JOURNAL OF GEOPHYSICAL
RESEARCH,
VOL. 99, NO. B7, PAGES 13,813-13,833, JULY 10, 1994
Numerical investigations of the mantle plume initiation
model
Cinzia
for
flood
G. Farnetani
basalt
and Mark
events
A. Richards
Departmentof GeologyandGeophysics,
Universityof California,Berkeley
Abstract. Recentstudieshavelinked boththe eruptionof continentalflood basaltsand the
emplacement
of largeoceanicplateausto theinitialphaseof mantleplumeactivity,i.e., the
"plumehead"model.Herewe developthisconceptfurtherthroughnumericalmodelsof a large
thermaldiapirrisingthroughthemantleandimpinginguponthebaseof thelithosphere.
A
finite elementanalysisin axisymmetricgeometryis usedto modelthe dynamicsof solidstate
convectiveflow andheattransportin the mantle,andan anhydrous
batchmeltingmodelis used
to estimatemelt volumesandcompositions
obtainedfrom partialmeltingin the shallowmantle.
We explorethe effectsof a numberof modelvariables,includingmantleviscositystructure,
plumetemperature
anddiameter,andthemechanical
response
of thelithosphere.
Our study
emphasizes
casesin whichthelithosphere
doesnotundergosignificant
extension
priorto largescalemelting.A "standardmodel"is foundto be consistentwith someobservedcharacteristics
of
flood basalt/plumeinitiationevents.This modelincludesan initial diapirof radius400 km and
initial excesstemperature
350øCrisingthrougha mantleof viscosity-102•Pas andimpinging
beneatha modeloceaniclithosphere
-100 Ma in age.If lithospheric
extensiondoesnotoccur,
meltingis almostentirelysublithospheric,
the melt volumeproducedis -3.5x106 km3 andits
composition
hashighMgO content(15-20 wt %). A time sequence
of precursorycentral(axial)
uplift of severalkilometersfollowedby majormelting(volcanism)is a robustfeatureof all the
models,regardless
of mantleviscositystructure
or lithospheric
response.
Low viscosityin the
uppermantlecompresses
thetimescalefor theseevents,andresultsin a constrictionof the
plume"head"initially impingingon the lithosphere.
The radialextentof the meltingregion
(about500 km at the time of maximummeltproduction)is only slightlyaffectedby the upper
mantleviscosity.For nonriftinglithosphere,no significantmelt generationoccursfor initial
plumeexcesstemperatures
lessthanabout300øC.The initial plumeradiushasonly a modest
effectuponthe volumeof meltobtained.The mostimportantaspectof lithospheric
response
is
whetheror nottheuppermost
crustandlithosphere
(above-40 km depth)undergoextension:
otherwise,the ductilestrengthof thelowerlithosphere
haslittle effect.If thelithosphere
is
allowedto extendfreely,themelt volumeincreases
by aboutan orderof magnitude,andit is
comparablewith someof thelargestoceanicplateaussuchasOntongJava.If continentalor
oceanicfloodbasalteventsoccuron old, nonriftinglithosphere,
theprimarymeltsarelikely to
be muchmoreMgO rich thanthebasaltseruptedat the surface.This is consistent
with abundant
evidencefor olivinefractionation
in manyfloodbasaltprovinces,alongwith theoccurrence
of
picritelavas,andwe hypothesize
thatfractionation
occursat a densitytrapat thecrust/mantle
boundary(Moho). At this stageandfollowing,it is likely thatsignificantlower crustaland
mantle-lithospheric
contamination
of mantleplume-derivedmagmasmay occur,both
isotopicallyandin thetraceelements.
The sequence
andtimingof bothprecursory
andpostmagmaticeventsin the vast,well-exposed
oceanicfloodbasaltterraneknownas "Wrangellia"
(SE Alaska;BritishColumbia)areconsistent
with the predictionsof our model.The uplift
predictedby our modelsis of order2-4 km if we requirethatmantleplumesarehotenoughto
melt beneathunriftedlithosphere.
Effectsnotmodeledhere,suchassmall-scaleconvectionand
hydrousmelting,will tendto reducethemodelexcesstemperature
anduplift.In orderto better
understand
the relationbetweenmantleplumesandlargeigneousprovinces,severalimportant
advancesarerequired:implementation
of a fractionalmeltingmodel,somerealisticassessment
of
melt transportthroughthemantleandcrust,anda fully three-dimensional
convectionmodel.
Introduction
Flood basalt eruptionsare extraordinaryvolcanic events
which give rise, literally, to floodsof basalticlava that cover
vast areasof the Earth'ssurfacevery rapidly. These eventsare
Copyfight1994 by the AmericanGeophysicalUnion.
Papernumber94JB00649.
0148-0227/94/94JB-00649505.00
not explained by normal plate tectonicactivity at convergent
or divergentmargins, and they occur in a variety of tectonic
settings [Hill et al., 1992]. Continental flood basalts are
commonly associated with lithospheric rifting and
continentalbreak-up [White and McKenzie, 1989], although
major crustalextensiondoesnot appearto be requiredfor flood
volcanism [Richards et al., 1989; Hooper, 1990].
Estimated extruded volumes for the largest flood basalt
events such as the Karoo, the Deccan traps, the Paranti-
13,813
13,814
FARNETANI
AND RICHARDS'
Etendeka,the Siberian traps, and the North Atlantic Province,
FLOOD BASALT
MODELS
Morgan [1972, 1981] noted the associationof presently
(Figure1) areof order1 or 2x10a km3 [Richards
et 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
("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. Magnetostratigraphic
and 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 generallyprecededby 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.
An alternativeproposedfor the origin of flood basaltsis the
timing and durationof uplift are often difficult to constrain.
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
estimatedvolumesfor someplateausare 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 KerguelenPlateauthe 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 OntongJava Plateauthe genesis.The passiverifting and plume initiation modelsshare
estimated
totalvolumerangesfrom30 to 60x106km3 [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)
lithosphericextem;ionhas 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 eruptionrateswould 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;
Hill et al., 1992; Heaman et al., 1992], that lithospheric
regionaluplift of the oceanfloor [Richardset al., 1991].
All these provincestypically cover areas-1000-2000 km in
i
i
i
i
!
i
Yellowstone
Onton[_.•g_•
i
i
I
I
'
I
I
t
,
......
/
\
\
..........
I
i
Figure 1. Schematicmap showingselectedflood basaltprovincesand oceanicplateaus.The associated
hotspots,whereknownor conjectured,
are indicated.(Adoptedfrom Duncanand Richards[1991]. For a more
completemap of large igneousprovinces,seeCoffin and Eldholm[1994].)
FARNETANI
AND
RICHARDS-
extensionis not required. We will not repeat those arguments
here, but the matter is not yet resolved and remains a
legitimate point for debate.
Important questions also remain concerning the specific
predictions of the theoretical models. The plume initiation
model has been developedon the basisof resultsfrom simple
laboratory fluid dynamical experiments [Whitehead and
Luther, 1975; Olson and Nam, 1986; Griffiths and Campbell,
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
models have been extremely useful, both qualitatively and
quantitatively,but they do not addresssome importantaspects
of plume dynamics. In particular, they cannot be applied
directly to partial melting processes,nor can they be used to
understandimportant physical effects arising from variations
in the mechanical properties of the deep mantle and
lithosphere.Such aspectsinsteadcan be better elucidatedby
numerical
models.
FLOOD
BASALT
MODELS
13,815
Third, we are particularly interested in applications to the
flood
basalt
formation
in the Triassic
strata
of the famous
Wrangellia terrain of Alaska and Vancouver Island, British
Columbia. This accretedoceanicplateau containsa remarkable
stratigraphic record of prevolcanic and postvolcanic events
[Richards et al., 1991], and the field evidence showsthat flood
volcanism occurred on old oceanic lithospherewithout major
crustal
extension.
Numerical
Finite
Element
Methods
Model
We use a finite element code (ConManCYL) for thermal
convection within the Earth's mantle in cylindrical
axisymmetric geometry. We have substantiallymodified the
original Cartesianversionof the code (ConMan, written by A.
