A coupled petrological±tectonic model for sedimentary basin evolution: the in¯uence of metamorphic reactions on basin subsidence K. Petrini, J. A. D. Connolly* and Yu. Yu. Podladchikov Earth Sciences Department, ETH Zurich, Sonneggstr. 58092 Zurich, Switzerland ABSTRACT The lithosphere is subject to ¯uctuations in temperature and stable over an increasing depth interval within the mantle, an pressure during the formation of sedimentary basins. These effect that ampli®es the crust±mantle density contrast. For ¯uctuations cause metamorphic reactions that change the models with an extraordinarily cold lithosphere, uplift is gener- density of the lithosphere, which, in turn, in¯uences basin ated as a late stage of basin evolution. In general, subsidence is subsidence. This contribution develops a model for sedimentary not smooth but occurs instead in small steps re¯ecting periods of basin formation to assess the importance of this coupling. The accelerated/decelerated subsidence. For typical crustal thick- model shows that basin subsidence is signi®cantly affected by nesses, subsidence is controlled largely by reactions in the metamorphic densi®cation. Compared to results obtained with mantle, and particularly those determining garnet stability. cruder density models, metamorphic densi®cation accelerates subsidence in the initial post-rifting stages as garnet becomes Terra Nova, 13, 354±359, 2001 of compressional tectonic settings establish the variation in rock density Introduction (Bousquet et al., 1997) and within the caused by mineral transformations. During the tectonic rifting that leads framework of extensional settings rele- The petrological calculations are to the formation of a sedimentary vant to basin formation (Podladchi- made for realistic approximations of basin, the lithosphere undergoes rapid kov et al., 1994; Yamasaki and natural rock compositions and ac- heating and decompression. Subse- Nakada, 1997). The latter two papers count for mineral solution behaviour. quently, the geotherm evolves toward consider a schematic discontinuous This model is then used to evaluate a steady-state thermal gradient as the spinel±garnet reaction in the mantle the eects of the density changes in lithosphere cools. The changes in tem- without specifying the chemical system the context of a simple basin model perature and pressure during this evo- considered; therefore, the pressure± after McKenzie (1978). lution cause metamorphic reactions temperature conditions for the reac- that aect the bulk physical properties tion are poorly constrained. In nature, Petrological model of the lithosphere. Sedimentary basin the reaction is continuous, and there- subsidence is dependent on these fore its realistic simulation requires the The relative proportions, composi- properties, particularly density, and use of a petrological model incorpor- tions and densities of the stable min- it is therefore to be expected that it ating solid solution behaviour. An erals as a function of pressure, will be aected by metamorphic reac- additional limitation of simpli®ed temperature and bulk composition tions. The potential in¯uence of models is that it is not possible to were computed from thermodynamic metamorphic reactions on subsidence determine a priori which reactions data with a free-energy minimization was recognized several decades ago have important effects on subsidence; program described in detail elsewhere (Lovering, 1958; Kennedy, 1959) and this is because the importance of a (Connolly, 1990; Connolly and Petrini, some subsequent authors have attrib- reaction with a large density difference 2002). This computational strategy uted subsidence entirely to metamor- may be overridden by the cumulative diers from more traditional thermo- phic densi®cation (e.g. Middleton, effect of several reactions with smaller dynamic approaches used previously 1980; Artyushkov, 1983; Artyushkov density changes, or by a reaction with to quantify lithospheric density (e.g. et al., 1991; Hadmani et al., 1991; smaller density change but stronger Sobolev and Babeyko, 1994) in that Naimark and Ismail-Zadeh, 1995; depth dependence, which thus affects a the nonlinear free-energy composition Lobkovsky et al., 1996; Ismail-Zadeh larger portion of the lithosphere. surfaces of solution phases are ap- 1et al., 1997). In recent work, meta- In order to determine the import- proximated by inscribed polyhedra. morphic densi®cation has been taken ance of metamorphic densi®cation As a consequence of this approxima- into consideration both in the context during sedimentary basin formation, tion, phase diagram sections de®ned it is crucial to take into consideration by environmental variables such as *Correspondence: J. A. D. Connolly, In- the bulk of the reactions likely to pressure and temperature are dis- stitut fuÈ r Mineralogie and Petrographie, occur within the lithosphere. The pre- cretized by a polygonal mesh. This Earth Sciences Department, ETH Zurich, sent contribution presents the results representation is particularly conveni- Sonneggstr. 