segment of a folded surfacefor analysis is a ‘quarter-wavelength’ unit between adjacenthinge and inflexion points. Such a choice of unit leads to aharmonic series consisting only of the odd terms of a sine130
DTD 5ARTICLE IN PRESSL. Baratoux et al. / Journal of Structural Geology xx (xxxx) 1–24 23series and the fold profile is thus approximated by theequation: f ðxÞ Z XN ð2n K1Þpxb 2nK1 sin2LnZ1The first few harmonic coefficients are sensitiveparameters of fold shape and most information about thefold shape can be gained from the first two coefficients, b 1and b 3 .To obtain these coefficients, a ‘quarter-wavelength’ unitof length L of the fold is divided into equal sectors on a line,which is perpendicular to the axial surface and passesthrough the inflection point. Pairs of f(x n ) and x n coordinatesare measured at each of these points. A system of linearequations is assembled from pairs {x n , f(x n )} and solved forunknown coefficients, so2 sin px 1sin 3px 1/ sin ð2n K1Þpx 312L 2L2L2 3sin px 2sin 3px 2/ sin ð2n K1Þpx b 122L 2L2Lb 3« « 1 «6«74 56 sin px nsin3px nsinð2n K1Þpx 745nb 2nK122L3 2L2Lf ðx 1 Þf ðx 2 ÞZ64 «75f ðx n ÞReferencesArbaret, L., Mancktelow, N.S., Burg, J.-P., 2001. Effect of shape andorientation on rigid particle rotation and matrix deformation in simpleshear flow. Journal of Structural Geology 23, 113–125.Baratoux, L., 2004. Petrology, deformation mechanisms, and fabricanisotropy of metabasites deformed at natural strain and metamorphicgradient. Ph.D. thesis, Charles University, Prague.Berger, A., Stünitz, H., 1996. Deformation mechanisms and reaction ofhornblende: examples from the Bergell tonalite (central Alps).Tectonophysics 257, 149–174.Biot, M.A., 1961. Theory of folding of stratified viscoelastic media and itsimplication in tectonics and orogenesis. Bulletin of the GeologicalSociety of America 72, 1595–1620.Biot, M.A., 1963a. Stability of multilayer continua including the effect ofgravity and visco elasticity. Journal of Franklin Institute 276, 231–252.Biot, M.A., 1963b. Theory of stability of multilayered continua in finite,anisotropic elasticity. Journal of Franklin Institute 276, 128–153.Biot, M.A., 1967. Rheological stability with couple stresses and itsimplication to geological folding. Proceedings of the Royal Society ofLondon, Series A 2298, 402–423.Brodie, K.H., Rutter, E.H., 1985. On the relationship between deformationand metamorphism, with special reference to the behavior of basicrocks. In: Thompson, A.B., Rubie, D.C. (Eds.), Metamorphic Reactions;Kinetics, Textures, and Deformation. Springer-Verlag, NewYork, pp. 138–179.Cháb, J., Žáček, V., 1994. Geology of the Žulová pluton mantle (Bohemianmassif, Central Europe). Věstník ÚÚG 69, 1–12.Chlupáč, I., 1994. Facies and biogeographic relationships in Devonian ofthe Bohemian massif. Corier Forschungsinstitut Senckenberg 169, 299–317.Cosgrove, J.W., 1976. The formation of crenulation cleavage. Journal of theGeological Society of London, 132(Part 2, 155–178.Dubey, A.K., 1980. Late stages in the development of folds as deducedfrom model experiments. Tectonophysics 65, 311–322.Dubey, A.K., Cobbold, P.R., 1977. Noncylindrical flexural slip folds innature and experiment. Tectonophysics 38, 223–239.Dudek, A., 1980. The crystalline basement block of the outer Carpathians inMoravia—Brunovistulicum. Rozpravy Československé Akademie věd,Rada matematika—prírodní vědy 90, 85pp.Fletcher, R.C., 1995. Three-dimensional folding and necking of a powerlawlayer: are folds cylindrical and do we understand why?Tectonophysics 247, 65–83.Fowler, T.J., Winsor, C.N., 1996. Evolution of chevron folds by profileshape changes; comparison between multilayer deformation experimentsand folds of the Bendigo–Castlemaine goldfields, Australia.Tectonophysics 258, 125–150.Ghosh, S.K., 1968. Experiments of buckling of multilayers which permitinterlayer gliding. Tectonophysics 6, 207–249.Halír, R., Flusser, J., 1998. Numerically stable direct least squares fitting ofellipses. In: Proceedings of the 6th International Conference in CentralEurope on Computer Graphics and Visualization, WSCG ’98. CZ,Plzeň, pp. 125–132.Handy, M.R., 1990. The solid-state flow of polymineralic rocks. Journal ofGeophysical Research, B 95, 8647–8661.Handy, M.R., 1994. Flow laws for rocks containing two non-linear viscousphases; a phenomenological approach. Journal of Structural Geology16, 287–301.Hobbs, B., 1971. The analysis of strain in folded layers. Tectonophysics 11,329–375.Hudleston, P.J., 1973. Fold morphology and some geometrical implicationsof theories of fold development. Tectonophysics 16, 1–46.Jehlička, J., 1995. The Žulová Massif in Silesian—its geochemistry andpetrogenesis. PhD thesis, Charles University, Prague.Jordan, P.G., 1988. The rheology of polymineralic rocks—an approach.Geologische Rundschau 77, 285–294.Kretz, R., 1994. Metamorphic Crystallization. Wiley, New York.Lexa, O., 2003. Numerical approach in structural and microstructuralanalyses. Ph.D. thesis, Charles University, Prague.Lisle, R.J., 1997. A fold classification scheme based on a polar plot ofinverse layer thickness. In: Sengupta, S. (Ed.), Evolution of GeologicalStructures in Micro- to Macro-scales. Chapman & Hall, London,pp. 323–339.Maluski, H., Rajlich, P., Souček, J., 1995. Pre-Variscan, Variscan, andEarly Alpine thermo-tectonic history of the north-eastern BohemianMassif: 40 Ar/ 39 Ar study. Geologishe Rundschau 84, 345–358.Mancktelow, N.S., Abbassi, M.R., 1992. Single layer buckle folding in nonlinearmaterials; II. Comparison between theory and experiment.Journal of Structural Geology 14, 105–120.Nyman, M.W., Law, R.D., Smelik, E.A., 1992. Cataclastic deformationmechanism for the development of core-mantle structures in amphibole.Geology 20, 455–458.Oertel, G., Ernst, W.G., 1978. Strain and rotation in a multilayered fold.Tectonophysics 48, 77–106.Panozzo, R.H., 1983. Two-dimensional analysis of shape-fabric usingprojections of digitized lines in a plane. Tectonophysics 95, 279–294.Panozzo, R.H., 1984. Two-dimensional strain from the orientation of linesin a plane. Journal of Structural Geology 6, 215–221.Passchier, C.W., Trouw, R.A.J., 1996. Microtectonics. Springer-Verlag,Berlin.Patočka, F., Valenta, J., 1990. Geochemistry of metatrachytes andmetarhyolites of the southern part of the Devonian Vrbno Group inthe Horní Město area and tectonic setting of the origin of themetavolcanic protholith. Časopis pro mineralogii a geologii 35, 41–64 (in Czech).131
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Contentsviii4.7 Schulmann, Konopás
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Dedicated to my wife Markéta, daug
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Foreword 2First topic “Quantitati
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