Raefsky and S. King) to satisfy the cylindrical geometry.The
code solvesthe advection-diffusionequationsfor a Newtonian,
incompressible and compositionally homogeneousviscous
fluid. In nondimensionalform the equationsare
In this paper we presentthe resultsof numericalmodelingof
ascendinglarge mantle diapirs in order to develop a broader
range of quantitative, testable hypothesesfrom the plume
initiation concept. Our finite element model in cylindrical Incompressibility
axisymmetric geometry combines the dynamics of solid state
V.U=O
(1)
convection in the mantle with a melting model. We start with
a hot, spherical diapir in the lower mantle and follow its
of momentum
for a fluid at infinite
Prandtl
evolution as it rises through the mantle and spreadsbeneath Conservation
number
the lithosphere.We calculate the history of surfaceuplift and
mantle melting due to the hot plume head. We implement the
-VP+V2U+
RaT•
=O
(2)
empirical batch melting model of McKenzie and Bickle [1988]
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
RF
V2r
--+(vr).v=
(3)
and timing of uplift, etc., are functionsof (1) buoyancyof the
thermal diapir (which dependson its initial size and excess
where U is the velocity vector, T is the temperature,p is the
temperature), (2) different mantle viscosity structures,and (3)
mechanical behavior of the lithosphere. The further step, dynamicpressure,t is time,Ra is the Rayleighnumber,and
is a unit vector in the vertical direction.The equationsare nonwhich is to comparethe resultsof the numerical model to the
dimensionalized
by scalingdistanceaccordingto the cylinder
correspondingparametersobservedor inferred in flood basalt
depthd, temperature
accordingto the temperature
contrast
provinces,can be done only at a very speculativelevel due to
acrossthe lithosphere,
andtime according
to d2/•, where•cis
the simplicity of our model. The equilibrium melting model
the thermal diffusivity. Numerical values of the scaling
does not account for the compositional evolution of the
parametersare given in Table 1. All the materialpropertiesare
residuum as melting proceedsand how this affects the melt
combined in the Rayleigh number:
fraction and its composition.Moreover, we do not model melt
extraction,nor do we model attendanteffects suchas pressure
changesresulting from melt extraction [White et al., 1992] and
heat transfer betweenthe rising magma and the lithosphere.
where g is the gravitational acceleration,tx is the coefficient
We also ignore the effect of volatile components,since the
batchmelting parameterization
is basedon anhydrousmelting of thermalexpansion,•cis 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.Densityvariationsdue
Hawkesworth, 1992].
to temperaturechangesare neglectedexceptin 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
in order to achieve correct results using the penalty
compared to continental lithosphere. Second, as will be
formulation in the axisymmetric case a mean-dilatational
shown below, the case of old, nonrifting lithosphere
constitutesthe most stringent test for the plume initiation
approach(B method)mustbe appliedto the stiffnessmatrix
model, especially with respectto melt production.We believe
of the momentumequation.The momentumequationis solved
that the field evidenceshowsthat at least somemantle plumes usinga Galerkin methodand bilinear shapefunctions,and we
must be hot enough to melt without lithospheric extension. apply the B methodin its completeformulation[Hughes,
Ra=gøtSFd3
p
(4)
13,816
FARNETANI
AND RICHARDS:
FLOOD BASALT MODELS
Table 1. Model Parametersand PhysicalConstants
d
g
Values
Model Parametersand Physical Constants
Symbol
2600
km
1280øC
dimensionaldepth of the cylinder
potential temperaturecontrastacrossthe lithosphere
gravitational acceleration
thermal expansioncoefficient
mantle density
thermal diffusivity
specific heat at constantpressure
1987]. The accuracy of the solutions for the velocity
components has been checked against analytical solutions,
calculated with a propagatormatrix techniquein cylindrical
geometry [Richards,
1986]. The error is defined as
10ms -2
3x10-5 oc-1
3500kg m-3
10-6 m2
1200J kg
that may arise becauseof initially high temperaturegradients.
When calculatingthe initial radius of the diapir, we take into
accountthe buoyancyinducedby the thermalhalo,so that R0
should be considered
an "effective"
initial radius.
œ=(UC- UA)x100/UA,
where
Uc isthefiniteelement
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
calculatethe topographicuplift inducedby 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
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
velocity field, which is then used to advect the temperatures
for the next time stepand solvefor a new temperaturefield.
,==
p
(5)
200
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
radial
distances
less
than
760
km
the
width
ofeach
element
is 1040
18.5 km,
elsewhere
the
width
is 27.8
km.
Atthesurface
weimpose
zero
vertical
velocity
(Uz=0)
ß
Forcases
in which
lithospheric
extension
isnotallowed
the
radial componentof the velocity is set to zero from the surface
toa depth
between
20and40km,depending
onthetypeof
lithosphere
(oldoryoung)
being
modeled.
Onthebottom
boundarywe imposezero vertical velocity and radial free slip
(U z = 0 = c)Ur/oaz
); while alongthe axisof symmetry
andthe
right side of the box, we impose zero radial velocity and
verticalfreeslip(U r = 0 = •Uz/oar).
In the initial temperatureconfigurationthe mantle has a
uniformpotentialtemperatureTm=1280øC,all boundariesare
insulatedexceptthe top surface,whichis assigneda constant
temperatureT•u=0øC.The initial temperatureprofile for the
oceaniclithosphereis given by an error functionconduction
profile corresponding
to the appropriateage. The spherical
thermal diapir, initially centered at 2000 km depth, is
characterizedby an initial excesspotentialtemperaturewith
respectto the mantle, AT0, and by its radius,R0. To avoid
high-temperaturegradientsbetween the boundaryof the
thermal diapir and the surroundingmantle, we impose a
"thermal halo", 130 l•m thick, in which the temperature
2600
0
780
1560
Distancefromaxis(km)
Figure 2.
The standard finite element grid (70x120
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 avoidnumericalinstabilities higherresolutionfrom the surfaceto 200 km depth.
decreases as a sine function with distance from the surface of
FARNETANI
AND RICHARDS:
FLOOD BASALT MODELS
where•l is the viscosity
andp is the dynamicpressure
given
13.817
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)
T'=Tr- (T/+
T•)/2
(10)
where)• =107 is thepenaltyparameter.
For eachelementwe calculate
the nondimensional
average The melt fraction X is expressed through a dimensionless
valueof •zz whichis assigned
to the centerof massof each temperatureT' :
element.Values of •zz have also been checkedagainst
analyticalsolutionscalculatedwith the propagatormatrix
technique.
Theerrorœ=(•zzC-•zzn)x100/•zzn,
where
•zzCis
the finite elementvalue and •zzn is the correspondingby requiringthatX=0 whenTr = T• andX=I when Tr = T/. The
analytical
value,is e<0.1%ona 66x66grid.Theelement
melt fraction at the center of each element is calculatedusing
the empirical expression
valuesare projectedto the nodesusinga modifiedversionof
the pressure-smoothing
technique[Hugheset el., 1979]. We
X- 0.5=T'+(T'2- 0.25)(a
+t,T')
dimensionalize
•zz by multiplyingit by pgdab•/Ra and
calculatethe surfacetopographic
uplift 6h:
6h
=(•zz
-•zz)
with the coefficients
a=0.4256
and b=2.988.
(11)
We also account
(7) for the changein temperaturedue to the latentheat of melting.
At constant pressurethe change in temperaturedT due to a
where•zz is the area-averaged
valueof the verticalnormal changein melt fraction dX is
stress
at thesurfaceand psuis the effectivedensitycontrastat
theuppersurface.
For continental
lithosphere,
p• equals
the
dT= AHx dX/Cp
mantle density ,Om (both crust and mantle material are
(12)
uplifted),whilefor oceaniclithosphere,
p• = ,om-,Ow,where for a reversible process the latent heat of melting AH is
Pwis thedensityof seawater
(Pw=1000kg m-3).
AH = AS X Tr; thus
Calculationsof melt volumeand composition
As the head of the thermal diapir spreadsbeneaththe
lithosphere,
we estimatethe total melt volumeproducedand
its composition.
We usea batchmeltingmodel,thusassuming
that the liquid remainsin chemicalequilibriumwith the solid
residueuntil mechanicalconditionsallow it to escapeas a
single "batch"of primary magma.The requirementthat no
relative movement occurs between the melt and the matrix is
probably unrealistic whenever the melt fraction exceeds 1 or
2% [McKenzie, 1984], and this will affect the total melt
volumeand its composition[McKenzieand Bickle, 1988]. We
do not attempt to model melt extractionand its effect on the
dT=ASXTrXdX/C
vß
(13)
We assumethat meltingoccursat constant
entropyof fusion
(AS=250J kg-1 øK-l,asin McKenzieand Bickle's[1988]
parameterization) and calculate the relation between melt
fraction,temperature,
and pressureusingthe equationsin
Appendix
D of McKenzie[1984],wherea fourth-order
RungeKuttascheme
is usedto integrate
theexpressions
relatingX, T,
P at constantAS. The valuesof the real temperature,
modified
by the latent heat of melting, are then convertedback to
dimensionless
potentialtemperatures
and usedin the diffusion
(conduction)term of the energy equationfor the next time
dynamicsof the plumeheadandof the lithosphere,
nor do we
includedirectlythe effectof meltbuoyancy.
Thoughit would step.
The melt fraction by weight X is related to the volume
be desirable
to usea morerealisticmodelfor partialmeltingof
a complexmineralassemblage,
suchas Rayleighmelting,the fractionof melt q through
parameterization
availableis basedon laboratoryexperiments
which involve batch melting.
In this study we implementthe parametrizationby
pf+X(p,
-pf)
(14)
garnet peridotite. We calculate the melt fraction and its
andweassume
thatthedensity
of thesolidPs andthedensity
of the melt pf are equal.The total melt volumeis then
compositionat eachtime stepfor depthsshallowerthan 220
obtainedby integrationof the volumefractionof melt of each
rangeof McKenzie and Bickle's[1988] parameterization).
As
discussedbelow, this does not seemto be a limitation, since
averagecomposition
of the melt in termsof the majorelement
oxides using the McKenzie and Bickle [1988]
parameterization.
