JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 99, NO. B7, PAGES 13,813-13,833, JULY 10, 1994

Numerical investigations of the mantle plume initiation model for flood basalt events

Cinzia G. Farnetani and Mark A. Richards Departmentof Geologyand Geophysics, University of California,Berkeley

Abstract. Recentstudies have linked both the eruptionof continentalflood basaltsand the emplacementof largeoceanic plateaus to the initialphase of mantleplume activity, i.e., the "plumehead" model. Here we developthis concept further through numerical models of a large thermaldiapir rising through the mantle and impinging upon the baseof the lithosphere.A finite elementanalysis in axisymmetricgeometry is usedto modelthe dynamicsof solid state convectiveflow andheat transport in the mantle,and an anhydrousbatch melting model is used to estimatemelt volumesand compositionsobtained from partialmelting in the shallowmantle. We explorethe effectsof a numberof modelvariables, including mantle viscosity structure, plumetemperature and diameter, and the mechanical response of thelithosphere. Our study emphasizescases in whichthe lithosphere does not undergo significant extension prior to large- scalemelting. A "standardmodel" is foundto be consistentwith someobserved characteristics of flood basalt/plumeinitiation events. This modelincludes an initial diapirof radius400 km and initial excesstemperature 350øC rising through a mantleof viscosity-102•Pa s andimpinging beneatha modeloceanic lithosphere -100 Ma in age.If lithosphericextension does not occur, meltingis almostentirely sublithospheric, the melt volumeproduced is -3.5x106 km3 andits compositionhas high MgO content(15-20 wt %). A time sequenceof precursorycentral (axial) uplift of severalkilometers followed by majormelting (volcanism) is a robustfeature of all the models,regardless of mantleviscosity structure or lithosphericresponse. Low viscosityin the uppermantle compresses the timescalefor theseevents, and results in a constrictionof the plume "head"initially impingingon the lithosphere.The radialextent of the meltingregion (about500 km at the time of maximummelt production)is only slightlyaffected by the upper mantleviscosity. For nonriftinglithosphere, no significantmelt generationoccurs for initial plumeexcess temperatures less than about 300øC. The initial plumeradius has only a modest effectupon the volumeof melt obtained.The mostimportant aspect of lithosphericresponse is whetheror not theuppermost crust and lithosphere (above -40 km depth)undergo extension: otherwise,the ductilestrength of thelower lithosphere has little effect.If thelithosphere is allowedto extendfreely, the melt volumeincreases by aboutan orderof magnitude,and it is comparablewith someof the largestoceanic plateaus such as OntongJava. If continentalor oceanicflood basalt events occur on old, nonriftinglithosphere, the primary melts are likely to be muchmore MgO rich thanthe basaltserupted at the surface.This is consistentwith abundant evidencefor olivinefractionation in manyflood basalt provinces, along with the occurrenceof picritelavas, and we hypothesizethat fractionation occurs at a densitytrap at thecrust/mantle boundary(Moho). At this stageand following, it is likely that significantlower crustaland mantle-lithosphericcontamination of mantleplume-derived magmas may occur,both isotopicallyand in thetrace elements. The sequenceand timing of bothprecursory and post- magmaticevents in the vast,well-exposed oceanic flood basaltterrane known as "Wrangellia" (SE Alaska;British Columbia)are consistentwith the predictionsof our model.The uplift predictedby our modelsis of order2-4 km if we requirethat mantle plumes are hot enoughto melt beneathunrifted lithosphere. Effects not modeledhere, such as small-scaleconvection and hydrousmelting, will tendto reducethe modelexcess temperature and uplift. In orderto better understandthe relationbetween mantle plumes and large igneous provinces, several important advancesare required:implementation of a fractionalmelting model, some realistic assessment of melt transportthrough the mantleand crust, and a fully three-dimensionalconvection model.

Introduction not explained by normal plate tectonic activity at convergent or divergent margins, and they occur in a variety of tectonic Flood basalt eruptionsare extraordinaryvolcanic events settings [Hill et al., 1992]. Continental flood basalts are which give rise, literally, to floodsof basalticlava that cover commonly associated with lithospheric rifting and vast areasof the Earth's surfacevery rapidly. These eventsare continentalbreak-up [White and McKenzie, 1989], although major crustalextension does not appearto be requiredfor flood Copyfight 1994 by the AmericanGeophysical Union. volcanism [Richards et al., 1989; Hooper, 1990]. Papernumber 94JB00649. Estimated extruded volumes for the largest flood basalt 0148-0227/94/94JB-00649505.00 events such as the Karoo, the Deccan traps, the Paranti-

13,813 13,814 FARNETANI AND RICHARDS' FLOOD BASALT MODELS

Etendeka,the Siberian traps, and the North Atlantic Province, Morgan [1972, 1981] noted the associationof presently (Figure1) areof order1 or 2x10a km3 [Richardset al., 1989], active hotspots with flood basalts and proposed that flood with perhaps similar (but unknown) volumes of intrusive basalts occurred at the initiation of mantle plume activity. magmatism.Recent estimatesof total melt volumesfor the Richards et al. [1989] discussedeight such pairings in the Deccan and the North Atlantic Province are of order 6 and Phanerozoic,noting that flood basaltstypically erupt at rates 8x106 km3, respectively[Coffin and Eldholm,1993, 1994]. an order of magnitude higher than associated continuous All these provincestypically cover areas -1000-2000 km in ("normal") hotspot track volcanism. According to the mantle radius [White and McKenzie, 1989], although the loci for plume initiation model [Richards et al., 1989; Campbell and eruptionsmay be more confined. Magnetostratigraphicand Griffiths, 1990; Griffiths and Campbell, 1990] the first radiometric age data indicate that the bulk of the volcanic massive volcanic event correspondsto melting of the large activity occursin just a few million years, yielding eruption leading diapir, or "head", of the plume, while the following rates of-1 km3/yr, or greater[e.g., Richardset al., 1989; magmatic activity of the hotspot is associated with the Renne et al., 1992; Coffin and Eldholm, 1994]. Flood basalt remaining plume conduit, or "tail". In this model, lithospheric eventsare generallypreceded by a period of thermaldoming rifting may occur before, during, or after the main phase of and uplift of order -2 km [e.g., Cox, 1989], although the volcanism,but it is not required. timing and durationof uplift are often difficult to constrain. An alternativeproposed for the origin of flood basaltsis the Large volcanic oceanic plateausare also likely to have rifting/decompression model [Morgan, 1981; White and resulted from flood volcanism [Richards et al., 1991], and McKenzie, 1989], in which abnormally hot asthenosphere estimatedvolumes for some plateausare very large indeed:at (associatedwith a mantle plume) wells up in passiveresponse least a few million cubic kilometers for the Caribbean Plateau; to continental stretching and rifting. This model seeks to for the KerguelenPlateau the extrusivecomponent is -8x10• explain the occurrence of flood basalts in association with km 3, and the estimatedtotal volume is -10-15x106 km3 continentalrifting and has not been appliedto oceanicplateau [Coffin and Eldholm, 1994]; for the Ontong Java Plateauthe genesis.The passiverifting and plume initiation modelsshare estimatedtotal volume ranges from 30 to 60x106km 3 [Coffin the common feature of mantle plume activity, but they differ and Eldholm, 1994]. Recent dating suggeststhat the bulk of markedly as to the role of the lithosphere. Clearly, the Ontong Java Plateau was erupted in just a few (-2-5) lithospheric extem;ion has a major effect on melt generation million years [Tardunoet al., 1991; Mahoneyet al., 1993], in [McKenzie and Bickle, 1988], so the questionis mainly one of which casethe eruptionrates would be comparableto or larger geological observation: Is flood volcanism always preceded than those for continental flood basalts. There is also by major lithosphericextension? We have arguedin the past evidence that oceanic plateau formation is accompaniedby [Richards et al., 1989, 1991], as have others [Hooper, 1990; regionaluplift of the oceanfloor [Richardset al., 1991]. Hill et al., 1992; Heaman et al., 1992], that lithospheric

