American Mineralogist, Volume 80, pages 1188-1207, 1995 Simulations of convectionwith crystallization in the systemKAISiTO6-CaMgSirOu: Implications for compositionallyzoned magma bodies Fuux J. Srrnl,, Cunrrs M. Or,nnxrunc, CoNsr,l,NcrCnmsrENsEN, Mrcor, Toorsco DepartmentorGeologicar ttn::';liiff orcarirornia' 3"'1,'#*,l;,:ff:t:t:"*'universitv Ansrnlcr A model has been developedand applied to study the origin of compositional and phase heterogeneityin magma bodies undergoing simultaneous convection and phase change. The simulator is applied to binary-component solidification of an initially superheated and homogeneousbatch of magma. The model accounts for solidified, mushy (two- or three-phase),and all-liquid regions self-consistently,including latent heat effects,perco- lative flow of melt through mush, and the variation of systementhalpy with composition, temperature, and solid fraction. Phaseequilibria and thermochemical and transport data for the system KAlSirOu-CaMgSirOuwere utilized to addressthe origin of compositional zonation in model peralkaline magmatic systems.Momentum transport is accomplished by Darcy percolation in solid-dominated regions and by internal viscous stressdiffusion in melt-dominated regions within which relative motion between solid and melt is not allowed. Otherwise, the mixture advectsas a pseudofluid with a viscosity that dependson the local crystallinity. Energy conservation is written as a mixture-enthalpy equation with subsidiary expressionsthat are based on thermochemical data and phase relations that relate the mixture enthalpy to temperature, composition, and phase abundancesat each location. Speciesconservation is written as the low-density component (KAlSirOu) and allows for advection and diffirsion as well as the relative motion betweensolid and melt. Systematic simulations were performed to assessthe role of thermal boundary condi- tions, solidification rates, and magma-body shape on the crystallization history. Exami- nation of animations showing the spatial development of the bulk (mixture) composition (C), melt composition (C,), temperature (7), solid fraction ({), mixture enthalpy (h), and velocity (V), reveals the unsteady and complex nature of convective solidification owing to nonlinear coupling among the momentum, energy,and speciesconservation equations. A consequenceof the coupling includes the spontaneousdevelopment of compositional heterogeneityin terms of the modal abundancesof diopside and leucite in the all-solid parts of the domain (i.e., modal mineralogical heterogeneity)as well as spatial variations in melt composition particularly within mushy regions where phase relations strongly couple compositional and thermal fields. Temporal changesin the rate of heat extraction becauseof bursts of crystallization and concommitant buoyancy generationare also found. Crystallization of diopside, the liquidus phasein all cases,enriches residual melt in low- density K-rich liquid. The upward flow of this material near the mush-liquid interface leads to the development of a strong vertical compositional gradient. The main effect of magma-body shapeand different thermal boundary conditions is in changing the rate of solidification; in all casescompositional heterogeneitiesdevelop. The rate of formation of the compositional stratification is highest for the sill-like body becauseof its high cooling rate. Compositional zonation in a fully solidified body is found to be both radial and vertical. The most salient feature of this simple model is the spontaneousdevelopment of large-scalemagma heterogeneityfrom homogeneousand slightly superheatedinitial states, assuminglocal equilibrium prevails during the course of phasechange. INrnouucrroN the discipline itself, and it would be difficult to review the subject in a single contribution. An adequatecritique One of the most important problems in igneous pe- would encompassthe entire field of igneous petrology, trology is elucidation of the mechanismsthat give rise to include the history of planetary differentiation and crustal magmatic diversity. This problem is practically as old as growth (e.9., Galer and Goldstein, l99l; Taylor and 0003-004x/95/rtt2-1 I 88$02.00 I 188 SPERA ET AL.: SIMULATION OF CONVECTION AND CRYSTALLIZATION I 189 Mclennan, 1985),and draw upon geochemicaldata from evidence that separation of crystals from melt had oc- hundreds if not thousands of ancient and modern mag- curred, although the mechanism and rate by which this matic centers. was accomplishedare not constrainedby the geochemical Sincethe pioneering work of Bowen ( I 928), it has been data. Evidently, the lack of interphenocryst chemical generally acceptedthat crystal fractionation is one of the variation and correlation between phenocryst