The valuesobtainedare probablyonly
McKenzieand Bickle [1988] of batchmeltingexperiments
on
thepoint
km (i.e., from 0 to -7 GPa,whichcorrespond
to the pressure elementovertheentiremeltingregion.We calculate
meltingneveroccursdeeperthan150km (i.e., -5 GPa)in any
of our modelcases.We first convertthe dimensional
potential indicative, since the method has some limitations when
temperatures
Tpto realtemperatures
Tr assuming
an adiabatic meltingoccursat highpressure[Watsonand McKenzie,1991].
gradient
and
using
Tv=Trxexp(-go•/Cv)
, whe.re
z isthe The
dimensional
depth.Thenumerical
valueof Cv is givenin
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
temperature(in degree Celsius) is obtained by numerical
solution
of
We assume that mantle plumes originate from a hot
boundarylayer in the mantle, possiblythe core-mantle
boundary(CMB). Laboratoryexperiments[Whiteheadand
13,818
FARNETANI AND RICHARDS' FLOOD BASALT MODELS
Luther, 1975; Campbell and Griffiths, 1990] show that a
newly formed thermal plume develops a large "head" and a
"tail". The head forms since a large amount of buoyancy is
needed before the plume is able to displace the overlying
colder fluid and rise. The "tail" of thermal plumes is
maintained by continued buoyancy flux from the bottom
boundary.This tail is a somewhatarbitrary feature of the fluid
dynamical experiments, since a constant buoyancy flux is
imposed. Natural boundary layer instabilities arising in free
convection may or may not be continuously fed from the
boundary layer, dependingon the particular conditions.
In the mantle plume initiation model, flood basalts are
generatedby melting of the head of the plume [Morgan, 1981;
Richards et al., 1989; Campbell and Griffiths, 1990], and in
this first phasethe contributionof the material rising through
the tail is of secondaryimportance. Given the uncertaintiesin
r/(T)= r/0exp(-4.60T)
(15)
which gives two orders of magnitudeviscositycontrastacross
the lithosphere.
Lithosphere
The lithosphere is modeled by imposing an initial
temperatureprofile and a viscosity structure(note that we
concentrate on oceanic lithosphere for the reasons stated in
the introduction). The initial temperatureprofile is given by
an error function conduction profile [Parson and $clater,
1977] accordingto the initial age. We investigateinitial ages
0 Ma, 20 Ma, and 100 Ma. For nontemperaturedependent
viscositycases,the viscosityof the lithosphere
is 1022Pa s
from the surfaceto 55 km depth (for 100 Ma old lithosphere),
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
viscositystructureof 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 temperaturedependentviscosity).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 temperatureAT
oi s
expected to be higher than the excess temperature (AT)
estimated from petrologic constraints.The excesstemperature
that best fits the Hawaii hotspot swell is 200-300øC [Sleep,
1990], in agreementwith a plume temperatureof ~1500øCfor
magma generationbeneathHawaii [Wyllie, 1988]. The range
of initial
radius
values
we model
is consistent
with
values
estimated from laboratory experiments [Campbell
Griffiths, 1990] scaled to mantle conditions.
ViscosityModels
200
and
600
Mantle Viscosity Structure
Laboratory experiments have investigated the rise of a
plume in a uniform viscosityfluid, but numericalmodelingcan
address the effect of more realistic viscosity structures.
Geophysical studies indicate that mantle viscosity may
increasefrom the upper to the lower mantleby 1 or 2 ordersof
magnitude [e.g., Hager, 1984; Nakada and Lambeck, 1990].
Viscosity may change discontinuouslyat depth where phase
changesoccur, and it might vary continuouslywith depth due
to the effects of pressureon the rheologyof mantle materials.
We consider several viscosity structures and some
temperaturedependentviscositycases.(We do not attemptto
model other thermodynamicaleffects of phase changes.)In
this studythe valuesof the lower mantle viscosity(r/ira) range
from 3x1022to 3x1021Pa s, andfor the uppermantleviscosity
1000
1400 -
1800 -
2200
(r/urn)valuesrangefrom3x1021
to 3x1019
Pa s. Thiscoversa
reasonablerange of mantle viscosities,thoughmore extreme
values are possible.The uniform mantle viscositymodel has
Ti=102• Pa s. Figure 3 showsthe viscosityprofilesfor the
"standard"
model(rhm=l022 Pa s) for viscositycontrasts
of
¾=10 and ¾=100 (¾= •im/ Tam)' The change in viscosity
between the lower and upper mantle is at 670 km depth. The
stiff rheology of the lithosphereis modeledby an increasein
-
2600
1019
1020
1021
1022
1023
LogViscosity(Pas)
Figure 3.
Mantle viscosity profiles for the two standard
uppermost
mantleviscosityup to 1022Pa s (seenextsection). models:¾=10(thin line) and ¾=100(thick line). ¾=film/rlumis
For temperaturedependentviscosity we adopt the following
exponential dependence:
the ratio of lower mantle viscosity(film) and upper mantle
viscosity (flure).
FARNETANI
AND RICHARDS- FLOOD BASALT MODELS
We also investigatethe effects of lithosphericextension.If
extensionis allowed, we simply use a free radial slip boundary
condition at the top surface nodes of the finite element grid.
This allows extension to occur naturally since all internal
nodes are unconstrained.For the majority of cases in which
extensionis not allowed, we imposezero radial velocity from
the surfaceto 40 km depth for an initial age of 100 Ma, or to
28 km depth for 20 Ma lithosphere.It is important to note
that the axisymmetry of our calculations requires that any
horizontal extension be radial, so that we cannot generate
more realistic models with unidirectional extension (rifting)
of the lithosphere.
Results
The
numerical
model
described
above
allows
us
to
investigatethe evolution of a thermal diapir as it rises in the
mantle and impinges on oceaniclithosphere.We calculatethe
temporaland spatial variationsof the surfaceuplift, the radial
deviatoric (extensional) stressinduced in the lithosphere,and
the total melt volume. The model parameters vary about a
"standard" case in which the thermal diapir has an initial
excess potential temperature AT0=350øC, an initial radius
Ro=400 km, the lower and upper mantle viscosities are
r//m=1022
Pa s and r/um=1021Pa
s, respectively
(y=10), the
lithosphereis nonrifting and its initial age is 100 Ma. Figure
4 shows the time evolution of the thermal diapir for this
standardmodel, starting from the initial condition (Figure 4a).
After 20 m.y. (Figure 4b) the head of the diapir is at 670 km
depth,while after 30 m.y. (Figure 4c) the plume head is at 180
km depth. Just prior to sublithosphericspreadingthe plume
radius is -350 km. Melting startsat 34 m.y. and increasesas
the plume head spreadsbeneaththe lithosphere.The melting
Initial condition
region(for melt fractionX>0%) is indicatedin Figure4d by the
white area beneath the lithosphere. The maximum melt
production occurs after 45 m.y. and the total melt volume
produced
is 3.7x106km3. At thistimetheradiusof theplume
head is -700 km and the radiusof the melting region for melt
fraction X>5% is -580 km. Melting occursat sublithospheric
depths (100-150 km) since not enough time has elapsedfor
conductiveheating the lithosphereabove the solidus.
Figure 5 shows the time evolution of the initial diapir
(Figure 5a) if the upper mantle viscosity is reduced to
rlum=l
020Pa s (y=100)in the standard
model.After 20 m.y.
(Figure 5b) the head of the diapir is at 670 km depth. As it
entersthe upper mantle, a narrow conduitdevelops(with radius
-100 km) through which the hot material ascendsat higher
velocity, so that after only 24 m.y. (Figure 5c) the plume head
is at-180 km depth.The narrowingeffect reducesthe radiusof
the plume head impinging on the lithosphere to -150 km.
Melting starts after 24 m.y. and reachesa maximum after 33
m.y. (Figure 5d), the total melt volumeproducedis 2.6x106
km3. The radiusof the plumeheadat this time is -620 km,
while the radiusof the melting region,for melt fractionX>5%,
is -360 km. The "narrowing" of the plume head is a
consequence
of the velocity increaseof the buoyantfluid when
it entersa lower-viscositymaterial [e.g., see Richards et al.,
1988]. The abovefiguresillustratethat the viscositystructure
of the mantle affectsthe dynamicsof a rising plume and that 2
orders of magnitude viscosity contrastbetween the lower and
upper mantle causes pronounced"necking". This ultimately
influencesthe shapeand size of the plume head and the radial
extent of the melting zone.
For comparison, Figure 6 shows the evolution of the
standarddiapir (AT0 and Ro as above) rising in a uniform
viscositymantle(Tl=1021Pa s). No neckingoccurs,andthe
After30m.y.
After
20m.y. b
...............
.
....
t.•....•:.:.:.
•.•'•...•..•:
..•.•.%:.
......
13,819
......
After45 m.y.
c
.....
d
.:::.z::•:.•
:•?
-•;•.•:a.
,;::.•:•.•..::
.•:,:.:...,.•;•.,;.•;•4....,,..
:.
26O
520
780
1040
1300
1560
1820
2080
2340
...
2600
260
520
780
1560
0
Distance
fromaxis(kin)
260
520
780
1560
0
Distance
fromaxis(km)
1024
260
520
780
Distance
fromaxis(kin)
i:•?:::::;•:.•..:L.%.•
..::.':.... ::
1560
0
260
520
780
Distance
fromaxis(kin)
1632
Potential
Temperature
(C)
Figure 4. The evolutionof the diapirwithinitialexcesstemperature
ATo=350øC
andinitialradiusRo=400
km. The mantlehas a potentialtemperatureTm=1280øC
and the mantleviscositymodelis r//m=1022
Pa
S,r/um=10
21Pas (¾=10).(a) The initialcondition.