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Figure 1. Schematicmap showingselected flood basaltprovinces and oceanicplateaus. The associated hotspots,where known or conjectured,are indicated.(Adopted from Duncanand Richards[1991]. For a more completemap of large igneousprovinces, see Coffin and Eldholm [1994].) FARNETANI AND RICHARDS- FLOOD BASALT MODELS 13,815 extensionis not required. We will not repeat those arguments Third, we are particularly interested in applications to the here, but the matter is not yet resolved and remains a flood basalt formation in the Triassic strata of the famous legitimate point for debate. Wrangellia terrain of Alaska and Vancouver Island, British Important questions also remain concerning the specific Columbia. This accretedoceanic plateau containsa remarkable predictions of the theoretical models. The plume initiation stratigraphic record of prevolcanic and postvolcanic events model has been developedon the basisof resultsfrom simple [Richards et al., 1991], and the field evidence shows that flood laboratory fluid dynamical experiments [Whitehead and volcanism occurred on old oceanic lithosphere without major Luther, 1975; Olson and Nam, 1986; Griffiths and Campbell, crustal extension. 1990], which show that hot, low-viscosity mantle plumes will develop a very large leading diapir, followed by a narrow conduit if the plume remains connectedto its source. These Numerical Methods models have been extremely useful, both qualitatively and Finite Element Model quantitatively,but they do not addresssome important aspects of plume dynamics. In particular, they cannot be applied We use a finite element code (ConManCYL) for thermal directly to partial melting processes,nor can they be used to convection within the Earth's mantle in cylindrical understandimportant physical effects arising from variations axisymmetric geometry. We have substantially modified the in the mechanical properties of the deep mantle and original Cartesianversion of the code (ConMan, written by A. lithosphere.Such aspectsinstead can be better elucidatedby Raefsky and S. King) to satisfy the cylindrical geometry. The numerical models. code solves the advection-diffusionequations for a Newtonian, In this paper we presentthe resultsof numericalmodeling of incompressible and compositionally homogeneousviscous ascendinglarge mantle diapirs in order to develop a broader fluid. In nondimensionalform the equationsare range of quantitative, testable hypotheses from the plume initiation concept. Our finite element model in cylindrical Incompressibility axisymmetric geometry combines the dynamics of solid state convection in the mantle with a melting model. We start with V.U=O (1) a hot, spherical diapir in the lower mantle and follow its evolution as it rises through the mantle and spreadsbeneath Conservation of momentum for a fluid at infinite Prandtl the lithosphere.We calculate the history of surfaceuplift and number mantle melting due to the hot plume head. We implement the empirical batch melting model of McKenzie and Bickle [1988] -VP+ V2U+ RaT• =O (2) to estimate the total melt volume, the melt production rate, and the melt composition.We can investigatehow parameters Conservation of energy such as the melt volume, its primary composition,the amount and timing of uplift, etc., are functionsof (1) buoyancyof the --+(vr).v=RF V2r (3) thermal diapir (which dependson its initial size and excess temperature), (2) different mantle viscosity structures,and (3) where U is the velocity vector, T is the temperature,p is the mechanical behavior of the lithosphere. The further step, dynamicpressure, t is time,Ra is the Rayleighnumber, and which is to compare the resultsof the numerical model to the is a unit vector in the vertical direction. The equationsare non- correspondingparameters observed or inferred in flood basalt dimensionalizedby scaling distanceaccording to the cylinder provinces,can be done only at a very speculativelevel due to depthd, temperatureaccording to the temperaturecontrast the simplicity of our model. The equilibrium melting model acrossthe lithosphere,and time accordingto d2/•, where•c is does not account for the compositional evolution of the the thermal diffusivity. Numerical values of the scaling residuum as melting proceedsand how this affects the melt parametersare given in Table 1. All the materialproperties are fraction and its composition.Moreover, we do not model melt combined in the Rayleigh number: extraction,nor do we model attendanteffects such as pressure changesresulting from melt extraction [White et al., 1992] and Ra= gøtSFd3 p (4) heat transfer between the rising magma and the lithosphere. We also ignore the effect of volatile components,since the where g is the gravitational acceleration,tx is the coefficient batchmelting parameterizationis basedon anhydrousmelting of thermalexpansion, •c is the thermaldiffusivity, and p is the experiments. This last restriction may be particularly density. In our models the Rayleigh number becomes important in addressing the trace element and isotopic effectively a measureof mantle referenceviscosity, and in (4), characteristicsof continental flood basalts [Gallagher and rl is the viscosityof the lower mantle.Density variations due Hawkesworth, 1992]. to temperaturechanges are neglectedexcept in the calculation We chooseto concentrateon the case of a mantle starting of the buoyancyforces (Boussinesqapproximation). plume impinging on nonrifting oceanic lithosphere.There are The incompressibility equation is used to constrain the several reasons for this: First, the composition and thermal momentum equation by means of a penalty function structure of oceanic lithosphere are rather well-understood formulation [Hugheset al., 1979]. Hughes [1980] showsthat compared to continental lithosphere. Second, as will be in order to achieve correct results using the penalty shown below, the case of old, nonrifting lithosphere formulation in the axisymmetric case a mean-dilatational constitutesthe most stringent test for the plume initiation approach(B method)must be appliedto the stiffnessmatrix model, especially with respectto melt production.We believe of the momentumequation. The momentumequation is solved that the field evidenceshows that at least somemantle plumes using a Galerkin methodand bilinear shapefunctions, and we must be hot enough to melt without lithospheric extension. apply the B methodin its completeformulation [Hughes, 13,816 FARNETANI AND RICHARDS: FLOOD BASALT MODELS

Table 1. Model Parametersand PhysicalConstants

Symbol Model Parametersand Physical Constants Values

d dimensionaldepth of the cylinder 2600 km potential temperaturecontrast across the lithosphere 1280øC g gravitational acceleration 10ms -2 thermal expansioncoefficient 3x10-5 oc-1 mantle density 3500kg m-3 thermal diffusivity 10-6 m 2 specific heat at constantpressure 1200J kg

1987]. The accuracy of the solutions for the velocity that may arise becauseof initially high temperaturegradients. components has been checked against analytical solutions, When calculating the initial radius of the diapir, we take into calculated with a propagator matrix techniquein cylindrical accountthe buoyancyinduced by the thermalhalo, so that R0 geometry [Richards, 1986]. The error is defined as should be considered an "effective" initial radius. œ= (UC - UA) x 100/UA, where Uc isthe finite element value of the velocity component at each node and UA is the Uplift Calculations corresponding analytical value. On a 66x66 test grid we Given the velocity components at each time step, we achievedan œ<0.01%, with errors scaling as the squareof the calculate the topographicuplift induced by the rising thermal grid spacing. diapir. In cylindrical geometrythe vertical normal stressis The energy equation is solved using a streamline-upwind Petrov-Galerkin formulation since it is more accurate for advection dominated flows [Brooks and Hughes, 1982]. The ,= = p (5) time steppingin the energy equationis done using an explicit predictor-correctoralgorithm, and the time step corresponds to the Courant time step [King et al., 1990]. For a given temperature field the code calculates the corresponding 200 velocity field, which is then used to advect the temperatures for the next time stepand solve for a new temperaturefield. The code uses an Eulerian grid of rectangularelements. In most of the models we presentthe size of the box is 1560 km in radiusby 2600 km in depth, and we use a nonuniformgrid with 70x120 elements(Figure 2). The height of each element is 13.8 km (from the surfaceto 200 km depth), 18.5 km (from 200 to 1000 km depth), and 26.0 km for greater depths. For 1040 radial18.5 km,distances elsewhere less thethan width 760 kmis 27.8 the km.width ofeach element is

Atthe surface weimpose zero vertical velocity (Uz =0) ß Forcases in whichlithospheric extension isnot allowed the radial componentof the velocity is set to zero from the surface toa depthbetween 20and 40 km, depending onthe type of lithosphere(oldor young) being modeled. Onthe bottom boundarywe impose zero vertical velocity and radial free slip (U z = 0 = c)Ur/oaz); while alongthe axisof symmetryand the right side of the box, we impose zero radial velocity and verticalfree slip(U r = 0 = •Uz/oar). In the initial temperatureconfiguration the mantle has a uniformpotential temperature Tm=1280øC, all boundariesare insulatedexcept the top surface,which is assigneda constant temperatureT•u=0øC. The initial temperatureprofile for the oceaniclithosphere is given by an error functionconduction profile correspondingto the appropriateage. The spherical thermal diapir, initially centered at 2000 km depth, is 2600 characterizedby an initial excesspotential temperature with respectto the mantle, AT0, and by its radius, R0. To avoid 0 780 1560 high-temperaturegradients between the boundaryof the thermal diapir and the surroundingmantle, we impose a Distancefrom axis (km) "thermal halo", 130 l•m thick, in which the temperature Figure 2. The standard finite element grid (70x120 decreases as a sine function with distance from the surface of elements).The left side is the axis of symmetry.The radiusof the diapir. A "thermal halo" would develop anyway by the cylinder is 1560 km, and the depth is 2600 km. Note the diffusion,but by imposingit we avoid numericalinstabilities higherresolution from the surfaceto 200 km depth. FARNETANI AND RICHARDS: FLOOD BASALT MODELS 13.817

where•l is the viscosityand p is the dynamicpressure given P=(T• - 1100)/136+4.968x10-4exp(1.2 x10-2(T•- 1100))(8) by while the liquidustemperature (in degreeCelsius) is given by p = -•,v ßu (6) T/=1736.2 + 4.343P + 180tan-I (P/2.2169). (9) where)• =107 is thepenalty parameter. For eachelement we calculatethe nondimensionalaverage The melt fraction X is expressed through a dimensionless valueof •zz which is assignedto the centerof massof each temperatureT' : element.Values of •zz have also been checkedagainst analyticalsolutions calculated with the propagatormatrix T' =Tr - (T/+ T•)/2 (10) technique.Theerror œ=(•zzC-•zzn)x100/•zzn, where•zzC is the finite elementvalue and •zzn is the correspondingby requiringthat X=0 whenT r = T• andX=I when Tr = T/. The analyticalvalue, is e <0.1%on a 66x66grid. The element melt fraction at the center of each element is calculatedusing valuesare projectedto the nodesusing a modifiedversion of the empirical expression the pressure-smoothingtechnique [Hughes et el., 1979]. We dimensionalize•zz by multiplyingit by pgdab•/Ra and X- 0.5= T' +(T '2 - 0.25)(a+t,T') (11) calculatethe surfacetopographic uplift 6h: with the coefficients a=0.4256 and b=2.988. We also account 6h=(•zz -•zz) (7) for the changein temperaturedue to the latent heat of melting. At constant pressure the change in temperature dT due to a where •zz is the area-averagedvalue of the verticalnormal change in melt fraction dX is stressat the surfaceand psuis the effectivedensity contrast at theupper surface. For continentallithosphere, p• equalsthe dT = AHx dX/Cp (12) mantle density ,Om (both crust and mantle material are uplifted),while for oceaniclithosphere, p• = ,om -,Ow, where for a reversible process the latent heat of melting AH is Pw is thedensity of seawater(Pw=1000 kg m-3). AH = AS X Tr; thus

