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_Journal of Structural Geology 33 (2011) 20-31_ _Contents lists available at ScienceDirect_ _Journal of Structural Geology_ _journal homepage: www.elsevier.com locate jsg_ _Application of the microboudin method to palaeodifferential stress analysis of deformed impure marbles from Syros, Greece: Implications for grain-size and calcite-twin palaeopiezometers_ _Toshiaki Masuda a,*, Tomoya Miyake a, Nozomi Kimura b, Atsushi Okamoto c Institute of Geosciences, Shizuoka University, Shizuoka 422-8529, Japan; Geological Survey of Japan, AIST, Tsukuba 305-8567, Japan; Graduate School of Environmental Studies, Tohoku University, Sendai 980-8579, Japan_ _article info_ _Article history: Received 18 September 2009; Received in revised form 18 October 2010; Accepted 2 November 2010; Available online 13 November 2010_ _Keywords: Calcite-twin palaeopiezometer; Differential stress; Grain-size palaeopiezometer; Marble; Microboudin method; Syros_ _abstract_ _Microboudinage structures developed within glaucophane are found in the calcite matrix of blueschist-facies impure marbles from Syros, Greece. The presence of these structures enables the successful application of the microboudin method for palaeodifferential stress analysis, which was originally developed for rocks with a quartzose matrix. Application of the microboudin method reveals that differential stress increased during exhumation of the marble; the estimated maximum palaeodifferential stress values are approximately 9-15 MPa, an order of magnitude lower than the values estimated using the calcite-twin palaeopiezometer. This discrepancy reflects the fact that the two methods assess differential stress at different stages in the deformation history. Differential stresses in the Syros samples estimated using three existing equations for grain-size palaeopiezometry show a high degree of scatter, and no reliable results were obtained by a comparison between the results of the microboudin method and grain-size palaeopiezometry._ _? 2010 Elsevier Ltd. All rights reserved._ _1. Introduction_ _Microboudinage structures developed within columnar mineral grains such as amphibole, tourmaline, and epidote are common in quartzose tectonites within high-pressure high-temperature metamorphic belts, and afford estimates of the magnitude of palaeodifferential stress when applying the microboudin method proposed by Masuda et al. (2003, 2008) and Kimura et al. (2006, 2010). This paper reports similar microboudinage structures, consisting of glaucophane embedded within a calcite matrix in two deformed impure marbles from Syros, Greece, and demonstrates that the microboudin method can be successfully applied to such marble tectonites._ _Palaeodifferential stress analyses of marble can also be performed based on calcite twinning or the grain size of dynamically recrystallised calcite grains (e.g., van der Pluijm and Marshak, 2004; Passchier and Trouw, 2005). We applied the calcite-twin palaeopiezometer developed by Rowe and Rutter (1990) and the grain-size palaeopiezometer for calcite (Schmid et al., 1980; Rutter, 1995) to the analysed marble samples to compare the obtained palaeodifferential stress values among the three methods, which yielded contrasting results. We discuss how these values are compatible in terms of the differential stress history experienced by the marbles._ _2. Samples of deformed marble_ _Microboudinage structures developed within glaucophane were found in two samples of impure marble collected as loose blocks (i.e., not in situ) from Kampos and Del?ni in Syros, Greece (Fig. 1). The Del?ni sample is the same as that described by Okamoto et al. (2006) in a study of chemical reactions during indentation at glaucophane-glaucophane contacts. The sampled marbles are part of the Cycladic blueschisteeclogite belt (e.g., Okrusch and Br?cker, 1990; Avigad and Garfunkel, 1991; Avigad et al., 1997; Trotet et al., 2001; Forster and Lister, 2005). They experienced blueschisteeclogite facies metamorphism during the Eocene (e.g., Maluski et al., 1987: Baldwin, 1996; Tomaschek et al., 2003; Forster and Lister, 2005). The peak temperature and pressure of the metamorphism were 450-520 x14C and 1.2-2.0 GPa, respectively (Dixon, 1976; Dixon and Ridley, 1987; Okrusch and Br?cker, 1990; Br?cker and Enders, 1999). The samples show little evidence of a Miocene greenschist-facies overprint that has been well established for the Cycladic area (e.g., Altherr et al., 1982; Lister et al., 1984). The samples are dominantly calcite (grain size, several tens of microns to >1 mm), with subordinate glaucophane, tourmaline, garnet, and muscovite. Calcite and glaucophane make up about 50% and 25%, respectively, of the rock mass. The samples contain a clear foliation defined by aligned muscovite and glaucophane grains. No folding is apparent in the samples._ _When viewing the foliation surface in thin section using an optical microscope, it is difficult to determine the mineral lineation visually (Fig. 2a). The mineral lineation was determined as the shape-preferred orientation of glaucophane, following the statistical method proposed by Masuda et al. (1999). We measured the angle between the long axis of the ith glaucophane grain and an arbitrarily drawn base line (qi), and a von Mises probability density function was applied to the results (Fig. 3) to determine the mean orientation (q), the confidence interval (d0), and the concentration parameter (k). The lineation is then taken as the orientation