(b) After20 m.y.(c) After30 m.y. (d) After45 m.y.The
meltingregionis the white areabeneaththe lithosphere.
To showthe temperature
structureof the diapir more
clearly, the minimumpotentialtemperaturein the gray scaleis 1024øC.This meansthe lithosphere(where
T<1024øC) is depictedin white.
1560
13,820
FARNETANI
AND
Initial
Condition
a
RICHARDS:
FLOOD
After
20m.y.
MODELS
After
24m.y.
b
.......................
. . -.................
•,•
......................
?..
BASALT
.•... ....... •.............
After
33m.y.
c
-+:::--.-:-*--------•................
d
...•
260
520
780
1040
1300
1560
1820
2080
2340
2600
0
260
520
780
1560 0
Distance
fromaxis(km)
260
520
780
1560 0
Distance
fromaxis(kin)
1024
260
520
780
1560 0
Distance
fromaxis(kin)
......
•i;
260
520
780
1560
Distance
fromaxis(kin)
1632
Potential
Temperature
(C)
Figure 5. The evolutionof the diapir with initial excesstemperatureAT0=350øCand initial radius R0=400
km. The mantleviscosity
modelis rhm
= 1022Pas, •lum
= 1020Pas (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
mantle (Figures 6a and 6b). When the plume head reachesthe
lithosphere,its radius is --600 km (Figure 6c) and most of the
buoyant material is contained in the head. Melting occurs at
sublithosphericdepths while the head spreadslaterally to a
radial distance of--780 km (Figure 6d) and the total melt
hand, a uniform viscosity mantle is an unlikely model for the
Earth, and we concentrateon caseswith a viscosity contrast
betweenupper and lower mantle.
Figures7a and 7b show surfaceuplift (calculatedon the axis
of symmetry), melt volume, and radial deviatoric stress Crrr
(calculated on the axis of symmetry, at 80 km depth) as a
volumeproducedis 3.5x106km3. The evolutionof the diapir functionof 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 plumeheadreaches
InitialCondition a
After2 m.y.
.......
b
7'.'77'............. 'W...%'7'7.772"7•;'•..."•".;•:
..... 7•.777"
After8 m.y.
c
After16m.y.
d
ß
.';;
:•"
;.;?....-!'*r"X.%.-:-*-•
.......
':..• ':.................
'":'
"•'-....•,,..".*.."'•
..............
y"•7
.......
;7
260
520
780
1040
1300
1560
1820
2080
2340
2600
260 520 780
Distance
fromaxis(km)
1560 0
260 520 780
1560 0
Distance
fromaxis(km)
1024
260 520 780
Distance
fromaxis(km)
•'•;i'- ......
..........
1560 0
260 520 780
Distance
fromaxis(km)
1632
Potential
Temperature
(C)
Figure 6. The evolutionof the diapirwith initial excesstemperatureATo=350øCandinitial radius Ro=400
km.The mantlehasa uniformviscosity
,1=102•Pas. (a) Theinitialcondition.
(b) After2 m.y.(c) After8 m.y.
(d) After 16 m.y. The melting region is the white area beneaththe lithosphere.
1560
FARNETANI AND RICHARDS. FLOOD BASALT MODELS
(a)
4.0
[1.90]
13,821
4.0
•lm
J]•um----10
Initial Lithospheric Age: 100 Ma
14
3.0
3.0
[1.43]
lO;
2.0
2.0
[0.95]
1.0
[0.47]
•Melt
,Volume•
ß
ß
ß
1.0
' •Stress
2
#
I
(b)
4.0
[1.90]
#
I
4.0
•11JT•u
m-' 100
Initial Lithospheric Age: 100 Ma
14
3.0
-
3.0
-
2.0
-
1.0
[1.43]
10
2.0
0.0
I
[0.95]
•
ß
=
el
6
Volurn
ß
m•mmmm
mmmm
m
1.0 [0.47]
t
2
15
t .....
Str••
t
20
25
30
Time
I
I
35
40
0.0
45
(m.y.)
Figure7. Uplift,radialdeviatoric
stress
((•rr)andmeltvolume
versus
elapsed
time.(a) Formantleviscosity
contrast¾=10.(b) For ¾=100.In bothcases,ATo=350øC
and Ro=400km. Note that the unbracketed
and
bracketed
numbers
on theupliftscalereferto maximum
andminimumvalues,respectively.
Maximumvalues
are for the uplift from abyssaloceanicdepthswith a thermalexpansion
coefficientof 3x10-5øC-1. Minimum
valuesare for subaerialuplift with a thermalexpansion
coefficientof 2x10-5øC-1.
the base of the lithosphere.Subsidenceof the central area plumehead rises throughthe uppermantle,while during
followsandaccompanies
the sublithospheric
spreading
of the sublithospheric
spreadingO'rrdecreases.
Notethatthe 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 precedes
the peakof melt volumeis reached,and the extractionof melt (whichwe do not
volume by -10 m.y., so that subsidenceof the central area model) would certainlyaffect both the uplift and the melt
occursduringthe phaseof maximumexpectedvolcanism.The volume.
radialdeviatoric(extensional)
stressO'rris in phasewith the
Comparison
of Figures7a and7b showsthatfor a higheruplift and the maximum extensional stress occurs when the viscositycontrast(i.e., ¾=100)both peaksin uplift and melt
plume head approaches
the lithosphere.During the major volume occur earlier in time, which is consistentwith the fact
melting phase, O'rrgraduallydecreases.
Figure7b showsthe that the headascendsmorerapidlyin the uppermantle.The
time relationamonguplift, melt volume,and radial deviatoric maximumamountof uplift decreases
and the total melt volume
stressO'rrfor the standard
casewith¾=100.The surfaceuplift is reducedmodestly,probablydue to the narrowingof the
increases
while the diapirrisesthroughthe mantle,while slow plume head. Reducingthe upper mantle viscosityserves
subsidence
occursduringthe sublithospheric
spreading
of the mainly to compressthe time scale for these eventsand, to a
head.The peakof uplift precedes
the peakof melt production lesser degree, the horizontal length scale of the plume
by -4 m.y. The deviatoricstressO'rrreaches
a maximumasthe 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
production,so that the model predictsa regulartime sequence
of uplift, thermal subsidence,and volcanic activity.
Figure 8 shows surfaceuplift as a function of radial distance
from the axis, at different time stepsand for the standardcase
(T=10). Note that the constraintsof conservationof massand
incompressibility cause negative values of uplift at the
extreme right of the cylinder. While the diapir rises through
the lower and upper mantle, the surfaceis affectedby a broad,
low-amplitude swell (see curves at elapsed time 22 and 26
m.y.). The central uplift increasesconsiderablyas the plume
head approachesthe lithosphere(26 to 34 m.y.) and affects an
area -400 km in radius.After 34 m.y., subsidencestartson the
axis, but at greater distances,uplift may continue for several
million years, as the plume head spreads beneath the
lithosphere. Consequently, the onset of thermal subsidence
does not occur simultaneouslyover the whole swell. Figure 8
also shows the radial extent of the melting region for melt
fractionsX>5% and X>10%. The extent of the melting region
reflects the progressivespreadingof the plume head, and it is
probably safe to assume that areas where X>_5% will
correspondto areasof surfacevolcanism.
The temporalrelationbetweenthe surfaceuplift and melting
will clearly differ with distancefrom the plume axis. Figure 9
shows uplift histories at radial distances0, 250, and 500 km
from the axis. The maximum uplift at 250 km distance is
reducedto -80%, comparedto the axis, but the timing for the
uplift peak and the onsetof subsidenceare comparable,so that
we can infer that a fairly regular time sequenceof uplift, onset
of subsidenceand volcanism should be expectedin a central
I Initial
Lithospheric
Age:
100
Ma Tlld]]um" 10
ß
(Uplift)
.•
/
f•Radial
extent
ofthe•
•
.... X>10%
-- -- X>5%
melting
region
.J
_•.......... • ••.._
,
45m.y.
42 m.y.
38 m.y.
2.0
34 m.y.
o.o
22 m.y.
i
0
260
i
i
520
780
Distance
from
i
i
1040
axis
1300
1560
(km)
Figure 8. Surface uplift versusaxial distanceat different elapsedtimes. The radial extent of the melting
regionfor melt fractionX>5% (long dashedline) andX>10% (shortdashedline) is indicated.The initial diapir
has ATo=350øC
and Ro=400 km andthe mantleviscositycontrastis ¾=10.The verticalexaggeration
is 50:1.
FARNETANI AND RICHARDS: FLOOD BASALT MODELS
13,823
TIiJTlum-10
Initial Lithospheric Age: 100 Ma
4.0 [1.90]
3.0 [1.43]
2.0 [0.95]
mmmmm
mmmmmmmmm
m•m
m•
m
1.0 [0.47]
(r=5•0)
15
20
25
30
35
40
45
Time (m.y.)
Figure 9. Uplift versuselapsedtime calculatedat radialdistancefrom the axis r-0, 250, and 500 km. The
initial diapirhas ATo=350øC
and Ro=400km, and the mantleviscositycontrastis T=10. Note that the
unbracketed
andbracketed
numbers
on theupliftscalereferto maximum
andminimum
values,respectively.