Calculationsof melt volumeand composition As the head of the thermal diapir spreadsbeneath the dT=ASXTrXdX/Cv ß (13) lithosphere,we estimatethe total melt volumeproduced and its composition.We usea batchmelting model, thus assuming We assumethat meltingoccurs at constantentropy of fusion that the liquid remainsin chemicalequilibrium with the solid (AS=250 J kg-1 øK-l,as in McKenzieand Bickle's[1988] residueuntil mechanicalconditions allow it to escapeas a parameterization) and calculate the relation between melt single "batch"of primary magma.The requirementthat no fraction,temperature, and pressureusing the equationsin relative movement occurs between the melt and the matrix is AppendixD of McKenzie[ 1984],where a fourth-orderRunge- probably unrealistic whenever the melt fraction exceeds 1 or Kuttascheme is usedto integratethe expressions relating X, T, 2% [McKenzie, 1984], and this will affect the total melt P at constantAS. The valuesof the real temperature,modified volumeand its composition[McKenzie and Bickle, 1988]. We by the latent heat of melting, are then convertedback to do not attempt to model melt extractionand its effect on the dimensionlesspotential temperatures and usedin the diffusion dynamicsof the plumehead and of the lithosphere,nor do we (conduction)term of the energy equationfor the next time includedirectly the effectof melt buoyancy.Though it would step. be desirableto usea morerealistic model for partialmelting of The melt fraction by weight X is related to the volume a complexmineral assemblage, such as Rayleighmelting, the fractionof melt q through parameterizationavailable is basedon laboratoryexperiments which involve batch melting. In this study we implement the parametrizationby pf+X(p, -pf) (14) McKenzieand Bickle [1988] of batchmelting experiments on andwe assumethat the density of thesolid Ps andthe density garnet peridotite. We calculate the melt fraction and its of the melt pf are equal.The total melt volumeis then compositionat each time step for depthsshallower than 220 obtainedby integrationof the volumefraction of melt of each km (i.e., from 0 to -7 GPa, whichcorrespond to the pressure elementover the entiremelting region. We calculatethe point rangeof McKenzie and Bickle's [1988] parameterization).As averagecomposition of the melt in termsof the majorelement discussedbelow, this does not seemto be a limitation, since oxides using the McKenzie and Bickle [1988] meltingnever occurs deeper than 150 km (i.e., -5 GPa)in any parameterization.The values obtainedare probablyonly of our modelcases. We first convertthe dimensionalpotential indicative, since the method has some limitations when temperaturesTp to realtemperatures Tr assumingan adiabatic meltingoccurs at highpressure [Watson and McKenzie,1991]. gradientandusing Tv = T r xexp(-go•/Cv) , whe.re z is the dimensionaldepth. The numerical value of Cv is givenin The Model Table 1. We calculate the lithostatic pressure P (in gigapascals)using the Preliminary ReferenceEarth Model Thermal Diapir (PREM) [Dziewonski and Anderson, 1981]. The solidus We assume that mantle plumes originate from a hot temperature(in degree Celsius) is obtained by numerical boundarylayer in the mantle, possiblythe core-mantle solution of boundary(CMB). Laboratoryexperiments [Whitehead and 13,818 FARNETANI AND RICHARDS' FLOOD BASALT MODELS

Luther, 1975; Campbell and Griffiths, 1990] show that a r/(T)= r/0exp(-4.60T) (15) newly formed thermal plume develops a large "head" and a "tail". The head forms since a large amount of buoyancy is which gives two orders of magnitudeviscosity contrast across needed before the plume is able to displace the overlying the lithosphere. colder fluid and rise. The "tail" of thermal plumes is maintained by continued buoyancy flux from the bottom Lithosphere boundary.This tail is a somewhatarbitrary feature of the fluid The lithosphere is modeled by imposing an initial dynamical experiments, since a constant buoyancy flux is temperatureprofile and a viscosity structure(note that we imposed. Natural boundary layer instabilities arising in free concentrate on oceanic lithosphere for the reasons stated in convection may or may not be continuously fed from the the introduction). The initial temperatureprofile is given by boundary layer, depending on the particular conditions. an error function conduction profile [Parson and $clater, In the mantle plume initiation model, flood basalts are 1977] accordingto the initial age. We investigateinitial ages generatedby melting of the head of the plume [Morgan, 1981; 0 Ma, 20 Ma, and 100 Ma. For nontemperaturedependent Richards et al., 1989; Campbell and Griffiths, 1990], and in viscositycases, the viscosityof the lithosphereis 1022Pa s this first phasethe contributionof the material rising through from the surfaceto 55 km depth (for 100 Ma old lithosphere), the tail is of secondaryimportance. Given the uncertaintiesin or to 41 km depth (for 20 Ma and 0 Ma lithosphere).The the details of how thermal instabilities would form at the viscosity decreasessmoothly below these depths to upper CMB, we simply consider a hot, spherical diapir placed mantle viscosityvalues (Figure 3). For a given initial age the initially at 2000 km depth, which is not connected to any viscosity structureof the uppermost80 km is kept constant, boundary layer. By doing this we avoid numerical modeling independent of the values of the upper mantle viscosity difficulties in resolving the tail, especially for the very thin (except for caseswith temperaturedependent viscosity). We conduits that would result in cases with strongly temperature note that these lithospheric viscositiesare rather modest, so dependent viscosity. The buoyancy of the thermal diapir is that we are generally modeling "best case" scenarios for proportional to the excess temperaturewith respect to the melting due to the rise of hot plume material into the lower mantle and to the cube of its radius. We investigatea range of lithosphere. initial radii 300 < Ro <500 km and initial excesstemperatures 300< ATo <400øC. The initial excess temperatureATo i s expected to be higher than the excess temperature (AT) estimated from petrologic constraints.The excesstemperature ViscosityModels that best fits the Hawaii hotspot swell is 200-300øC [Sleep, 1990], in agreementwith a plume temperatureof ~1500øCfor magma generationbeneath Hawaii [Wyllie, 1988]. The range 200 of initial radius values we model is consistent with values estimated from laboratory experiments [Campbell and Griffiths, 1990] scaled to mantle conditions. 600 Mantle Viscosity Structure Laboratory experiments have investigated the rise of a plume in a uniform viscosityfluid, but numericalmodeling can 1000 address the effect of more realistic viscosity structures. Geophysical studies indicate that mantle viscosity may increasefrom the upper to the lower mantle by 1 or 2 ordersof magnitude [e.g., Hager, 1984; Nakada and Lambeck, 1990]. 1400 - Viscosity may change discontinuouslyat depth where phase changesoccur, and it might vary continuouslywith depth due to the effects of pressureon the rheology of mantle materials. We consider several viscosity structures and some 1800 - temperaturedependent viscosity cases. (We do not attemptto model other thermodynamicaleffects of phase changes.)In this studythe values of the lower mantle viscosity(r/ira) range 2200 - from 3x1022to 3x1021Pa s, andfor the uppermantle viscosity

(r/urn)values range from 3x1021 to 3x1019Pa s. Thiscovers a - reasonablerange of mantle viscosities,though more extreme values are possible.The uniform mantle viscosity model has 2600 Ti=102• Pa s. Figure 3 showsthe viscosityprofiles for the 1019 1020 1021 1022 1023 "standard"model (rhm=l 0 22 Pa s) for viscositycontrasts of ¾=10 and ¾=100 (¾= •im/ Tam)' The change in viscosity LogViscosity (Pa s) between the lower and upper mantle is at 670 km depth. The stiff rheology of the lithosphereis modeledby an increasein Figure 3. Mantle viscosity profiles for the two standard uppermostmantle viscosity up to 1022 Pa s (seenext section). models:¾=10 (thin line) and ¾=100(thick line). ¾=film/rlum is For temperaturedependent viscosity we adopt the following the ratio of lower mantle viscosity (film) and upper mantle exponential dependence: viscosity (flure). FARNETANI AND RICHARDS- FLOOD BASALT MODELS 13,819

We also investigate the effects of lithosphericextension. If region(for melt fractionX>0%) is indicatedin Figure4d by the extensionis allowed, we simply use a free radial slip boundary white area beneath the lithosphere. The maximum melt condition at the top surface nodes of the finite element grid. production occurs after 45 m.y. and the total melt volume This allows extension to occur naturally since all internal producedis 3.7x106km 3. At thistime the radiusof the plume nodes are unconstrained.For the majority of cases in which head is -700 km and the radius of the melting region for melt extensionis not allowed, we impose zero radial velocity from fraction X>5% is -580 km. Melting occursat sublithospheric the surfaceto 40 km depth for an initial age of 100 Ma, or to depths (100-150 km) since not enough time has elapsedfor 28 km depth for 20 Ma lithosphere.It is important to note conductiveheating the lithosphereabove the solidus. that the axisymmetry of our calculations requires that any Figure 5 shows the time evolution of the initial diapir horizontal extension be radial, so that we cannot generate (Figure 5a) if the upper mantle viscosity is reduced to more realistic models with unidirectional extension (rifting) rlum=l020 Pa s (y=100)in the standardmodel. After 20 m.y. of the lithosphere. (Figure 5b) the head of the diapir is at 670 km depth. As it entersthe upper mantle, a narrow conduitdevelops (with radius Results -100 km) through which the hot material ascendsat higher velocity, so that after only 24 m.y. (Figure 5c) the plume head The numerical model described above allows us to is at-180 km depth.The narrowingeffect reducesthe radiusof investigatethe evolution of a thermal diapir as it rises in the the plume head impinging on the lithosphere to -150 km. mantle and impinges on oceanic lithosphere.We calculate the Melting starts after 24 m.y. and reaches a maximum after 33 temporaland spatial variationsof the surfaceuplift, the radial m.y. (Figure 5d), the total melt volume producedis 2.6x106 deviatoric (extensional) stressinduced in the lithosphere, and km3. The radiusof the plumehead at this time is -620 km, the total melt volume. The model parameters vary about a while the radiusof the melting region, for melt fractionX>5%, "standard" case in which the thermal diapir has an initial is -360 km. The "narrowing" of the plume head is a excess potential temperature AT0=350øC, an initial radius consequenceof the velocity increaseof the buoyantfluid when Ro=400 km, the lower and upper mantle viscosities are it entersa lower-viscositymaterial [e.g., see Richards et al., r//m=1022Pa s and r/um=1021Pas, respectively(y=10), the 1988]. The above figuresillustrate that the viscositystructure lithosphereis nonrifting and its initial age is 100 Ma. Figure of the mantle affectsthe dynamicsof a rising plume and that 2 4 shows the time evolution of the thermal diapir for this orders of magnitude viscosity contrastbetween the lower and standardmodel, starting from the initial condition (Figure 4a). upper mantle causes pronounced "necking". This ultimately After 20 m.y. (Figure 4b) the head of the diapir is at 670 km influencesthe shapeand size of the plume head and the radial depth, while after 30 m.y. (Figure 4c) the plume head is at 180 extent of the melting zone. km depth. Just prior to sublithosphericspreading the plume For comparison, Figure 6 shows the evolution of the radius is -350 km. Melting startsat 34 m.y. and increasesas standarddiapir (AT0 and Ro as above) rising in a uniform the plume head spreadsbeneath the lithosphere.The melting viscositymantle (Tl=1021 Pa s). No neckingoccurs, and the

