Quantitative structural analyses and numerical modelling of ...

98 O. LEXA ET AL.of momentum (Eqn A.1) and energy (Eqn A.3), subjectto an incompressibility constraint (Eqn A.2) known asthe Boussinesq approximation (Hansen & Yuen, 2000):@r ij¼ @P qg i ; ðA:1Þ@x i @x i@v i@x i¼ 0;@T@t þ v @Ti ¼ 1 @ @TjqC p þ A ;@x i qC p @x i @x i qC pðA:2ÞðA:3Þwhere x denotes the coordinates in m, v velocity inms )1 , t time in s; r ij is stress tensor, P is pressure in Pa,g is gravitational acceleration (9.81 m s )2 ), T is temperaturein K, j denotes thermal diffusivity and C pdenotes the specific heat capacity. The constitutiverelationship between stress and strain is governed bythe transport coefficient g representing viscosity:r ij ¼ 2g_e ij ;ðA:4Þwhere _e ij is the strain-rate tensor in s )1 . For the purposeof this work, we used a simplified flow law withonly temperature-dependent viscosity according to thesimple exponential equation:g ¼ C 1 e C 2ð T Þ ;ðA:5Þwhere C 1 and C 2 are coefficients used to calculateeffective viscosity from prescribed range (see Table 2).Density q is given by equation of state:q ¼ q 0 ½1 aðT T 0 ÞŠ; ðA:6Þwhere a is the coefficient of thermal expansion and q 0is the reference density at reference temperature T 0 .Thermal diffusivity j and specific heat capacity C p arerecalculated according to temperature using the followingequations (Whittington et al., 2009):j ¼ 3:19 10 7 þ 1:214 10 6 eð 273:15285:2T Þ ; ðA:7Þ3:224 10 5 2:714 107C p ¼ 1538:39þTT 2 ; ðA:8Þderived from laser-flash analysis to provide realisticvalues for geologically relevant temperatures. Theseequations are solved for temperature and velocity anddescribe the fundamental physics required for modellingthe thermal evolution during crustal diapirism.Calculation methods used for thermodynamic modellingThe pseudosections were calculated using THERMOCALC3.30 (Powell et al., 1998) and the data set 5.5 (Holland& Powell, 1998; November 2003 upgrade), in the systemNa 2 O–CaO–K 2 O–FeO–MgO–Al 2 O 3 –SiO 2 –H 2 O–TiO 2 –O (NCKFMASHTO) with the biotite and meltmodels from White et al. (2007), garnet from Dieneret al. (2008), ilmenite from White et al. (2000), feldsparfrom Holland & Powell (2003), white mica fromCoggon & Holland (2002) and cordierite fromTHERMOCALC documentation (Powell & Holland, 2004).The analysed rock composition of sample H296 (inwt% SiO 2 =71.98, TiO 2 =0.42, Al 2 O 3 =13.53,FeO=2.1, MnO=0.03, MgO=0.73, CaO=1.93,Na 2 O=2.76, K 2 O=4.01, P 2 O 5 =0.15, H 2 O ) =0.22,H 2 O + =0.56, CO 2 =0.03), was modified for modellingby adding 1 mol.% of kyanite to enable a smallamount of aluminosilicate to be stable at the estimatedpeak metamorphic conditions, as is observed in thinsection.The reconstruction of a biotite–muscovite graniteprotolith requires several steps. It involves determinationof the H 2 O content in the final assemblage, considerationof open-system behaviour with respect tomelt, and modification of the whole-rock compositionby adding melt (White & Powell, 2002; White et al.,2004; Sˇtı´pska´ et al., 2008). Tracking of the P–T path istherefore undertaken backwards in time, from thematrix assemblage to the early prograde evolution andto the protolith mineralogical composition. Theamount of H 2 O for the modelling shown in Fig. 12a isset such that it allows the stability of the observedmatrix assemblage with garnet rim chemistry oncooling (not shown; see Franeˇk et al., 2011b; seeHasalova´ et al., 2008b for the approach followed). Asthe whole-rock composition is expected to changealong the P–T path as a result of loss of melt, it has tobe decided from which point on the P–T path the meltcomposition will be taken. Crossing the upper stabilityof muscovite causes an abrupt increase in melt proportionand is considered a likely condition for meltloss (White & Powell, 2002; White et al., 2004);therefore, melt composition reintegrated was undertakenat 16 kbar and 860 °C.REFERENCESAckerman, L., Jelínek, E., Medaris, G., Jezˇek, J., Siebel, W. &Strnad, L., 2009. Geochemistry of Fe-rich peridotites andassociated pyroxenites from Horní Bory, Bohemian Massif:insights into subduction-related melt-rock reactions. ChemicalGeology, 259, 152–167.Aftalion, M., Bowes, D. & Vrána, S., 1989. Early CarboniferousU-Pb zircon age for garnetiferous, perpotassic granulites,Blansky´ les massif, Czechoslovakia. Neues Jahrbuch fu¨rMineralogie-Monatshefte, 4, 145–152.Avouac, J.P., 2008. Dynamic processes in extensional andcompressional settings – mountain building: from earthquakesto geological deformation. In: Treatise on Geophysics, Volumes1-11 (ed. Schubert, G.), pp. 377–439. Elsevier, Amsterdam.Babusˇka, V., Fiala, J. & Plomerova´, J., 2010. Bottom to top lithospherestructure and evolution of western Eger Rift (CentralEurope). International Journal of Earth Sciences, 99, 891–907.Bea, F., 1996. Residence of REE, Y, Th and U in granites andcrustal protoliths; implications for the chemistry of crustalmelts. Journal of Petrology, 37, 521–552.Ó 2010 Blackwell Publishing Ltd200