Maximumvaluesare for the uplift from abyssaloceanicdepthsandwith a thermalexpansion
coefficientof
3x10-5øC-•. Minimum
values
areforsubaerial
upliftwitha thermal
expansion
coefficient
of 2x10-5øC-•.
area-300-350km in radius.At a distance
of 500 km theuplift
occursonly in the latest stages,after the plume head has
Figure 10 comparesthe uplift andmeltinghistoryfor three
mantle viscosity models. The lower mantle viscosity is
spreadbeneaththe lithosphere,
andthusthe volcanicactivity r/lm=3X102•
Pas (for modelA), rhm=102•
Pas (formodelB),
may be synchronous
with the uplift phase.
andrhm=3X10
TM
Pa s (for modelC), thecorresponding
upper
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(solidline)andmeltvolume
(dashed
line)history
forviscosity
modelA, r//m=3X102•
Pas,
r/um=3X102ø
Pas;viscosity
model
B, r//m=10
22Pas, r/um=1021Pa
s; viscosity
modelC,r//m=3X10
22Pas,
r/um=3X102•
Pas. Forall models
theinitialdiapirhasATo=350øC,
Ro=400km andtheinitialageof the
lithosphere
is 100Ma. Notethattheunbracketed
andbracketed
numbers
ontheupliftscalereferto maximum
andminimumvalues,respectively.
Maximumvaluesarefor theupliftfromabyssal
oceanic
depthsandwitha
thermal
expansion
coefficient
of 3x10-5øC-•. Minimum
values
areforsubaerial
upliftwitha thermal
expansion
coefficient of 2x10 '5 øC-•.
13,824
FARNETANI AND RICHARDS' FLOOD BASALT MODELS
Viscosity
model
A)
(a)
(d)
Temperature profile
of the lithosphere at 115 rn.y.
50
• lOO
Initial temperature profile
of the lithosphere
r--0
..
•*
•
', r=606
......
•....r•0
,
I
150
Error
function
conduction
<•..r=600 '"G
I
profile at age 115 Ma
I
I
I
I
I
200
0
(b)
Viscosity
model
B)
Temperature profile
of the lithosphere at 145 m.y.
50
r=0
•
100
r=600
Error
150
function
•).,r=600
conduction
profileat age145Ma -•
200
0
Temperature profile
of the lithosphere at 210 m.y.
50
•
(f)
(c)
Viscosity
model
C)
100
r=0
m•mmmmm
Q
!
Error
150
function
.¸
r=600
conduction
.67"
profile at age 210 Ma
200
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Dimensionless Potential Temperature
1.4
0
I
I
•
5
10
15
20
Melt fraction (wt%)
Figure11. (left)Dimensionless
potential
temperature
versus
depth.
Thesolidlineis theerrorfunction
conduction
profilecalculated
at thetimeof maximum
meltproduction.
Thetemperature
profileof the
lithosphere
is indicated
atradialdistance
r=0kmfromtheaxis(solid
linewithcircles)
andr=-600
km(solid
linewithdiamonds).
Notethateachsymbol
corresponds
to a nodein thefiniteelement
grid.Thedashed
linein
Figure1l ais theinitialtemperature
profilefora 100Ma oldlithosphere
imposed
asinitialcondition
in all
models.
(a)Forviscosity
model
A, r//m=3X1021Pa
s, r/um=3X102ø
Pa•s.
(b)Forviscosity
model
B, r//m=10
:: Pa
S,?•um----1021Pa
s.(c)Forviscosity
model
C, r//m=3X10
• Pas,r/um=3X1021Pa
s.(fight)
Distribution
ofthemelt
fraction
withdepth
atradialdistance
r=0andr=-600
km.(d)Forviscosity
model
A. (e)Forviscosity
model
B.
(f) Forviscosity
modelC. In all themodels
theinitialdiapirhasAT0=350øC,
R0=400km.
FARNETANI AND RICHARDS-FLOOD BASALT MODELS
mantle viscosities satisfy ¾=10. For all models the initial
13,s25
dinpithasAT0=350øC
and R0=400km, the initial ageof the
sublithospheric
mantlefacilitatesthe radial spreadingof the
plumehead.By contrastfor viscositymodelC (Figure1l c) the
lithosphere is 100 Ma and extension is not allowed. The
temperaturesfrom 20 to 100 km depth, can be 20 to 70%
viscosity
of the mantlegovernsthe ascentrateof the diapir. higherthan the expectedvalues,at radial distancesr=0 km. In
For the two extremeviscositymodelsconsidered(i.e., A and thiscasethe plumeheadtendsto pondbeneath
thelithosphere
C), the diapirrise timesdiffer by an orderof magnitude(10 sinceits radialspreading
is inhibitedby the highviscosityof
m.y. versus100 m.y.). Higher valuesof the mantleviscosity
increasethe lag time betweenpeakuplift andmagmatism
and
increasethe maximumuplift. The total melt volumeis instead
reduced(-30%), sincethe progressive
agingand coolingof
the lithospheretend to inhibit melting.Figures1l a, 1lb, and
1l c showthe temperature
profile of the lithospherefor the
viscositymodelsA, B, andC, respectively.
The profilesare
given at radial distancesr=0 and r=600 km from the axis of
symmetry and are calculated at the time of maximum melt
production.
The temperature
differencebetweentheseprofiles
and the theoretical error function profile, calculatedat the
same age, indicatesthe amountof "thermalrejuvenation"of
the lithosphere. For viscosity model A (Figure l 1a) the
temperaturesare higher than the expected(-20-30%) only
from 60 km depth to the base of the lithosphere(-100 km
depth), thus suggesting that the lithosphere is not
significantlyheatedby conduction.The profile at r=-600km is
similar to the one on the axis, sincethe low viscosityof the
the upper mantle. This also explainsthe modestincreasein
temperatureat distancer=600 km, comparedto the profile at
r=0 km. However, we note that melting always occursat
sublithosphericdepths (i.e., deeper than-100 km), as
indicated
in Figures11d,11e,and11f, wherewe plotthemelt
fractionversusdepth for the viscositymodelsA, B, and C,
respectively.
We alsofind thatoverthewholerangeof mantle
viscositystructuresinvestigatedthe variationin melt volume
is very modest(from 2 to 4x106 km3), probably because
thermalrejuvenation
counterbalances
the progressive
agingof
the lithosphere.
For a few
models we have considered the effect
temperaturedependentviscosity.As discussed
previously,we
usethe law r/(T)=r/0exp(-n.60T
). The viscositycontrast
acrossthe lithosphereis 2 orders of magnitude,while the
diapirviscosityis 3.5 timeslessthanthatof the surrounding
material(for an initial excesstemperature
of 350øC).Figure12
shows the uplift and melting history for a temperature
5.0
(a)
Temperature dependent viscosity
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
0.0
i
Standard
viscosity
model
4.0 [1.90]
(b)
Initial
Lithospheric
Age:
20Ma•
10.0
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
15
of
I
I
I
20
25
30
•
.•
35
40
0.0
45
Time (m.y.)
Figure12. Upliftandmeltvolumeversus
elapsed
time.(a) Forthetemperature
dependent
viscosity
case.(b)
Forthe standard
viscosity
model.In bothcases,AT0=350øC
and R0=400km. Notethattheunbracketed
and
bracketed
numbers
on the uplift scalereferto maximumandminimumvalues,respectively.
Maximumvalues
are for the uplift from abyssaloceanicdepthsand with a thermalexpansioncoefficientof 3x10-5 øC-1.
Minimumvaluesarefor subaerial
uplift with a thermalexpansion
coefficientof 2x10'5 øC-1.
13,826
FARNETANI AND RICHARDS' FLOOD BASALT MODELS
dependent viscosity case (Figure 12a) and for the standard
viscosity model (Figure 12b). In both cases the initial
lithospheric age is 20 Ma and lithospheric extension above
30 km depth is prevented by setting the radial velocity to
zero. For the case with temperaturedependentviscosity, both
uplift and melt productionpeak earlier in time, since the lowviscosity thermal diapir rises more rapidly in the mantle.
Because of the stiffer behavior of the lithosphere, melting
occurs at greater depth, and thus the total melt volume
is intersectedare functions of the excesstemperatureof the
diapir. The melt volume also increaseswith increasingR0;
this result is fairly intuitive, but we also find that the melt
volumesproducedfor R0=500 km at AT0-300-330øC are
relatively low. We find that the curvatureof the upper part of
the plume head first impinging on the lithospheredecreases
with increasing R0. A large flat head does not seem to
efficiently remove, by lateral flow, the thin layer of material
trappedbetween the stiff lithosphereand the plume head. The
produced
is reducedto -4x106km3 (for the standard
modelthe behavior of this "squeeze layer" [Griffiths and Campbell,
melt volumeis -9x106 km3).This suggests
that the standard 1991] and its ability to drain horizontally affect the depth to
lithosphericstructureis 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 temperaturedependentviscosity AT0-300-330øC. For AT0>330øCthis 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-temperature
gradients.(We checkedthat this
the model we have specified, little softening of the effect is not a function of the width of the finite element
lithosphereoccursprior 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.)