Initial condition After30 m.y. After45 m.y. After20 m.y. b c d ...... t.•....•:.:.:.•.•'•...•..•: ..•.•.%:...... :::.z::•:.• :•?-•;•.• :a. ,;::.•:•.•..:: .•:,:.:...,.•;•.,;.•;•4....,,.. 26O :.

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... 2600 260 520 780 1560 0 260 520 780 1560 0 260 520 780 1560 0 260 520 780 1560 Distancefrom axis (kin) Distancefrom axis (km) Distancefrom axis (kin) Distancefrom axis (kin)

1024 i:•?:::::;•:.•..:L.%.•..:: .': .... :: 1632 PotentialTemperature (C)

Figure 4. The evolutionof the diapirwith initial excesstemperature ATo=350øC and initial radiusR o =400 km. The mantlehas a potentialtemperature Tm=1280øC and the mantleviscosity model is r//m=1022Pa S,r/um=1021Pa s (¾=10).(a) The initialcondition. (b) After20 m.y.(c) After 30 m.y. (d) After45 m.y. The meltingregion is the white areabeneath the lithosphere.To showthe temperaturestructure of the diapir more clearly, the minimum potentialtemperature in the gray scaleis 1024øC.This meansthe lithosphere(where T<1024øC) is depictedin white. 13,820 FARNETANI AND RICHARDS: FLOOD BASALT MODELS

InitialCondition a After20 m.y. b After24 m.y. c After33 m.y. d

...... -...... •,•...... ?.. .•...... •...... -+:::--.-:-*------•-...... • 260

520

780

1040

1300

1560

1820

2080

2340

2600 0 260 520 780 1560 0 260 520 780 1560 0 260 520 780 1560 0 260 520 780 1560 Distancefrom axis (km) Distancefrom axis (kin) Distancefrom axis (kin) Distancefrom axis (kin)

1024 ...... •i; 1632 PotentialTemperature (C) Figure 5. The evolutionof the diapir with initial excesstemperature AT0=350øC and initial radius R0=400 km. The mantleviscosity model is rhm=1022 Pa s, •lum= 1020 Pa s (y=100). (a) The initialcondition. (b) After 20 m.y. (c) After 24 m.y. Note the narrowingof the plume head ("necking"effect). (d) After 33 m.y. The melting region is the white area beneaththe lithosphere.

diapir maintains a spherical shape as it ascendsthrough the hand, a uniform viscosity mantle is an unlikely model for the mantle (Figures 6a and 6b). When the plume head reachesthe Earth, and we concentrateon cases with a viscosity contrast lithosphere,its radius is --600 km (Figure 6c) and most of the betweenupper and lower mantle. buoyant material is contained in the head. Melting occurs at Figures7a and 7b show surfaceuplift (calculatedon the axis sublithosphericdepths while the head spreadslaterally to a of symmetry), melt volume, and radial deviatoric stress Crrr radial distance of--780 km (Figure 6d) and the total melt (calculated on the axis of symmetry, at 80 km depth) as a volumeproduced is 3.5x106km 3. The evolutionof the diapir function of time. For the standardcase with ¾=10 (Figure 7a), in this case closely resembles that suggestedby laboratory surfaceuplift occurswhile the thermal diapir rises throughthe experiments [Griffiths and Campbell, 1990]. On the other mantle, and the uplift peak occurswhen the plume head reaches

InitialCondition After2 m.y. a b After8 m.y. c After16 m.y. d

ß ...... 7'.'77'...... 'W...%'7'7.772"7 •;'•..."•".;•: ..... 7•.777" .';;:•";.;?....-!'*- r"X.%.-:-*-• ...... ':..• ':...... '":' "•'-....•,,..".*.."'• ...... y"•7...... ;7 260

520

780

1040

1300

1560

1820

2080

2340

2600 260 520 780 1560 0 260 520 780 1560 0 260 520 780 1560 0 260 520 780 1560 Distancefrom axis (km) Distancefrom axis (km) Distancefrom axis (km) Distancefrom axis (km)

1024 ...... •'•;i'- ...... 1632 PotentialTemperature (C)

Figure 6. The evolutionof the diapir with initial excesstemperature ATo=350øC and initial radius Ro=400 km. The mantlehas a uniformviscosity ,1=102• Pa s. (a) Theinitial condition. (b) After2 m.y.(c) After8 m.y. (d) After 16 m.y. The melting region is the white area beneaththe lithosphere. FARNETANI AND RICHARDS. FLOOD BASALT MODELS 13,821

4.0 (a) •lmJ]•um ---- 10 4.0 [1.90] Initial Lithospheric Age: 100 Ma

14 3.0

3.0 [1.43]

lO; 2.0 2.0 [0.95] •Melt,Volume•

ß ß ß 1.0 1.0 [0.47]

2 ' •Stress

# I # I I 0.0

4.0 (b) •11JT•um-' 100 4.0 [1.90] Initial Lithospheric Age: 100 Ma

14 - 3.0

3.0 [1.43]

10 • ß - 2.0 2.0 [0.95] = el Volurn

6 ß m•mmmm mmmmm - 1.0 1.0 [0.47] t t ..... Str••

2 t

I I 0.0 15 20 25 30 35 40 45 Time (m.y.)

Figure7. Uplift,radial deviatoric stress ((•rr) and melt volume versus elapsed time. (a) Formantle viscosity contrast¾=10. (b) For ¾=100.In bothcases, ATo=350øC and Ro=400km. Note that the unbracketedand bracketednumbers on theuplift scale refer to maximumand minimum values, respectively. Maximum values are for the uplift from abyssaloceanic depths with a thermalexpansion coefficient of 3x10-5 øC -1. Minimum valuesare for subaerialuplift with a thermalexpansion coefficient of 2x10-5 øC -1. the base of the lithosphere.Subsidence of the central area plume head rises throughthe upper mantle,while during followsand accompaniesthe sublithosphericspreading of the sublithosphericspreading O'rr decreases. Note thatthe curves head and melt production,as pointedout by Griffiths and in Figures 7a and 7b terminate when the maximum melt Campbell[1991]. The peakof uplift precedesthe peakof melt volumeis reached,and the extractionof melt (whichwe do not volume by -10 m.y., so that subsidenceof the central area model) would certainly affect both the uplift and the melt occursduring the phaseof maximumexpected volcanism. The volume. radialdeviatoric (extensional) stress O'rr is in phasewith the Comparisonof Figures7a and7b showsthat for a higher- uplift and the maximum extensional stress occurs when the viscositycontrast (i.e., ¾=100)both peaksin uplift and melt plume head approachesthe lithosphere.During the major volume occur earlier in time, which is consistentwith the fact melting phase, O'rrgradually decreases. Figure 7b showsthe that the head ascendsmore rapidly in the uppermantle. The time relation amonguplift, melt volume,and radial deviatoric maximumamount of uplift decreasesand the total melt volume stressO'rr for the standardcase with ¾=100.The surfaceuplift is reducedmodestly, probably due to the narrowingof the increaseswhile the diapirrises through the mantle,while slow plume head. Reducingthe upper mantle viscosityserves subsidenceoccurs during the sublithosphericspreading of the mainly to compressthe time scale for these events and, to a head.The peakof uplift precedesthe peakof melt production lesser degree, the horizontal length scale of the plume by -4 m.y. The deviatoricstress O'rr reaches a maximumas the activity. We also see that, independentof the viscosity 13,822 FARNETANI AND RICHARDS: FLOOD BASALT MODELS structure, the peak of uplift precedes the peak of melt lithosphere. Consequently, the onset of thermal subsidence production,so that the model predictsa regulartime sequence does not occur simultaneouslyover the whole swell. Figure 8 of uplift, thermal subsidence,and volcanic activity. also shows the radial extent of the melting region for melt Figure 8 shows surfaceuplift as a function of radial distance fractionsX>5% and X>10%. The extent of the melting region from the axis, at different time stepsand for the standardcase reflects the progressivespreading of the plume head, and it is (T=10). Note that the constraintsof conservationof massand probably safe to assume that areas where X>_5% will incompressibility cause negative values of uplift at the correspondto areasof surfacevolcanism. extreme right of the cylinder. While the diapir rises through The temporalrelation betweenthe surfaceuplift and melting the lower and upper mantle, the surfaceis affectedby a broad, will clearly differ with distancefrom the plume axis. Figure 9 low-amplitude swell (see curves at elapsed time 22 and 26 shows uplift histories at radial distances0, 250, and 500 km m.y.). The central uplift increasesconsiderably as the plume from the axis. The maximum uplift at 250 km distance is head approachesthe lithosphere(26 to 34 m.y.) and affects an reducedto -80%, comparedto the axis, but the timing for the area -400 km in radius. After 34 m.y., subsidencestarts on the uplift peak and the onsetof subsidenceare comparable,so that axis, but at greater distances,uplift may continue for several we can infer that a fairly regular time sequenceof uplift, onset million years, as the plume head spreads beneath the of subsidenceand volcanism should be expectedin a central

I InitialLithospheric Age:100Ma Tlld]]um" 10 ß (Uplift) .... X>10% .• / f•Radial extent of the• -- -- X>5% • meltingregion .J _•...... • ••.._ , 45m.y.