58092 Zurich, Switzerland. of a coupled petrological±geodynamic ent for geodynamic modelling because Tel.: +41 1632 78 04; fax: +41 1632 10 model for basin formation in which once such a mesh has been computed 88; e-mail: [email protected] the petrological component is used to all aspects of the thermodynamic state 354 Ó 2001 Blackwell Science Ltd Terra Nova, Vol 13, No. 5, 354±359 K.Petrini et al. · Metamorphic reactions and basin subsidence ............................................................................................................................................................. of the system can be recovered easily Table 2 Mineral solution notation, formulae and model sources (see table footnote). at any point within the mesh by The compositional variables w, x, y, and z may vary between zero and unity and are automated procedures. For present determined as a function of pressure and temperature by free-energy minimization purposes, fertile lherzolitic and grano- Solution Symbol Formula Source dioritic bulk chemical compositions were taken to represent the composi- Amphibole Amph Ca2NawMgxFe1±xAl3w+4ySi8±2w±2yO22(OH)2 1 tions of the mantle and crust, respect- Biotite Bio KMg(3±y)xFe(3±y)(1±x)Al1+2ySi3±yO10(OH)2 1 ively (Table 1). Thermodynamic data Chlorite Chl Mg(5±y+z)xFe(5±y+z)(1±x)Al2(1+y±z)Si3±y+zO10(OH)8 2 provided by Holland and Powell Clinopyroxene Cpx Na1±yCayMgxyFe1±xyAlySi2O6 3 (1998) were used for all end-member Glaucophane Gl Ca2±2zNazMgxFe(1±x)Al3w+4y Si8±2w±2yO22(OH)2 1 phase compositions, the mineral solu- Garnet Gt Fe3xCa3yMg31±x±yAl2Si3O12 1 tion models employed are detailed in Alkali feldspar Kf NaxKyAlSi3O8 4 Table 2, and the accuracy of the Olivine Ol MgxFe1±xSiO4 1 discretization was speci®ed so as to Orthopyroxene Opx Mgx(2±y)Fe(1±x)(2±y)Al2ySi2±yO6 1 Phengite Phen K Na Mg Fe Al Si O (OH) 1, 5 resolve mineral compositions with a x 1±x y z 3±2(y+z) 3+y+z 10 2 Plagioclase Pl Na Ca Al Si O 6 maximum error of 3 mol%. Calcula- x 1±x 2±x 2+x 8 Sanidine San Na K AlSi O 4 tions for the crust were performed x y 3 8 Spinel Sp Mg Fe AlO 1 assuming water saturation, whereas x 1±x 3 the mantle was assumed to be anhy- Sources: 1, Holland and Powell (1998); 2, Holland et al. (1998); 3, Gasparik (1985a,b); 4, Thompson and drous. The stable mineral assemblages Waldbaum (1969); 5, Chatterjee and Froese (1975); 6, Newton et al. (1980). as a function of pressure (P) and temperature (T) for the two bulk compositions are shown in Fig. 1. where t is time vz is vertical velocity, k comparison with the analytical solu- The computed densities are shown in is thermal diffusivity, q is density, c is tion (McKenzie, 1978). Fig. 2. Choosing a granodioritic com- speci®c heat per unit mass, A is volumetric heat production and z is position for the crust leads to relat- Results ively low densities at eclogite facies the coordinate in the vertical direc- conditions compared to those for a tion. The vertical velocity vz is calcu- The ®nal subsidence for the `real' more ma®c crustal model (e.g. Arty- lated to correspond to: density model is given approximately by the `conventional' model (3) with ushkov et al., 1991; Lobkovsky et al., mz log d=trift z; 2 1996; Bousquet et al., 1997). This a reference mantle density of )3 effect is of little consequence for where d is the ratio between initial 3340 kg m and density contrast )3 results reported here, because the lithospheric thickness and post-rift Dq = qmantle ) qcrust of 590 kg m model crust has a maximum thickness lithospheric thickness and trift is the (Fig. 3). However, in detail, the `real- of 35 km. total time during which the basin is density' model evolution re¯ects the stretching. The parameter values ad- continuous variation in both absolute opted for the calculations are listed in densities and density contrast between Basin model Table 3. mantle and crust. The density contrast Basin subsidence is calculated using a Initially the model basin consists of increases progressively, enhancing 1D implicit ®nite-dierence model. two layers: crust and mantle. During subsidence as an increasing portion The thermal evolution of the litho- rifting the base of the model is in- of the mantle reaches conditions of sphere is computed from the heat ®lled with asthenospheric material garnet stability. The resulting subsi- conduction±advection equation with where as sediments (with a density dence is not smooth, but occurs in- )3 radioactive heat production: of 2200 kg m ) are added at the stead in small steps re¯ecting periods upper boundary to compensate for of accelerated/decelerated subsidence @T @T k @2T A subsidence. Calculations are per- (Fig. 3). The steps correspond to peri- m ; 1 @t z @t qc @z2 qc formed using both a `conventional' ods in which the geotherm intersects model and the `real' densities ob- the conditions for garnet-forming re- tained from the petrological model.