The next set of models addresses the effect of the initial
not attemptedto model that effect. Still, we are confidentthat
the most important factor is whether or not the uppermost lithosphericage on the total melt volume. Figure 14 shows
lithosphereextendsfreely, and a more sophisticatedtreatment the melt volume as a functionof 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,lithosphericextensionis prevented,
the excess temperature. Figure 13 shows the maximum melt andweuseR0=400 km, Illm= 1022Pas andtlum=
1021Pa s. For
volume as a function of the initial excess temperature the case of a young oceaniclithosphere,the total melt volume
(300 <-ATo <-400øC) and initial radius (300<-R0 <-500 km),
produced
rangesbetween1 and 17x106km3, whilefor an old
for a modelwith •/tm=10
22Pas and•/um=10
21Pas (y=10)anda
lithospherethe melt volumes are reducedapproximatelyby a
factor of 2 over the temperaturerange investigated.We also
show the effect of varying the entropy of fusion from the
nonrifting lithospherewith initial age of 20 Ma. For an initial
excesstemperatureof 300øC, independentof the initial radius
of the diapir, the melt volume generatedis equal or less than
usuallyadoptedvalueof 250 J kg-1øK-1(solidline), to 400 J
106km3. Givensucha low value,compared
with theestimates kg-1øK-1(dashedline). The melt volumeis reducedby -30%
for large flood basalts and oceanic plateaus, we consider
AT0=300øCas a lower boundfor the initial excesstemperature
of the diapir (for nonrifting lithosphere). The melt volume
strongly depends on AT0, since both the melt fraction
producedat a given depth and the pressureat which the solidus
over the whole temperaturerange investigated.McKenzie and
Bickle[1988]suggest
thatif AS=400J kg-• øK-1is usedin the
melting model, then the required potential temperatureof the
mantle (Tm) is 1300øC, rather than 1280øC. The solid
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
oø R =500
0
-
o•OO•øø
6.o
8.0
-
0.0
300
320
340
360
380
400
Initial Excess Temperature (øC)
Figure13. Totalmeltvolumeversus
initialexcess
temperature
for initialdiapirradiusR0=300km (long
dashed
line), R0=400 km (solidline), R0=500km (shortdashed
line).
FARNETANI AND RICHARDS' FLOOD BASALT MODELS
13,827
Initial Diapir Radius = 400 km
111dqum
= 10
16.0
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 volumeversusthe initial excesstemperature
for initial lithospheric
ageof 100 Ma
(lineswith opencircles)and20 Ma (lineswith opentriangles).The entropyof fusionusedin the melting
modelis •S=250 J kg-• øK-•(solidlines)and•S=400 J kg-• øK-• (dashed
lines).In all casesthepotential
temperature
of the m•tle is T• =1280øC.The two solidsymbolsare calculatedusing•S=400 J kg-• øK-• and
•øK'• and Tm=1300øC,
and indeedthe melt volumesare -28xl 06km3, whileif extension
is prevented
the meltvolume
comparablewith the ones of the standardmodel.
The case of initially zero age lithosphere is treated
separately,since we also changethe top boundarycondition
to radial free slip, thus allowing the lithosphereto extend.
This hasa majoreffecton the meltvolumes,whichincreaseby
producedis negligibly small (0.03x106km3). However, the
axisymmetric geometry is not entirely appropriate to
modeling unidirectional extension (rifting) over a mantle
plume, and thus the calculated melt volumes should be
consideredas upper bounds,approximatingthe scenarioof a
an orderof magnitude
(i.e., -50x106km3,for AT0=350øC
and plume head impingingon a ridge-ridge-ridgetriple junction.
R0=400 km) as meltingoccursat shallowdepths(20-100 km)
with melt fractionsas high as -30%. Table 2 showsthe melt
volumes,the depthof the meltingzone, and the meanMgO
concentrationfor initial lithosphericages of 0, 20, and 100
Ma, if extensionis allowed. Melt volumesgeneratedwith
Figure 15 illustratesthe uplift and melt volume calculated
when lithosphericextensionis allowed. The uplift generated
for rifting modelsappearsto be very large,exceeding5 km in
some cases. However,
this is somewhat an artifact of the
referencelevel chosen.Calculateduplift is the total amplitude
AT0=350øCare of order40-50x106km3, independent
of the of surfacedeformationfrom the axis to the outsideedgeof our
initial age of the lithosphereand the viscositymodel. (The model domain, so "extra" uplift arises from lithospheric
results
aregivenfor thestandard
modelwith film
= 1022Pa s and thinningabovethe plume and lithospheresinkingat the outer
r/um=1021
Pa s, andfor a modelwithtemperature
dependent 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
temperature
as low as ATo=250øCcanproducemelt volumesof depth,so that even a model uplift of the oceanfloor of 5 km
Table 2. Models with LithosphericExtensionAllowed
AT0'
Initial
Age,
Extension Viscosity
Allowed
Model
Melt
Volume,
Depth of
Melting,
Maximum
Melt
Mean
MgO,
Fraction,
øC
Ma
x 106 km 3
25 0
20
no
standard
25 0
20
yes
standard
28
35 0
20
no
standard
9
35 0
350
20
20
yes
yes
standard
rl(T)
49
35 0
100
no
standard
4
350
350
35 0
100
100
0
yes
yes
yes
standard
rl(T)
standard
km
wt%
wt%
~30
15.5
18
18
0.03
45
20-100
75-150
20-130
20-100
100-150
20-130
39
5O
20-110
20-130
41
-22
-34
-28
18
-14
17.5
-30
18
-30
17.5
18.5
-35
13,828
FARNETANI AND RICHARDS' FLOOD BASALT MODELS
7.0
60
[3.32]
Extension
allowed
Initial Lithospheric Age: 20 Ma
5.0
so
[2.37]
40
•
30
e•
3.0 [1.43]
2O
10
1.0
[0.47]
15
20
25
30
35
40
I
I
45
50
55
Time (m.y.)
Figure 15. Uplift and melt volumeversuselapsedtime if extensionallowed.The initial age of the
lithosphere
is 20 Ma, thediapirhasATo=350øC
andRo=400
km,themantle
viscosity
modelis rllm=1022
Pas,
11um=1021Pa
s. Notethattheunbracketed
andbracketed
numbers
on theupliftscalereferto maximum
and
minimumvalues,respectively.
Maximumvaluesare for the uplift from abyssaloceanicdepthsand with a
thermalexpansion
coefficient
of 3x10'5øC'•.Minimumvaluesarefor subaerial
upliftwitha thermalexpansion
coefficient of 2x10 -5 øC-•.
may not representuplift above sea level. Thus the "dynamic" etc., which are comparableto thoseobservedor inferredfrom
componentof uplift due to the plume does not exceedthat field studies.
obtained in the nonrifting case.
The batch melting model of McKenzie and Bickle [1988]
allows us to estimate the average melt compositionsin each
model.Thoughwe calculatethe concentrations
of all the major
oxides in the melt, we considerMgO concentrationto be the
most indicative concerningthe nature of the primary magma.
The mean MgO concentration is obtained as a weighted
average over the whole melting region. Figure 16 showsthe
mean MgO concentration,evaluated at the time of maximum
melt production,as a functionof the initial excesstemperature
of the diapir. The resultsare given for initial lithosphericages
of 100 and 20 Ma, when the initial radius of the diapir is 400
km. The mean MgO concentrationrangesbetween 16 and 19
wt %, the higher values being obtained for higher initial
excesstemperaturesand for youngerlithosphericages.These
very high MgO concentrations
resultfrom the greatdepthand
the large degree of melting in all cases.Similar values for
MgO are found also for the rifting models(seeTable 2).
Discussion
One issue we set out to address was the effect of mantle
viscositystructureon observableaspectsof mantleplumes.
We have investigatedviscositycontrasts(7= rltrn/•um)from
lower to uppermantleof 1 (7=10) and 2 (7=100) ordersof
magnitude.A high-viscositycontrastinducesa narrowingof
the plumeheadas it entersthe uppermantle.This "necking"
occursbecausethe rise velocityof the plumeheadincreasesas
the viscosityof the surroundingmediumis decreased.The
neckingof theplumeheadcauses
a reduction
of boththeradius
of the plumeheadfirst impingingon the lithosphere
and the
radial extent of the melting region. Moreover, for a model
with 7=100, a largevolumeof the diapirremainsin the lower
mantle for 10-20 m.y., favoring the entrainmentof lower
mantlematerial,while uppermantlematerialseemsto be less
easilyentrainedgiventhe limitedsurfaceextentof the narrow
conduit. Thus the effect of thermal entrainment in this case
would differ in detail from the one suggestedby Griffiths and
Campbell[1990] for a uniformviscositymantle.
