Quantitative structural analyses and numerical modelling of ...

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