composi- most effective magmatic differentiation processes.By tion and enclosingmelt (glass)composition arguesagainst some means, crystals become separatedfrom the melts simple crystal settling. Similar conclusionswere reached in which they crystallize. Despite the generalsignificance by Dunbar and Hervig (Dunbar and Hervig, 1992; Her- of this problem, the mechanism of crystal fractionation vig and Dunbar, 1992) in their detailed study of melt- and the associatedquestion ofthe vigor ofconvection in inclusion traceelement abundances and comparisonswith magma bodies remain controversial(e.g., Marsh, 1989; enclosingpumice and whole-rock compositions. Martin and Nokes, 1989; Gibb and Henderson, 1992., A popular scenario whereby compositionally evolved Huppert and Worster, 1992). The problem is challenging melt becomes separated from associatedcrystals is by mainly becauseof the enormous changesin magma vis- maryinal upflow, a mechanismfirst hypothesizedby Shaw cosity that occur in the crystallization interval. Although (1974) and extensively investigated theoretically, exper- adequatemodels exist for the calculation of melt viscos- imentally, and by numerical simulation since then (e.g., ity as a function of temperature and composition (e.g., Turner, 1980;Chen and Turner, 1980;Turner and Gus- Shaw,1972;Bottinga and Weill, L972;Urbainet al., 1982; tafson,198 l; Speraetal., 1982,1984,1989; Huppert and see also Stein and Spera, 1993), accurate description of Sparks,1984; Turner, 1985; Nilson et al., 1985; Mc- the complex rheological behavior of magmatic mixtures Birney et al., 1985;Lowell, 1985;Huppert et al., 1986; is a far more difrcult task (Lejeune and Richet, 1995). Bergantzand Lowell, 1987;Trial and Spera,1988; kitch, Because,in general,there can be relative motion between 1989;Langmuir, 1989;Huppert, 1990).The essentialidea the constituent solid, melt, and vapor phasesand because is that in systemswhere phasechange occurs along a sub- component phases have such widely different physical vertical sidewall (e.g., solidification or anatexis),the ini- properties, the characterization of the rheology of mag- tial downward flow of cooled marginal magma can be matic mixtures presents a formidable problem. Briefly reversed if phase change enriches melt in low-density stated, it is difficult to describe simply and'accurately components(e.g., SiOr, NarO, KrO, and HrO) sufficiently both the rheological properties of magma and the rela- to overcome negative thermal buoyancy effects. In this tionship between phase fraction (e.9., fraction solid, f,) model, accumulation by advective transport of the cooler and permeability of magmatic multiphasemixtures across but chemically enriched (and buoyant) melt at the top of the wide range of conditions relevant to magma transport the magma body produces a thermally and chemically and evolution. The problem is particularly acute in silicic zoned layer. Additional in situ crystallization within the and intermediate-composition systemsfor which there is roofward layer then producesa magmatic mixture with a overwhelming and incontrovertible evidence that large phenocryst content inconsistent with any single-stage, volumes of evolved magma, sometimesexceeding several closed-systemfractionation scheme,but consistent with thousand cubic kilometers, exist within the crust. Fur- trends expected from crystal-fractionation processesas thermore, differentiation may occur at geologicallyrapid commonlynoted (Michael, l9B3; Wolffand Storey,1984). rates(e.g., lO-'zkm3/yr) prior either to solidifyingto form If HrO is significantly enriched upward, then the local mineralogically zoned or layered plutons or other com- (compositionally dependent)liquidus to solidus temper- posite batholiths or to erupting to form compositionally ature interval, as well as the liquidus temperature itself, zoned ignimbrites or lava flows (Smith, 1979; Hildreth, varies with depth within the magma body. This leads to l98l; Trial and Spera,1990; Wiebe, 1993). A classicex- variation in phenocryst content with location within the ample is the 600 km3 Bishop Tuff in eastern California body independent of the effectsof crystal settling. (Hildreth, 1979) emplaced as a plinian pumice fall, fol- Although the simple version of the marginal upflow lowed by a sequenceof pyroclastic flows. Hildreth con- hypothesisis conceptually pleasingand there is no doubt cluded that no mixing of crystalsby gravitational settling that marginal upwelling occursin laboratory experiments had occurred prior to the eruption. His conclusion was with aqueous solutions, its relevance to magma differ- basedprincipally on the observationthat individual hand- entiation has been questioned (see review by Trial and sized pyroclasts had compositionally uniform popula-