We have also attempted to constrainthe initial excess
temperatureof rising plume heads,treating the case of
nonriftinglithosphere
as the moststringenttest.We find that
We have investigatedthe rise of a thermal diapir in the
mantle and its interaction with the lithosphereprior to and
for the McKenzie and Bickle [1988] batch melting model
field and analytical data. In this study we did not attemptto
satisfy the specific characteristicsof any single flood basalt
or oceanic plateau. Instead, we wanted to explore the
conditionsunder which it is possibleto obtain melt volumes
and compositions,melt productionrates, degreesof uplift,
initial
employed,risingplumeheadsmustbe at least300øChotter
duringmelting,usinga numericalmodelthatcombinesmantle 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
is ~100øC higher than
approachallows us to developmore fully somepredictionsof boundon initial excesstemperatures
the mantle plume initiation model and to analyze the one estimatedfrom laboratoryexperiments[Griffiths and
of
quantitatively their dependenceon the model parameters. Campbell,1990], whichdoesnot accountfor the presence
Hopefully, this will form a strongerbasisfor comparisonwith the lithosphere.Furthermore,we find that a diapir with an
radius of 400 km needs to have an initial
excess
temperature
of 350øCin orderto generatemelt volumesof ~39x106 km3 if the lithosphereis older than 20 Ma and if
extensionis prevented.(Note that the results for initial
lithosphericage of 100 Ma might be consideredas "upper
FARNETANI
AND RICHARDS:
FLOOD
BASALT
MODELS
13,829
20.0
Initial Diapir Radius = 400 km
T]l
dT•um---10
19.0
2o
180
170
160
I
300
I
I
320
I
I
340
I
I
360
I
I
I
380
I
400
Initial Excess Temperature (øC)
Figure 16. Mean MgO concentrationof the melt versusthe initial excesstemperatureof the diapir for
modelswith initial lithosphericage of 100 and 20 Ma.
bounds" for an ancient cratonic continental lithosphere,
whose thickness may, in fact, be considerablygreater than
that of old oceanic lithosphere.) At the onset of melting the
potential temperatureof the plume head is •-1600øC, although
it decreasessomewhatin time due to the latentheat of melting.
The melt volume generated from these hot plume heads
greatly depends on the ability of the plume to ascend to
shallower depths, and decompressionmelting is an efficient
way to produce large melt volumes. We found that for the
modelswhere surfaceextensionis not allowed, the depthrange
of partial melting is mostly (•-90%) sublithospheric, since
there is not enoughtime to heat the lithosphereby conduction
abovethe solidusbeforethe plumeheadhas spreadand cooled
considerably.This conclusionis in agreementwith the work
of Arndt and Christensen [1992] on the role of lithospheric
approximately doubles as the initial lithospheric age is
reduced from 100 to 20 Ma.
The most importantincreasein melt volume (up to 1 order
of magnitude)is obtainedfor the casein which lithospheric
extension is allowed. However, given the geometry of our
model, the melt volumes obtained under radial free-slip
boundary conditions represent upper bounds, possibly
obtainedwhen a mantle plume is in the proximity of a ridge
triple junction. We suggestthat variationsin the degreeof
lithosphericextension may be reflected in the differences
between the melt volumes produced in continental flood
basalts and in oceanic plateaus. The melt volumes of
continental flood basalt provinces, though difficult to
reconstructbecauseof erosion,are of order 1-2x106km3 (but
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
sublithosphericdepths(>100 km). The geochemicalsignature
of the volcanic productscan constrainthe depth of melting,
and indeed,there is growingevidencethat someof the earliest
magmasin flood basaltsrepresentlow degreesof partial melt
formedin the garnetstabilityfield. For the SiberianTraps this
is indicated by the depletion of heavy rare earth elements,
combined with high incompatible element contents in the
initial lava suites [Wooden et al., 1993]. Similarly, for the
KerguelenPlateau, trace element and isotopic characteristics
indicate that the onset of melting has to be placed in the
garnet stability field [Salterset al., 1992]. Also the depthof
melting derived from rare earth element inversions over
plumes [White et al., 1992] is consistentwith initial low
degreesof melting in the garnetstabilityfield. A robustresult
in our modeling is that the conductive heating of the
lithosphereis not sufficientto induce large degreesof partial
melting in the lithosphere;this, of course,doesnot rule out
the likelihood of various degrees of lithospheric
contamination as the magma rises to shallower depths.
Certainlythe age and the behaviorof the lithosphereaffect the
depth of melting and thus the total melt volume, which
estimated
volumefor theKerguelen
Plateauis 9-15x10• km3 (if
BrokenRidge is included,the total volumeis •-15-24x10
•
km3), and the volume of the Ontong Java Plateau is •-3060x10• km3 [seeCoffinand Eldholm,1994].We speculate
that
such volume variationscould result entirely from differences
in the age and behavior of the lithosphere, rather than
differences in plume characteristics.The Kerguelen Plateau
probablyformedin a new oceanbasin,in closeproximityto
rifting continentallithosphere,just after the breakupbetween
Indo-Madagascarfrom Antarctica-Australia[e.g., Storeyet al.,
1992; Royer and Coffin, 1992]. The Ontong Java Plateau
instead formed in an intraoceanicsetting, far away from any
sizable continental mass [Mahoney at al., 1993; Tarduno et
al., 1991]. A near-ridge hotspot environment satisfies
geophysical and geochemical evidence [Mahoney and
Spencer,1991], thoughit can not be confirmedby studieson
magnetic anomaly lineations [Nakanishi et al., 1992].
Anyway, the scenarioof ridge jumping or a migratingtriple
junctionover a plumeheadcouldexplainthe melt volumeand
the high degreesof partial melting (~30%) [Mahoney et al.,
1993] for the Ontong Java Plateau. For the Shatsky Rise,
magnetic lineations indicate that the plateau formed on
13,83o
FARNETANI
AND RICHARDS:
oceanic lithospherealong the trace of a triple junction [Sager
and Hah, 1993].
The depth of melting affectsthe compositionof the primary
magma, and in our model, melt compositionsare rich in MgO.
This is a result of the high excess plume temperatures
(>300øC) required for sublithospheric melting without
extension. The mean MgO concentrationsrange between 16
and 19 wt %, with the higher values for younger oceanic
lithosphere and for higher excess temperaturesof the plume
head. The relation between the primary magmasat depth and
the volcanic products erupted or intruded at shallow depths
may be very complicated,and inferencesfrom a simple batch
melting model are not entirely satisfactory. However, it is
clear that if melting occurs beneath mature lithosphere, the
primary magma will have a "picritic-type" composition,so
that the erupted tholeiitic basaltsare likely derived via crystal
fractionation.
The majority of flows in flood basalt provinces are
tholeiitic basalts(MgO -5-8 wt %), and only at the initial and
waning stages of volcanism are there differentiated products,
from nephelinites to rhyolites. However, the restricted
occurrence of picrite basalts (MgO up to 12-16 wt %) is
observed in the Karoo [Cox,
1972], in the Deccan
[Krishnamurthy and Cox, 1977], in the North Atlantic
Tertiary province [Clarke, 1970], and in the Siberian Traps
[Zolotukhin and Al'mukhamedov, 1988; Wooden et al., 1993].
For the Siberian Traps there is evidence that the parental
magma of the entire suite of volcanic productswas close in
compositionto a picritic magma and that the primary process
of deep-seatedevolution was crystal fractionation [Zolotukhin
and
Al'mukhamedov,
1988; Wooden
et al.,
1993].
Krishnamurthy and Cox [1977] find that the picrite basaltsof
the Deccan crystallizedfrom ultramafic liquids containingin
some casesat least 16 wt % MgO and that the picrites show
bulk compositional variation generatedby the fractionation
of olivine and chromite. Moreover, the evolved picrite basalt
magma appears to have given rise to the basalts by the
fractionation of olivine and clinopyroxene.For the Karoo the
MgO contentsof the picrite basalt range from 10 to 24 wt %,
with an average close to 15 wt % [Cox, 1988]. Cox and
Jamieson [1974] suggestthat the less magnesian-richpicrite
basalts have compositions which closely approximate those
of the original liquids and that the major elementvariation of
the volcanic products is dominated by the fractionation at
high pressure(-10 kbar) of olivine and orthopyroxene.
The compositionof the plateausseemsto be predominantly
tholeiitic [Davies et al., 1989]; for the KerguelenPlateau the
tholeiiteshave 4-10 wt % MgO [e.g., Storey et al., 1992], and
similar values (MgO 4-9 wt %) generally characterize the
Ontong Java basalts [Mahoney et al., 1993]. On the other
hand, the volcanic sequenceof the oceanic plateauscan be
investigated only through drilling, which is limited to the
uppermost part of a plateau. An alternative approach to
elucidate the deeper crustal levels is through the study of
fragments preserved in allochtonousterranes,like Gorgona
Island (Colombia), probably a fragment of the Cretaceous
CaribbeanPlateau [Storeyat al., 1991]. The most magnesianrich flows are komatiites, with MgO up to 24 wt %. Their
textural and mineralogical features indicate that they
crystallizedfrom superheatedliquids, with estimatederuption
temperatureof order 1500øC,and that the primarymagmahad
an MgO contentof-20 wt % [Aikten and Echeverrfa, 1984].