42 m.y.

38 m.y.

2.0 34 m.y. o.o

22 m.y.

i i i i i 0 260 520 780 1040 1300 1560 Distance from axis (km)

Figure 8. Surface uplift versusaxial distanceat different elapsedtimes. The radial extent of the melting regionfor melt fractionX>5% (long dashedline) and X>10% (shortdashed line) is indicated.The initial diapir has ATo=350øCand Ro =400 km andthe mantleviscosity contrast is ¾=10.The verticalexaggeration is 50:1. FARNETANI AND RICHARDS: FLOOD BASALT MODELS 13,823

TIiJTlum-- 10 4.0 [1.90] Initial Lithospheric Age: 100 Ma

3.0 [1.43]

2.0 [0.95] mmmmmmmmmmmmmm m•m m•m

1.0 [0.47] (r=5•0)

15 20 25 30 35 40 45 Time (m.y.) Figure 9. Uplift versuselapsed time calculatedat radial distancefrom the axis r-0, 250, and 500 km. The initial diapir has ATo=350øCand Ro=400km, and the mantleviscosity contrast is T=10. Note that the unbracketedand bracketed numbers on theuplift scale refer to maximumand minimum values, respectively. Maximumvalues are for the uplift from abyssaloceanic depths and with a thermalexpansion coefficient of 3x10-5 øC -•. Minimumvalues are for subaerialuplift with a thermalexpansion coefficient of 2x10-5 øC -•. area-300-350 km in radius.At a distanceof 500 km theuplift Figure 10 comparesthe uplift and meltinghistory for three occursonly in the latest stages,after the plume head has mantle viscosity models. The lower mantle viscosity is spreadbeneath the lithosphere,and thus the volcanicactivity r/lm=3X102•Pa s (for modelA), rhm=102•Pa s (for modelB), may be synchronouswith the uplift phase. andrhm=3X10 TMPa s (for modelC), the correspondingupper

5.0 Melt Volume Uplift 5.0 [2.37] 4.0

3.0

3.0 [1.43]

2.0

1.0 1.0 [0.47]

0.0

0 20 40 60 80 100 120 Time (m.y.)

Figure10. Uplift(solid line) and melt volume (dashed line) history for viscositymodel A, r//m=3X102•Pa s, r/um=3X102øPas; viscositymodel B, r//m=1022 Pa s, r/um=1021Pas; viscosity model C,r//m=3X10 22Pa s, r/um=3X102•Pa s. Forall modelsthe initial diapir has ATo=350øC, Ro=400 km andthe initialage of the lithosphereis 100Ma. Notethat the unbracketed and bracketed numbers on theuplift scale refer to maximum andminimum values, respectively. Maximum values are for theuplift from abyssal oceanic depths and with a thermalexpansion coefficient of 3x10-5 øC -•. Minimumvalues are for subaerialuplift with a thermalexpansion coefficient of 2x10 '5 øC-•. 13,824 FARNETANI AND RICHARDS' FLOOD BASALT MODELS

Viscositymodel A ) (a) (d)

50 Temperature profile of the lithosphere at 115 rn.y. • lOO Initial temperature profile r--0 .. of the lithosphere , •* ...... •....r•0 150 I • <•..r=600 '"G Error function conduction ',I r=606 profile at age 115 Ma I I I I I 200 0 Viscositymodel B ) (b) Temperature profile of the lithosphere at 145 m.y. 50

r=0 • 100

r=600

Error function conduction •).,r=600 150 profileat age145 Ma -•

200 0 Viscositymodel C ) (c) (f) Temperature profile of the lithosphere at 210 m.y. 50

• 100 r=0

m•mmmmmQ ! r=600 .¸ Error function conduction 150 .67" profile at age 210 Ma

200 I I • 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 5 10 15 20 Dimensionless Potential Temperature Melt fraction (wt%) Figure11. (left)Dimensionless potential temperature versus depth. The solid line is theerror function conductionprofile calculated at thetime of maximummelt production. The temperature profile of the lithosphereis indicated at radial distance r=0 km from the axis (solid line with circles) and r=-600 km (solid linewith diamonds). Note that each symbol corresponds to a nodein thefinite element grid. The dashed line in Figure1 l a is theinitial temperature profile for a 100Ma oldlithosphere imposed as initial condition in all models.(a) For viscosity model A, r//m=3X1021Pas, r/um=3X102ø Pa•s.(b) For viscosity model B, r//m=10:: Pa S,?•um----1021Pa s.(c) For viscosity model C, r//m=3X10• Pa s, r/um=3X1021Pa s.(fight) Distribution ofthe melt fractionwith depth at radialdistance r=0 and r=-600 km. (d) For viscosity model A. (e)For viscosity model B. (f) Forviscosity model C. In all themodels the initial diapir has AT0=350øC, R0=400 km. FARNETANI AND RICHARDS-FLOOD BASALT MODELS 13,s25 mantle viscosities satisfy ¾=10. For all models the initial sublithosphericmantle facilitates the radial spreadingof the dinpithas AT0=350øCand R0=400km, the initial age of the plumehead. By contrastfor viscositymodel C (Figure1 l c) the lithosphere is 100 Ma and extension is not allowed. The temperaturesfrom 20 to 100 km depth, can be 20 to 70% viscosityof the mantlegoverns the ascentrate of the diapir. higher than the expectedvalues, at radial distancesr=0 km. In For the two extreme viscositymodels considered (i.e., A and thiscase the plumehead tends to pondbeneath the lithosphere C), the diapirrise timesdiffer by an orderof magnitude(10 sinceits radialspreading is inhibitedby the highviscosity of m.y. versus100 m.y.). Higher valuesof the mantleviscosity the upper mantle. This also explainsthe modestincrease in increasethe lag time betweenpeak uplift andmagmatism and temperatureat distancer=600 km, comparedto the profile at increasethe maximumuplift. The total melt volumeis instead r=0 km. However, we note that melting always occursat reduced(-30%), sincethe progressiveaging and coolingof sublithosphericdepths (i.e., deeper than-100 km), as the lithospheretend to inhibit melting.Figures 1 l a, 1lb, and indicatedin Figures11d, 11e,and 11f, wherewe plotthe melt 1l c showthe temperatureprofile of the lithospherefor the fraction versusdepth for the viscositymodels A, B, and C, viscositymodels A, B, and C, respectively.The profilesare respectively.We alsofind thatover the whole range of mantle given at radial distances r=0 and r=600 km from the axis of viscositystructures investigated the variationin melt volume symmetry and are calculated at the time of maximum melt is very modest(from 2 to 4x106 km3), probably because production.The temperaturedifference between these profiles thermalrejuvenation counterbalances the progressiveaging of and the theoretical error function profile, calculated at the the lithosphere. same age, indicatesthe amountof "thermalrejuvenation" of For a few models we have considered the effect of the lithosphere. For viscosity model A (Figure l 1a) the temperaturedependent viscosity. As discussedpreviously, we temperaturesare higher than the expected(-20-30%) only use the law r/(T)=r/0exp(-n.60T). The viscositycontrast from 60 km depth to the base of the lithosphere(-100 km acrossthe lithosphereis 2 orders of magnitude,while the depth), thus suggesting that the lithosphere is not diapirviscosity is 3.5 timesless than that of the surrounding significantlyheated by conduction.The profile at r=-600km is material(for an initial excesstemperature of 350øC).Figure 12 similar to the one on the axis, sincethe low viscosityof the shows the uplift and melting history for a temperature

5.0 Temperature dependent viscosity (a) 4.0 [1.90] Initial LithosphericAge: 20 Ma 4.0

3.0 [1.4:3] :3.0

:•.0 [0.9S] 2.0 (Melt.Volume) 1.0 [0.47] 1.0

I I i 0.0

10.0 Standardviscosity model (b) 4.0 [1.90] InitialLithospheric Age:20 Ma • ß,, ß' 8.0

3.0 [1.43] 6.0

2.0 [0.95]