of q. The samples from Kampos and Del?ni yielded k values of 2.1 and 0.35, respectively. The distribution of long axes in the Kampos sample is narrower than that in the Del?ni sample (Fig. 3)._ _3. Estimation of palaeodifferential stress using the microboudin method_ _The microboudin method of palaeodifferential stress analysis (Masuda et al., 1989, 1990) was originally inspired by the studies of Peter Misch, Colin C. Ferguson, and Geoffrey E. Lloyd, who presented beautiful examples of microboudins of chemically zoned amphibole (Misch, 1969, 1970), performed thoughtful strain analyses based on the boudins (Ferguson, 1981, 1985, 1987; Ferguson and Lloyd, 1984; Lloyd and Condliffe, 2003), demonstrated the difference in stress magnitude between that generated within boudins and that experienced by the surrounding matrix (Lloyd et al., 1982), and challenged existing methods of estimating palaeostress and strain (Ferguson and Lloyd, 1982). The microboudin method is also based on the Weibull statistics of the fracture strength of materials, especially the weakest-link theory (e.g., Weibull, 1951)._ _The method of palaeodifferential stress analysis performed using the microboudin technique was revised by Masuda et al. (2003), who incorporated the shear-lag model of Zhao and Ji (1997) into the model. Recent studies have advanced the microboudin method in the following four areas: (1) quantitative determination of the influence of the size of columnar minerals (Kimura et al., 2006, 2010), (2) consideration of the influence of time on the fracture strength of boudinaged minerals (Masuda et al., 2008), (3) experimental determination of the fracture strength of tourmaline and epidote (Kimura et al., 2006), and (4) determination of the fracture strength of amphibole (Kimura et al., 2010)._ _The microboudin method consists of two components: measurement of the length and width of microboudinaged and intact grains in metamorphic tectonites, and a theoretical analysis of fracturing. The analytical procedure is briefly described below. A full description of the mechanical and statistical aspects of the technique can be found in Masuda et al. (1989, 1990, 2003) and Kimura et al. (2010)._ _3.1. Observations of microboudinage of glaucophane_ _In the studied samples, the long axes of most glaucophane grains lie within the plane of the foliation. Fig. 2 shows photomicrographs of thin sections cut parallel to the foliation. Some columnar glaucophane grains are oriented at a high angle to the lineation (Fig. 3). Microboudinage structures are observed within columnar glaucophane grains in various orientations within the calcite matrix (Fig. 2b, d), which are fractured perpendicular to the long axis and pulled apart parallel to the long axis._ Ключевые слова: fracture strength, total number, marble, grain size, aspect ratio, rock mass, calcite twinning, considered, misch, developed, geophysical, okamoto, equation, microboudin method, plastic, glaucophane microboudins, syros, stress magnitude, boudinaged, del?ni sample, microboudinage occurred, palaeodifferential stress, burkhard, metamorphic, frequency distribution, gently curving, determination, time, differential stress, applied, stress data, calcite-twin method, mpa delni, technique, wa, palaeopiezometer, ded plastic, delni sample, journal structural, migration recrystallisation, calcite, structure, foliation, plastic strain, dynamic recrystallization, sample, elsevier, high, glaucophane grain, microboudinage technique, ferrill, twin, excellent, sspb, loggaussian distribution, weibull, ?ow, p?ffner, size, twinned grain, mpa, american, twiss, cut parallel, extension, microboudin, ded, calcite matrix, interboudin gap, microboudinage, frequency, high-ds stage, dixon, differential, straight, masuda shibutani, rutter, fracturing event, mineralogy, shimizu, plastic deformation, bresser, deformation, grain, calcite-twin data, del?ni, tectonophysics, sellars, palaeodifferential, distribution, microboudins, rotation recrystallisation, lloyd lloyd, lacombe, fracture, tectonites, altherr, calculated, columnar mineral, boudinaged grain, grain-size, calcite grain, journal structural geology, journal, intact, grain-size palaeopiezometry, strain rate, calcite twin, kampos del?ni, greece, horizontal dashed, long, estimated, foliation surface, belt, calcite-twin, study, petrology, temperature, quartzose tectonites, stretched belemnite, data, ratio, grain-size method, kampos sample, microboudinage analysis, number, deformation history, twin type, point, christie, determined, aspect, natural deformation, occurred, twinning, kampos, structural geology, lister, columnar grain, condence interval, syros greece, rotation relative, kimura, sr, strain, result, method, stress, mineral, fractured, based, company, masuda, stress analysis, journal geophysical, long axis, measurement point, tectonics, shear-lag model, structural, laurent, magnitude higher, geological, eds, syros sample, rock, magnitude, mercier, calcite-twin palaeopiezometer, concentration parameter, br?cker, glaucophane, eq, steady-state, microboudinaged grain, geology, natural, steady-state microstructures, pre-boudinage stage, lineation, stage, increasing strain, schmid, intact grain, measured grain, matrix, type, fracturing, analysed sample, lloyd, japanese, fractured grain, measured, time lag, dynamic recrystallisation, shizuoka, passchier, twin density, ferguson, lamella, proposed, microboudin technique, paracrystalline microboudinage, masuda journal, respect, analysis, history, orientation