Petrological evidence thus indicates that at least some
primary magmas likely have a picritic composition,possibly
FLOOD BASALT MODELS
with even higher MgO contentsin the caseof oceanicplateaus
[Storey at al., 1991]. However, it is no surprise that the
picrites appear only rarely at shallow crustal levels, since
their density is higher than either average continental or
oceanic upper crust. We suggestthat large volumes of crystal
cumulates may reside at the crust/mantle interface beneath
major flood basalt provinces. They should show up as highvelocity lower crustal layers, and there is, in fact, evidencefor
such layers beneath the Columbia River Basalt province
[Catchings and Mooney, 1988] and beneaththe DeccanTraps
[Verma and Banerjee,
1992]. Moreover, refraction
experiments on the Kerguelen Plateau [Charvis and Operto,
1992] and on Broken Ridge [Francis and Raitt, 1967] indicate
the presence of a lower crustal body with high seismic
velocities (7.3 km/s); similarly, a -16-km-thick lower crustal
body with high seismic velocities (7.4-7.7 km/s), is found in
the central Ontong Java Plateau [Furumoto et al., 1976]. This
suggeststhat residual magmaswould be tapped episodically
from the top of a broad, lenticular magma chamber at the
Moho which would be undergoing continual crystal
fractionation. We make no attempt here to guessthe residence
time of such magmas,but there would certainly be opportunity
for geochemicalinteraction with the lower crust and mantle
lithosphere.This agrees with Cox's [1980] model for flood
basalt volcanism, according to which the uniform
compositionof the tholeiitic basalts (MgO 4-7 wt %) can be
obtained from polybaric evolution of a picritic parent magma
(MgO up to 18 wt %). The first phaseof crystallization(-25%)
is mainly of olivine, and it is followed by the crystallization
(another -25%) of olivine-clinopyroxene-plagioclase at
shallower depths, probably in sills intruded at the Moho. Cox
[1980] concluded that the minimum volume of concealed
cumulatescan be at least as large as the amountof the erupted
surface lavas.
In attempting to model uplift history we have only
accountedfor thermal buoyancyeffects. We have not included
specific volume changes due to crystal fractionation or
metamorphismin the deepcrust[Falvey and Middleton, 1981],
nor have we includedthe effect of magmaticunderplating[Cox,
1989], even though these processescould influence the uplift
and subsidencehistory of a flood basalt province. In general,
surfaceuplift starts at least 10-20 m.y. prior to the expected
volcanic activity. Regardlessof the mantle viscositystructure
we have found that the time sequenceof dynamic uplift,
subsidence,and volcanic activity occursover an area within a
radial distanceof-350-400 km from the plume axis. At greater
distances the uplift phase is induced mainly by the
sublithosphericspreadingof the plume head, and it may be
synchronous
with the volcanicactivity. For many flood basalt
provinces there is growing geological evidence that uplift
started at least several million years before volcanism,
although it is generally difficult to quantify uplift for
continental
flood basalt events. For the Karoo and the Deccan
[Cox, 1989, and references therein] and for the Paran•i
[Piccirillo et al., 1988] the stratigraphic sequence and
geomorphologicalevidence indicate the progressivechange
from marine to subaereal
conditions
over broad areas before
flood volcanism. In the Siberian Traps, doming and the
formation of arch structuresprecededvolcanism[Zolotukhin
and
Al'mukhamedov,
1988].
Postvolcanic evolution is
generallycharacterizedby subsidence,
but as pointedout by
Cox [1988], provincessuch as Deccan, Paran•i,and Karoo
show evidence of postvolcanic uplift, so that uplift and
erosionappearto be long-livedand continuingphenomenain
FARNETANI
AND RICHARDS: FLOOD BASALT MODELS
these areas. Cox [1988] suggested that the pattern of
highlands may simply be a map of the zones of maximum
magmaticunderplatingor that the dynamicsof such areasis
further complicated by the subsequentevolution of the
continentalmargins.For the oceanicplateausit is difficult to
reconstruct the sequence of prevolcanic and postvolcanic
events since the plateaus are presently submerged, but
subsidence
analysisindicatesthat at least part of the Ontong
Java Plateau was emplaced in shallow water conditions
[Tarduno, 1991], while the KerguelenPlateaueruptionswere
apparently subaerial, with subsidence below sea level
occurring up' to 40 m.y. after the cessation of volcanism
[Coffin, 1992].
Our models,which are constrained
to produceat leastseveral
million cubic kilometersof melt beneathunriftedlithosphere,
predict rather large uplifts of order 2-4 km, dependingon
whetherthe environmentis continentalor oceanic.Perhaps
the mostdetailedevidencefor uplift accompanying
an oceanic
flood basalt province is found in the Triassic strataof the wellknown Wrangellia terrane of SE Alaska and British Columbia
[Joneset al., 1977]. Wrangelliais an accretedoceanicplateau
containing a 3-6 km thick tholeiitic flood basalt, sandwiched
betweenTriassic stratathat recordthe entire uplift/subsidence
history of the province. The largely subaerialflood basalts
were eruptedin at most a few million yearsand were followed
by gradualthermalsubsidence
of the plateau.Eventspreceding
flood volcanisminclude rapid emergencefrom conditionsof
deep, open ocean (chert) deposition,as well as several lesspronounced,perhapslocally varying, subsidenceand uplift
events just prior to eruption. The magnitude of uplift is
inferred to be of the order of several kilometers. There is no
evidenceof significantcrustalextensionaccompanyingany
of these events. This sequenceof events is in excellent
agreementwith the "nonrifting"modelsdevelopedhere, and
we have previously suggestedthat Wrangellia is an almost
ideal exampleof flood volcanismdue to a new mantleplume
impinging on old oceanic (actually, extinct island arc)
lithosphere[Richards et al., 1991]. Our modelscannotaddress
the complexity of the crustal/mantlestructureunder a volcanic
arc, but the likely presence of volatiles would certainly
enhance melting without substantially changing the time
evolution of uplift and melting.
A related and long-debatedproblem is the relation between
flood volcanism and continental break-up. As we already
pointed out, some flood basalt provinces (e.g., the Siberian
Traps, the Columbia River basalts,and a major event of the
Karoo at 193 Ma) were not associatedwith the openingof a
new ocean or with major extension. For other provinces,
which are associatedwith continental rifting, there is often
geological evidence suggestingthat the volcanism predates
the major extension. This is the case for the Paranti [Piccirillo
et al., 1988], as shown by recent high-precision radiometric
dating [Renne et al., 1992] which indicatesthat the volcanism
predatedthe opening of the SouthAtlantic by -5 m.y. On the
other hand, lithospheric uplift causedby the thermal diapir
results in horizontal deviatoric stress, and such extensional
stresses may at times be sufficient to induce continental
extension. Hill [1991] and Houseman and England [1986]
conclude that uplift of-1-2 km of continental lithosphereis
insufficient to provide the driving force for continentalbreakup, even if it may produce sufficient gravitational potential to
induce a local tectonic reorganization. We find that
extensional
deviatoric
stresses
stress
are
occurs
modest
well
and
before
that
the
the
maximum
maximum
melt
13,831
production. However, some thermal weakening must occur,
especially after melt intrusion, and this may facilitate
extension during volcanism. The particular regional
lithosphericresponseto the arrival of a new plumewill depend
on the nature of the lithosphere itself, other plate tectonic
forcesactingon it at the time, and perhapsalso the motionof
the lithospherewith respectto the plume.
The great variability of geologicalcircumstancesattendant
to flood volcanism
attests to the fact that interaction
between
a thermal plume and the lithosphereis very complex, and our
simple model must surely be inadequate after the onset of
melting. We have ignoredthe physicsof magmamigration,as
well as many effectsof temperatureand pressurein the melting
zone. Axisymmetric geometrydoesnot allow us to investigate
the effects of unidirectional rifting over a plume or the
development of small-scale convective instabilities within
the plume as it spreadsbeneaththe lithosphere[Griffiths and
Campbell, 1991]. A fully 3-D model could treat these
problems,and it would alsobe possibleto calculatethe effects
of external forces (i.e., those driving plate motions) or
preexistingzones of weaknessin the lithosphere.
Perhaps our most significant assumptionsinvolve the
melting model itself, and implementationof a more realistic
melting scheme could yield important new insights. A
fractional or Rayleigh melting scheme would allow us to
calculate how the composition of the residuum varies as
melting progresses.In this case the melt fraction would be a
function not only of the pressureand temperature(as used in
the batch melting model) but also of the evolving bulk
compositionof the residual matrix.
The melting model we have used is anhydrous,and small
amountsof water in the mantle can lower the peridotitesolidus
by severalhundreddegrees[Bonatti, 1990; Jaquesand Green,
1980]. A compelling case has been made recently by
Gallagher and Hawkesworth [1992] for the potential
importance of water in the mantle lithosphere, and they
suggestthat flood basaltsmay be generatedby the melting of
hydrous phases in the lower continental lithosphere due to
impingementof a mantle plume. Obviously,our resultsdo not
addressthis petrologicalmodel, and we hopeto includemodels
for hydrous melting in future work. However, our focus here
has been on plume interaction with a model oceanic
lithosphere, and it seems unlikely that the oceanic mantle
lithosphere, having been depleted by extensive partial
melting at a mid-ocean ridge, would retain a significant
volatile content. The high plume temperatureswe infer from
modeling of sublithospheric, anhydrous melting in the
absenceof extensionrepresent,as we said at the start, an endmember result from perhaps the simplest geologically
relevant
case.
Acknowledgments.
The authors are grateful to Scott King for
providingthe codeConMan in the originalCartesianversionand for his
helpful suggestions.We thank Louise Kellogg and Chi Wang for useful
technicaldiscussions.
We also thank LouiseKellogg, RobertWhite and
Mike Coffin for constructivereviews of the paper. Carolina LithgowBertelloni and Chuck Wicks are thanked for their generoushelp and
encouragement.This work was supportedby NSF grantsEAR9018507
and EAR9057012
awarded
to M.A.R.
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