(Melt_ Volume) 4.0•'"

i 1.0 [0.47] - i 20 i I - i ß

I I I .• • 0.0 15 20 25 30 35 40 45 Time (m.y.) Figure12. Upliftand melt volume versus elapsed time. (a) Forthe temperature dependent viscosity case. (b) For the standardviscosity model. In bothcases, AT0=350øC and R0 =400 km. Notethat the unbracketedand bracketednumbers on the uplift scalerefer to maximumand minimum values, respectively. Maximum values are for the uplift from abyssaloceanic depths and with a thermalexpansion coefficient of 3x10-5 øC-1. Minimumvalues are for subaerialuplift with a thermalexpansion coefficient of 2x10'5 øC-1. 13,826 FARNETANI AND RICHARDS' FLOOD BASALT MODELS dependent viscosity case (Figure 12a) and for the standard is intersectedare functions of the excess temperatureof the viscosity model (Figure 12b). In both cases the initial diapir. The melt volume also increaseswith increasingR0; lithospheric age is 20 Ma and lithospheric extension above this result is fairly intuitive, but we also find that the melt 30 km depth is prevented by setting the radial velocity to volumesproduced for R0=500 km at AT0-300-330øC are zero. For the case with temperaturedependent viscosity, both relatively low. We find that the curvatureof the upper part of uplift and melt productionpeak earlier in time, since the low- the plume head first impinging on the lithospheredecreases viscosity thermal diapir rises more rapidly in the mantle. with increasing R0. A large flat head does not seem to Because of the stiffer behavior of the lithosphere, melting efficiently remove, by lateral flow, the thin layer of material occurs at greater depth, and thus the total melt volume trapped between the stiff lithosphereand the plume head. The producedis reducedto -4x106 km3 (for the standardmodel the behavior of this "squeeze layer" [Griffiths and Campbell, melt volumeis -9x106 km3).This suggeststhat the standard 1991] and its ability to drain horizontally affect the depth to lithosphericstructure is fairly weak and thus representsa "best which the plume head ascendsand melts and may explain the case" scenario for the rise of the plume head to shallower relative low melt volumes obtained for R0=500 km at depths. We have found that temperaturedependent viscosity AT0-300-330øC. For AT0>330øC this effect becomesless has only modest (and quite predictable) effects upon the relevant, probably because the conductive heat transport sublithosphericfluid dynamics of our model. Little heat is between the plume head and the lithosphereis more efficient conductedinto the upper lithosphereand crust, so that, within due to the higher-temperaturegradients. (We checkedthat this the model we have specified, little softening of the effect is not a function of the width of the finite element lithosphereoccurs prior to melting. Of course,heat transferby domain by increasing the radius of the domain to 2300 km masstransfer (melt migration) may be important,but we have while maintainingthe sameelement size.) not attemptedto model that effect. Still, we are confidentthat The next set of models addresses the effect of the initial the most important factor is whether or not the uppermost lithospheric age on the total melt volume. Figure 14 shows lithosphereextends freely, and a more sophisticatedtreatment the melt volume as a function of the initial excesstemperature is neededto addressthis issuefully. (300<_AT0 <_400øC)for initial lithospheric ages of 20 and We next investigate the effect of the initial diapir size and 100 Ma. In these models, lithosphericextension is prevented, the excess temperature. Figure 13 shows the maximum melt andwe use R 0 =400 km, Illm = 1022 Pa s and tlum=1021 Pa s. For volume as a function of the initial excess temperature the case of a young oceaniclithosphere, the total melt volume (300 <-AT o <-400øC) and initial radius (300 <- R0 <-500 km), producedranges between 1 and 17x106km 3, whilefor an old for a modelwith •/tm=1022 Pa s and•/um=10 21 Pa s (y=10)and a lithospherethe melt volumes are reducedapproximately by a nonrifting lithospherewith initial age of 20 Ma. For an initial factor of 2 over the temperaturerange investigated.We also excesstemperature of 300øC, independentof the initial radius show the effect of varying the entropy of fusion from the of the diapir, the melt volume generatedis equal or less than usuallyadopted value of 250 J kg-1 øK-1 (solid line), to 400 J 106km 3. Given sucha low value,compared with the estimates kg-1 øK-1 (dashed line). The melt volumeis reducedby -30% for large flood basalts and oceanic plateaus, we consider over the whole temperaturerange investigated.McKenzie and AT0=300øCas a lower boundfor the initial excesstemperature Bickle[1988] suggest that if AS=400J kg-• øK-1is usedin the of the diapir (for nonrifting lithosphere). The melt volume melting model, then the required potential temperatureof the strongly depends on AT0, since both the melt fraction mantle (Tm) is 1300øC, rather than 1280øC. The solid producedat a given depth and the pressureat which the solidus symbolsin Figure 14 are for two test cases,with AS=400 J kg-

32.0 Initial Lithospheric age: 20 Ma qldqum= 10

24.0 oø R =500 oø 0 -

6.o o•OO•øø

8.0 -

0.0 300 320 340 360 380 400 Initial Excess Temperature (øC) Figure 13. Totalmelt volume versus initial excess temperature for initialdiapir radius R0=300 km (long dashedline), R0 =400 km (solidline), R0=500km (shortdashed line). FARNETANI AND RICHARDS' FLOOD BASALT MODELS 13,827

Initial Diapir Radius = 400 km 16.0 111dqum= 10

12.0 - 20 Ma aS=401} - L -- • 8.0- 0 - o :• 4.0 - 100Ma_

300 320 340 360 380 400 Initial Excess Temperature (øC) Figure 14. Total melt volumeversus the initial excesstemperature for initial lithosphericage of 100 Ma (lineswith opencircles) and 20 Ma (lineswith opentriangles). The entropyof fusionused in the melting modelis •S=250 J kg-• øK-•(solid lines) and •S=400 J kg-• øK-• (dashedlines). In all casesthe potential temperatureof the m•tle is T• =1280øC.The two solidsymbols are calculatedusing •S=400 J kg-• øK-• and

•øK'• and Tm=1300øC,and indeedthe melt volumesare -28xl 06 km3, whileif extensionis preventedthe melt volume comparablewith the ones of the standardmodel. producedis negligibly small (0.03x106km3). However, the The case of initially zero age lithosphere is treated axisymmetric geometry is not entirely appropriate to separately,since we also changethe top boundarycondition modeling unidirectional extension (rifting) over a mantle to radial free slip, thus allowing the lithosphereto extend. plume, and thus the calculated melt volumes should be This hasa majoreffect on the melt volumes,which increase by consideredas upper bounds,approximating the scenarioof a an orderof magnitude(i.e., -50x106km 3, for AT0=350øCand plume head impinging on a ridge-ridge-ridgetriple junction. R0=400 km) as melting occursat shallowdepths (20-100 km) Figure 15 illustratesthe uplift and melt volume calculated with melt fractionsas high as -30%. Table 2 showsthe melt when lithosphericextension is allowed. The uplift generated volumes,the depthof the meltingzone, and the meanMgO for rifting modelsappears to be very large, exceeding5 km in concentrationfor initial lithosphericages of 0, 20, and 100 some cases. However, this is somewhat an artifact of the Ma, if extensionis allowed. Melt volumesgenerated with referencelevel chosen.Calculated uplift is the total amplitude AT0=350øCare of order40-50x106 km 3, independentof the of surfacedeformation from the axis to the outsideedge of our initial age of the lithosphereand the viscositymodel. (The model domain, so "extra" uplift arises from lithospheric resultsare given for thestandard model with film= 1022Pa s and thinning above the plume and lithospheresinking at the outer r/um=1021Pa s, andfor a modelwith temperaturedependent edge. In other words, the uplift is effectively referencedto viscosity.) For a rifting case, even an initial excess abyssaldepths (typically 5-6 km) as opposedto normalridge temperatureas low as ATo=250øCcan producemelt volumesof depth, so that even a model uplift of the oceanfloor of 5 km

Table 2. Models with LithosphericExtension Allowed

AT0' Initial Extension Viscosity Melt Depth of Maximum Mean Age, Allowed Model Volume, Melting, Melt MgO, Fraction,

øC Ma x 106 km 3 km wt% wt%

25 0 2 0 n o standard 0.03 25 0 2 0 yes standard 28 20-100 ~30 15.5 35 0 2 0 n o standard 9 75-150 -22 18 35 0 2 0 yes standard 49 20-130 -34 18 350 20 yes rl(T) 41 20-100 -28 18 35 0 100 n o standard 4 100-150 -14 17.5 350 100 yes standard 45 20-130 -30 18 350 100 yes rl(T) 39 20-110 -30 17.5 35 0 0 yes standard 5O 20-130 -35 18.5 13,828 FARNETANI AND RICHARDS' FLOOD BASALT MODELS

7.0 [3.32] 60 Initial Lithospheric Age: 20 Ma Extensionallowed so

5.0 [2.37] 40 •

30 e•

3.0 [1.43]

2O

10 1.0 [0.47]

I I 15 20 25 30 35 40 45 50 55 Time (m.y.)

Figure 15. Uplift and melt volumeversus elapsed time if extensionallowed. The initial age of the lithosphereis 20 Ma, thediapir has ATo=350øC and Ro=400 km, the mantle viscosity model is rllm=1022Pas, 11um=1021Pas. Note that the unbracketed and bracketed numbers on theuplift scale refer to maximumand minimumvalues, respectively. Maximum values are for the uplift from abyssaloceanic depths and with a thermalexpansion coefficient of 3x10'5 øC'•. Minimum values are for subaerialuplift with a thermalexpansion coefficient of 2x10 -5 øC-•.

