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 e€ects 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 a€ect 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 a€ected 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 di€ers 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 ˆ †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-di€erence 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 ˆ ‡ ; 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. actions at temperatures characterized Table 1 Crust and mantle model com- In the `conventional' model densities by important density contrasts, e.g. positions (weight percentage, Taylor and for the crust and mantle are calcula-  800 °C,  500 °C (Fig. 2). Subsi- McLennan, 1985) ted as: dence is also affected by the lower Crust Mantle q ˆ q †1 aT ‡ bP ; 3† boundary temperature imposed for 0 the model. To illustrate this effect, SiO 66.0 45.0 2 where q0 is the reference density for ®ve experiments were performed with Al2O3 15.2 3.3 the lithology, a is the thermal expan- different boundary temperatures FeO 4.5 8.0 sivity and b is the compressibility 2(Fig. 4). The ®rst four experiments, MgO 2.2 36.3 (Table 3). Tectonic subsidence is com- with temperatures ranging from 1400 CaO 4.2 2.6 puted iteratively in order to preserve to 900 °C, result in ®nal subsidence Na O 3.9 0.34 2 isostatic equilibrium. The results differing by about 200 m. Greater K O 3.4 0 2 obtained numerically for the con- deviations occur in the last case, which H O saturated 0 2 ventional model were veri®ed by presents an especially cold scenario

Ó 2001 Blackwell Science Ltd 355 Metamorphic reactions and basin subsidence · K. Petrini et al. Terra Nova, Vol 13, No. 5, 354±359 ......

Fig. 1 Stable mineral assemblages for model mantle (a) and crust (b). See Table 1 for bulk chemical compositions. Quartz is stable in all phase ®elds for the crustal model. Shading indicates phase ®eld variance, white ®elds are divariant, higher variance ®elds are progressively darker, univariant ®elds are shown by heavy solid curves. The identities of phases in unlabelled ®elds can be de- duced from neighbouring ®elds by the consideration that adjacent phase ®elds di€er by exactly one phase. See Table 2 for solution models and abbreviations, lower-case abbreviations indicate the phase is modelled as a stoichiometric compound (ab, albite; cor, corundum; law, lawsonite; pre, prehnite; pump, pumpellite; zo, zoisite).

with a bottom temperature of 650 °C. In this case, rapid initial subsidence is followed by uplift late in the evolution of the basin. Initial subsidence and later uplift are the result of the cold geotherm intersecting the boundary of the garnet-stability ®eld at conditions where it has a negative P±T slope. As a consequence, garnet becomes stable at progressively shallower depths as the basin rifts, increasing average mantle density, the crust±mantle den- sity contrast and initial subsidence. As the mantle cools in the post-rift stage, the garnet stability is displaced to greater depth so that the density increase caused by decreasing temper- atures is eventually compensated and overridden by the effect resulting from increasingly smaller portions of the mantle being within the garnet-stabil- ity ®eld. Subsidence is affected greatly by the relative thickness of mantle and lithosphere, with considerable depths of subsidence reached in the case of crustal thickness of 40 km and above and smaller subsidence achieved by basins with thinner initial crust. The experiments with thinner crust show more pronounced steps in the subsi- dence curve, emphasizing the relative importance of reactions in the man- tle compared to reactions in the crust, where the P±T conditions do not induce reactions with important density contrasts.

Discussion A major assumption in the petrologi- cal model is that reactions take place

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Fig. 2 False-colour density maps computed by free-energy minimization for mantle and crust model compositions (Table 1). The contour interval for both maps is 25 kg m±3.

at equilibrium pressure and tempera- ture conditions irrespective of reaction kinetics or of the previous history of Table 3 Model parameters the rock (e.g. Bousquet et al., 1997). Parameter Symbol Value In nature, reactions may occur at pressures and temperatures different Thermal diffusivity k 1 ´ 10)6 (m2 s)1) from those predicted by an equilib- Speci®c heat per unit mass c 1 ´ 103 (J kg)1 K)1) rium model. Additionally, crustal )6 )3 Crustal volumetric heat production A 1 ´ 10 (W m ) metamorphism is generally not )5 )1 Isobaric thermal expansivity a 3 ´ 10 K isochemical, most notably with regard )11 )1 Isothermal compressibility b 1 ´ 10 Pa to volatile components and it is to be

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the resulting subsidence curves are not affected by the omission of retrogres- sive reactions. This result reiterates the relative importance of mantle reactions. It has been proposed previously that sharp steps in subsidence curves ± in some cases even leading to phases of uplift ± result from dis- continuous mantle reactions (e.g. Pod- ladchikov et al., 1994; Yamasaki and Nakada, 1997). With the present model, reaction-related uplift is ob- served only in extreme cases (cold scenarios) and only in the later stages of basin evolution; furthermore, the steps in the subsidence curves are smooth compared with those of dis- continuous models. Nevertheless, the overall effects are still important and, as reactions are an almost inevitable Fig. 3 Tectonic subsidence as a function of time for d ˆ 1.5 (eqn 2), initial crustal result of variations in pressure and thickness ˆ 30 km, lithospheric thickness ˆ 125 km, bottom temperature ˆ 1000 °C, temperature, exclusion of these effects ±3 sediment density ˆ 2200 kg m . Other parameters as in Table 3. The solid curve will result in inaccurate subsidence corresponds to the subsidence curve obtained with densities from the petrological curves. model. Dashed curves correspond to subsidence obtained with assumed a reference )3 mantle density (q0) of 3340 kg and density contrasts between crust and mantle of 490, 540, 590 and 640 kg m)3, corrected for thermal and pressure effects as in (3). Conclusion Incorporation of the densi®cation ef- expected that volatile loss during found that assemblages with the low- fects caused by metamorphic reactions prograde metamorphism may hinder est water content achieved by the in models for sedimentary basin for- retrograde hydration (Connolly and rocks were preserved throughout the mation lead to signi®cant changes in Thompson, 1989; Rubie, 1990). To subsequent history. In the present predicted subsidence curves compared approximate this effect, an experiment model, this effect is only important to those obtained with the conven- was carried out in which rehydration in the crust as the mantle is anhy- tional density model. Although these reactions were suppressed: it was drous. For average crustal thickness, e€ects are quantitatively signi®cant, metamorphic densi®cation does not substantially alter the qualitative be- haviour predicted by the conventional model. Metamorphic reactions cause faster subsidence rates in the initial stages of post-rift subsidence. This behaviour is induced by an increase in density contrast between the crust and the mantle. In the case of cold lithosphere, uplift is observed as a late stage of basin evolution. The subsi- dence curves produced with the den- sity model presented herein show periods of faster and slower subsi- dence caused by variations in the density across mineral stability ®elds. For typical crustal thickness, subsi- dence is controlled largely by the reactions occurring in the mantle, and particularly by those a€ecting garnet stability.

Acknowledgements Fig. 4 Tectonic subsidence as a function of time and bottom temperature with all We are grateful to Kurt Stuewe and other parameters as indicated for Fig. 3. an anonymous reviewer for constructive

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comments. This work was supported by 15±34 kbar. Geochim. Cosmochim. Acta, deep crustal metamorphism. Geophys., research funds granted by the Swiss Fed- 49, 865±870. J. R. Astr. Soc., 62, 1±14. eral Institute of Technology to Alan B. Gasparik, T., 1985b. Experimental-study Naimark, B.M. and Ismail-Zadeh, A.T., Thompson and Jean-Pierre Burg (ETH of subsolidus phase-relations and mixing 1995. Numerical models of a subsidence Project 0-20272-96). properties of pyroxene and plagioclase in mechanism in intracratonic basins:

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