may not representuplift above sea level. Thus the "dynamic" etc., which are comparableto thoseobserved or inferredfrom componentof uplift due to the plume does not exceed that field studies. obtained in the nonrifting case. One issue we set out to address was the effect of mantle The batch melting model of McKenzie and Bickle [1988] viscositystructure on observableaspects of mantleplumes. allows us to estimate the average melt compositionsin each We have investigatedviscosity contrasts(7= rltrn/•um)from model. Though we calculatethe concentrationsof all the major lower to uppermantle of 1 (7=10) and 2 (7=100) ordersof oxides in the melt, we considerMgO concentrationto be the magnitude.A high-viscositycontrast induces a narrowingof most indicative concerningthe nature of the primary magma. the plumehead as it entersthe uppermantle. This "necking" The mean MgO concentration is obtained as a weighted occursbecause the rise velocity of the plume headincreases as average over the whole melting region. Figure 16 showsthe the viscosityof the surroundingmedium is decreased.The mean MgO concentration,evaluated at the time of maximum neckingof the plumehead causes a reductionof boththe radius melt production,as a function of the initial excesstemperature of the plumehead first impingingon the lithosphereand the of the diapir. The resultsare given for initial lithosphericages radial extent of the melting region. Moreover, for a model of 100 and 20 Ma, when the initial radius of the diapir is 400 with 7=100, a largevolume of the diapirremains in the lower km. The mean MgO concentrationranges between 16 and 19 mantle for 10-20 m.y., favoring the entrainmentof lower wt %, the higher values being obtained for higher initial mantlematerial, while uppermantle material seems to be less excesstemperatures and for younger lithosphericages. These easilyentrained given the limitedsurface extent of the narrow very high MgO concentrationsresult from the great depthand conduit. Thus the effect of thermal entrainment in this case the large degree of melting in all cases. Similar values for would differ in detail from the one suggestedby Griffiths and MgO are found also for the rifting models(see Table 2). Campbell[1990] for a uniformviscosity mantle. We have also attempted to constrain the initial excess Discussion temperatureof rising plume heads, treating the case of nonriftinglithosphere as the moststringent test. We find that We have investigatedthe rise of a thermal diapir in the for the McKenzie and Bickle [1988] batch melting model mantle and its interaction with the lithosphereprior to and employed,rising plume heads must be at least300øC hotter duringmelting, using a numericalmodel that combinesmantle than normal mantle in order to obtain melt volumesof ~lx106 flow dynamics with a batch melting model. Our numerical km 3 for models without lithosphericextension. This lower approachallows us to developmore fully somepredictions of boundon initial excesstemperatures is ~100øC higher than the mantle plume initiation model and to analyze the one estimatedfrom laboratoryexperiments [Griffiths and quantitatively their dependenceon the model parameters. Campbell,1990], whichdoes not accountfor the presenceof Hopefully, this will form a strongerbasis for comparisonwith the lithosphere.Furthermore, we find that a diapir with an field and analytical data. In this study we did not attempt to initial radius of 400 km needs to have an initial excess satisfy the specific characteristicsof any single flood basalt temperatureof 350øCin orderto generatemelt volumesof ~3- or oceanic plateau. Instead, we wanted to explore the 9x106 km3 if the lithosphereis older than 20 Ma and if conditionsunder which it is possibleto obtain melt volumes extensionis prevented.(Note that the results for initial and compositions,melt productionrates, degreesof uplift, lithosphericage of 100 Ma might be consideredas "upper FARNETANI AND RICHARDS: FLOOD BASALT MODELS 13,829

20.0 Initial Diapir Radius = 400 km T]ldT•um---- 10

19.0 2o 180

170

160

I I I I I I I I I I I

300 320 340 360 380 400 Initial Excess Temperature (øC)

Figure 16. Mean MgO concentrationof the melt versusthe initial excesstemperature of the diapir for modelswith initial lithosphericage of 100 and 20 Ma. bounds" for an ancient cratonic continental lithosphere, approximately doubles as the initial lithospheric age is whose thickness may, in fact, be considerablygreater than reduced from 100 to 20 Ma. that of old oceanic lithosphere.) At the onset of melting the The most importantincrease in melt volume (up to 1 order potential temperatureof the plume head is •-1600øC, although of magnitude)is obtainedfor the case in which lithospheric it decreasessomewhat in time due to the latent heat of melting. extension is allowed. However, given the geometry of our The melt volume generated from these hot plume heads model, the melt volumes obtained under radial free-slip greatly depends on the ability of the plume to ascend to boundary conditions represent upper bounds, possibly shallower depths, and decompressionmelting is an efficient obtainedwhen a mantle plume is in the proximity of a ridge way to produce large melt volumes. We found that for the triple junction. We suggestthat variationsin the degreeof modelswhere surfaceextension is not allowed, the depth range lithospheric extension may be reflected in the differences of partial melting is mostly (•-90%) sublithospheric, since between the melt volumes produced in continental flood there is not enough time to heat the lithosphereby conduction basalts and in oceanic plateaus. The melt volumes of abovethe solidusbefore the plume headhas spreadand cooled continental flood basalt provinces, though difficult to considerably.This conclusionis in agreementwith the work reconstructbecause of erosion,are of order 1-2x106km 3 (but of Arndt and Christensen [1992] on the role of lithospheric perhapsas high as 6-8x106 km3 if intrusiverocks are mantle in continental flood volcanism, which shows that the considered). Oceanic plateaus show a great variability, the bulk of primary magmasis producedby meltingof a plume at estimatedvolume for theKerguelen Plateau is 9-15x10• km3 (if sublithosphericdepths (>100 km). The geochemicalsignature BrokenRidge is included,the total volumeis •-15-24x10• of the volcanic productscan constrainthe depth of melting, km3), and the volume of the Ontong Java Plateau is •-30- and indeed,there is growing evidencethat someof the earliest 60x10• km3 [seeCoffin and Eldholm,1994]. We speculatethat magmasin flood basaltsrepresent low degreesof partial melt such volume variations could result entirely from differences formedin the garnetstability field. For the SiberianTraps this in the age and behavior of the lithosphere, rather than is indicated by the depletion of heavy rare earth elements, differences in plume characteristics.The Kerguelen Plateau combined with high incompatible element contents in the probablyformed in a new oceanbasin, in closeproximity to initial lava suites [Wooden et al., 1993]. Similarly, for the rifting continentallithosphere, just after the breakupbetween Kerguelen Plateau, trace element and isotopic characteristics Indo-Madagascarfrom Antarctica-Australia[e.g., Storeyet al., indicate that the onset of melting has to be placed in the 1992; Royer and Coffin, 1992]. The Ontong Java Plateau garnet stability field [Salters et al., 1992]. Also the depth of instead formed in an intraoceanic setting, far away from any melting derived from rare earth element inversions over sizable continental mass [Mahoney at al., 1993; Tarduno et plumes [White et al., 1992] is consistentwith initial low al., 1991]. A near-ridge hotspot environment satisfies degreesof melting in the garnetstability field. A robustresult geophysical and geochemical evidence [Mahoney and in our modeling is that the conductive heating of the Spencer,1991], thoughit can not be confirmedby studieson lithosphereis not sufficient to induce large degreesof partial magnetic anomaly lineations [Nakanishi et al., 1992]. melting in the lithosphere;this, of course,does not rule out Anyway, the scenarioof ridge jumping or a migrating triple the likelihood of various degrees of lithospheric junctionover a plume headcould explain the melt volumeand contamination as the magma rises to shallower depths. the high degreesof partial melting (~30%) [Mahoney et al., Certainlythe age and the behaviorof the lithosphereaffect the 1993] for the Ontong Java Plateau. For the Shatsky Rise, depth of melting and thus the total melt volume, which magnetic lineations indicate that the plateau formed on 13,83o FARNETANI AND RICHARDS: FLOOD BASALT MODELS

oceanic lithospherealong the trace of a triple junction [Sager with even higher MgO contentsin the case of oceanicplateaus and Hah, 1993]. [Storey at al., 1991]. However, it is no surprise that the The depth of melting affectsthe compositionof the primary picrites appear only rarely at shallow crustal levels, since magma, and in our model, melt compositionsare rich in MgO. their density is higher than either average continental or This is a result of the high excess plume temperatures oceanic upper crust. We suggestthat large volumes of crystal (>300øC) required for sublithospheric melting without cumulates may reside at the crust/mantle interface beneath extension. The mean MgO concentrationsrange between 16 major flood basalt provinces. They should show up as high- and 19 wt %, with the higher values for younger oceanic velocity lower crustal layers, and there is, in fact, evidencefor lithosphere and for higher excess temperaturesof the plume such layers beneath the Columbia River Basalt province head. The relation between the primary magmasat depth and [Catchings and Mooney, 1988] and beneaththe Deccan Traps the volcanic products erupted or intruded at shallow depths [Verma and Banerjee, 1992]. Moreover, refraction may be very complicated, and inferencesfrom a simple batch experiments on the Kerguelen Plateau [Charvis and Operto, melting model are not entirely satisfactory. However, it is 1992] and on Broken Ridge [Francis and Raitt, 1967] indicate clear that if melting occurs beneath mature lithosphere, the the presence of a lower crustal body with high seismic primary magma will have a "picritic-type" composition,so velocities (7.3 km/s); similarly, a -16-km-thick lower crustal that the erupted tholeiitic basaltsare likely derived via crystal body with high seismic velocities (7.4-7.7 km/s), is found in fractionation. the central Ontong Java Plateau [Furumoto et al., 1976]. This The majority of flows in flood basalt provinces are suggeststhat residual magmas would be tapped episodically tholeiitic basalts(MgO -5-8 wt %), and only at the initial and from the top of a broad, lenticular magma chamber at the waning stages of volcanism are there differentiated products, Moho which would be undergoing continual crystal from nephelinites to rhyolites. However, the restricted fractionation. We make no attempt here to guessthe residence occurrence of picrite basalts (MgO up to 12-16 wt %) is time of such magmas,but there would certainly be opportunity observed in the Karoo [Cox, 1972], in the Deccan for geochemical interaction with the lower crust and mantle [Krishnamurthy and Cox, 1977], in the North Atlantic lithosphere. This agrees with Cox's [1980] model for flood Tertiary province [Clarke, 1970], and in the Siberian Traps basalt volcanism, according to which the uniform [Zolotukhin and Al'mukhamedov, 1988; Wooden et al., 1993]. composition of the tholeiitic basalts (MgO 4-7 wt %) can be For the Siberian Traps there is evidence that the parental obtained from polybaric evolution of a picritic parent magma magma of the entire suite of volcanic productswas close in (MgO up to 18 wt %). The first phaseof crystallization(-25%) compositionto a picritic magma and that the primary process is mainly of olivine, and it is followed by the crystallization of deep-seatedevolution was crystal fractionation [Zolotukhin (another -25%) of olivine-clinopyroxene-plagioclase at and Al'mukhamedov, 1988; Wooden et al., 1993]. shallower depths, probably in sills intruded at the Moho. Cox Krishnamurthy and Cox [1977] find that the picrite basaltsof [1980] concluded that the minimum volume of concealed the Deccan crystallized from ultramafic liquids containingin cumulatescan be at least as large as the amountof the erupted some cases at least 16 wt % MgO and that the picrites show surface lavas. bulk compositional variation generated by the fractionation In attempting to model uplift history we have only of olivine and chromite. Moreover, the evolved picrite basalt accountedfor thermal buoyancy effects. We have not included magma appears to have given rise to the basalts by the specific volume changes due to crystal fractionation or fractionation of olivine and clinopyroxene.For the Karoo the metamorphismin the deep crust [Falvey and Middleton, 1981], MgO contentsof the picrite basalt range from 10 to 24 wt %, nor have we includedthe effect of magmaticunderplating [Cox, with an average close to 15 wt % [Cox, 1988]. Cox and 1989], even though these processescould influence the uplift Jamieson [1974] suggestthat the less magnesian-richpicrite and subsidencehistory of a flood basalt province. In general, basalts have compositions which closely approximate those surfaceuplift starts at least 10-20 m.y. prior to the expected of the original liquids and that the major elementvariation of volcanic activity. Regardlessof the mantle viscositystructure the volcanic products is dominated by the fractionation at we have found that the time sequenceof dynamic uplift, high pressure(-10 kbar) of olivine and orthopyroxene. subsidence,and volcanic activity occurs over an area within a The compositionof the plateausseems to be predominantly radial distanceof-350-400 km from the plume axis. At greater tholeiitic [Davies et al., 1989]; for the KerguelenPlateau the distances the uplift phase is induced mainly by the tholeiites have 4-10 wt % MgO [e.g., Storey et al., 1992], and sublithosphericspreading of the plume head, and it may be similar values (MgO 4-9 wt %) generally characterize the synchronouswith the volcanic activity. For many flood basalt Ontong Java basalts [Mahoney et al., 1993]. On the other provinces there is growing geological evidence that uplift hand, the volcanic sequenceof the oceanic plateaus can be started at least several million years before volcanism, investigated only through drilling, which is limited to the although it is generally difficult to quantify uplift for uppermost part of a plateau. An alternative approach to continental flood basalt events. For the Karoo and the Deccan elucidate the deeper crustal levels is through the study of [Cox, 1989, and references therein] and for the Paran•i fragments preserved in allochtonousterranes, like Gorgona [Piccirillo et al., 1988] the stratigraphic sequence and Island (Colombia), probably a fragment of the Cretaceous geomorphologicalevidence indicate the progressivechange CaribbeanPlateau [Storeyat al., 1991]. The most magnesian- from marine to subaereal conditions over broad areas before rich flows are komatiites, with MgO up to 24 wt %. Their flood volcanism. In the Siberian Traps, doming and the textural and mineralogical features indicate that they formation of arch structurespreceded volcanism [Zolotukhin crystallized from superheatedliquids, with estimatederuption and Al'mukhamedov, 1988]. Postvolcanic evolution is temperatureof order 1500øC,and that the primarymagma had generallycharacterized by subsidence,but as pointedout by an MgO content of-20 wt % [Aikten and Echeverrfa, 1984]. Cox [1988], provincessuch as Deccan, Paran•i,and Karoo Petrological evidence thus indicates that at least some show evidence of postvolcanic uplift, so that uplift and primary magmas likely have a picritic composition,possibly erosionappear to be long-lived and continuingphenomena in FARNETANI AND RICHARDS: FLOOD BASALT MODELS 13,831 these areas. Cox [1988] suggested that the pattern of production. However, some thermal weakening must occur, highlands may simply be a map of the zones of maximum especially after melt intrusion, and this may facilitate magmaticunderplating or that the dynamicsof such areasis extension during volcanism. The particular regional further complicated by the subsequentevolution of the lithosphericresponse to the arrival of a new plume will depend continentalmargins. For the oceanicplateaus it is difficult to on the nature of the lithosphere itself, other plate tectonic reconstruct the sequence of prevolcanic and postvolcanic forcesacting on it at the time, and perhapsalso the motionof events since the plateaus are presently submerged, but the lithospherewith respectto the plume. subsidenceanalysis indicates that at least part of the Ontong The great variability of geologicalcircumstances attendant Java Plateau was emplaced in shallow water conditions to flood volcanism attests to the fact that interaction between [Tarduno, 1991], while the KerguelenPlateau eruptions were a thermal plume and the lithosphereis very complex, and our apparently subaerial, with subsidence below sea level simple model must surely be inadequate after the onset of occurring up' to 40 m.y. after the cessation of volcanism melting. We have ignored the physicsof magma migration,as [Coffin, 1992]. well as many effectsof temperatureand pressurein the melting Our models,which are constrainedto produceat leastseveral zone. Axisymmetric geometrydoes not allow us to investigate million cubic kilometersof melt beneathunrifted lithosphere, the effects of unidirectional rifting over a plume or the predict rather large uplifts of order 2-4 km, dependingon development of small-scale convective instabilities within whetherthe environmentis continentalor oceanic.Perhaps the plume as it spreadsbeneath the lithosphere[Griffiths and the mostdetailed evidence for uplift accompanyingan oceanic Campbell, 1991]. A fully 3-D model could treat these flood basalt province is found in the Triassic strataof the well- problems,and it would also be possibleto calculatethe effects known Wrangellia terrane of SE Alaska and British Columbia of external forces (i.e., those driving plate motions) or [Joneset al., 1977]. Wrangelliais an accretedoceanic plateau preexistingzones of weaknessin the lithosphere. containing a 3-6 km thick tholeiitic flood basalt, sandwiched Perhaps our most significant assumptions involve the betweenTriassic stratathat recordthe entire uplift/subsidence melting model itself, and implementationof a more realistic history of the province. The largely subaerialflood basalts melting scheme could yield important new insights. A were eruptedin at most a few million years and were followed fractional or Rayleigh melting scheme would allow us to by gradualthermal subsidence of the plateau.Events preceding calculate how the composition of the residuum varies as flood volcanisminclude rapid emergencefrom conditionsof melting progresses.In this case the melt fraction would be a deep, open ocean (chert) deposition,as well as several less- function not only of the pressureand temperature(as used in pronounced,perhaps locally varying, subsidenceand uplift the batch melting model) but also of the evolving bulk events just prior to eruption. The magnitude of uplift is composition of the residual matrix. inferred to be of the order of several kilometers. There is no The melting model we have used is anhydrous,and small evidenceof significantcrustal extensionaccompanying any amountsof water in the mantle can lower the peridotitesolidus of these events. This sequence of events is in excellent by severalhundred degrees [Bonatti, 1990; Jaquesand Green, agreementwith the "nonrifting" models developedhere, and 1980]. A compelling case has been made recently by we have previously suggestedthat Wrangellia is an almost Gallagher and Hawkesworth [1992] for the potential ideal exampleof flood volcanismdue to a new mantleplume importance of water in the mantle lithosphere, and they impinging on old oceanic (actually, extinct island arc) suggestthat flood basaltsmay be generatedby the melting of lithosphere[Richards et al., 1991]. Our models cannotaddress hydrous phases in the lower continental lithosphere due to the complexity of the crustal/mantlestructure under a volcanic impingementof a mantle plume. Obviously,our resultsdo not arc, but the likely presence of volatiles would certainly addressthis petrologicalmodel, and we hope to includemodels enhance melting without substantially changing the time for hydrous melting in future work. However, our focus here evolution of uplift and melting. has been on plume interaction with a model oceanic A related and long-debatedproblem is the relation between lithosphere, and it seems unlikely that the oceanic mantle flood volcanism and continental break-up. As we already lithosphere, having been depleted by extensive partial pointed out, some flood basalt provinces (e.g., the Siberian melting at a mid-ocean ridge, would retain a significant Traps, the Columbia River basalts,and a major event of the volatile content. The high plume temperatureswe infer from Karoo at 193 Ma) were not associatedwith the opening of a modeling of sublithospheric, anhydrous melting in the new ocean or with major extension. For other provinces, absenceof extension represent,as we said at the start, an end- which are associatedwith continental rifting, there is often member result from perhaps the simplest geologically geological evidence suggestingthat the volcanism predates relevant case. the major extension. This is the case for the Paranti [Piccirillo et al., 1988], as shown by recent high-precision radiometric Acknowledgments. The authors are grateful to Scott King for dating [Renne et al., 1992] which indicates that the volcanism providingthe code ConMan in the original Cartesianversion and for his predatedthe opening of the South Atlantic by -5 m.y. On the helpful suggestions.We thank Louise Kellogg and Chi Wang for useful other hand, lithospheric uplift caused by the thermal diapir technicaldiscussions. We also thank Louise Kellogg, RobertWhite and results in horizontal deviatoric stress, and such extensional Mike Coffin for constructivereviews of the paper. Carolina Lithgow- Bertelloni and Chuck Wicks are thanked for their generoushelp and stresses may at times be sufficient to induce continental encouragement.This work was supportedby NSF grantsEAR9018507 extension. Hill [1991] and Houseman and England [1986] and EAR9057012 awarded to M.A.R. conclude that uplift of-1-2 km of continental lithosphereis insufficient to provide the driving force for continentalbreak- References up, even if it may produce sufficient gravitational potential to induce a local tectonic reorganization. We find that Aitken, B. G., and L. M. Echeverr/a,Petrology and geochemistryof extensional stresses are modest and that the maximum komatiitesand tholeiitesfrom GorgonaIsland, Colombia, Contrib. deviatoric stress occurs well before the maximum melt Mineral. Petrol., 86, 94-105, 1984. 13,832 FARNETANI AND RICHARDS: FLOOD BASALT MODELS

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