Download Evolution of Seafloor Spreading Rate Based on 40Ar

GEOPHYSICALRESEARCHLETTERS, VOL. 20, NO. 9, PAGES851-854,MAY 5, 1993
EVOLUTION OF SEAFLOORSPREADING RATE BASED ON 4øAtDEGASSING HISTORY
EiichiTajika1 and TakafumiMatsui
Departmentof EarthandPlanetaryPhysics,
Universityof Tokyo
Abstract A new degassing
modelof 4øAt coupledwith
thermal evolution of the mantle is constructedto constrain the
temporalvariationof seafloorspreading
rate. In thismodel,we
take into accountthe effectsof elementalpartition and solubil-
ity duringmeltgeneration
andbubbleformation,andchanges
in both seafloorspreading
rate andmelt generation
depthin
the mantle. It is suggested
that the seafloorspreading
rate
wouldhavebeen almostthe sameas that of today over the
historyof the Earth in orderto explainthe presentamountof
4øAtin theatmosphere.
Thisresultmayalsoimplythemild
mantle potassiumconcentratesinto melt being associatedwith
melt generationin the mantle belowthe mid-oceanridge, and
eventually solidifiesas the oceanic crusts. Thus, potassium
concentrates
into the oceanic crust from the mantle
concur-
rentlywith4øAtdegassing.
Potassium
in theoceanic
crustalso
decayto 4øAtwhichwoulddegasto the atmosphere
probably
by diffusionthrough the oceaniccrust or by arc volcanismsat
the subductionzone. Potassiumremainingin the oceaniccrust
would finally return to the mantle.
The continental crust is consideredto have formed by
remelting of the oceanic crust with water at the subduction
zone[e.g.,Campbelland Taylor, 1983]. If this werethe case,
degassinghistory of volatilesfrom the mantle.
the parts of potassiumin the subductingoceaniccrustsmight
be transported to the continental crust at the time of its for-
Introduction
mation. 4øAtproducedby potassium
in the continentalcrust
Temporalvariationof seafloorspreadingrate overthe his-
KAr
hasdegassed
to theatmosphere
withdecayconstant
D,cc--
tory of the Earth hasprofoundinfluences
on the globalgeo3.71 x 10-•ø yr-1 whichis estimatedfroma relationbetween
chemical
cyclethroughvolatiledegassing
fromandregassing K-At mineral ages and Rb-Sr whole rock agesfor the same
into the mantle. In other words, it affectsthe evolutionsof
crustalrock [Hamanoand Ozima,1978].
the atmosphereand oceans,and thus the terrestrialenviron-
ment[e.g.,McGovern
andSchubert,
1989;TajikaandMatsui,
1992,1993].It is, however,difficultto reconstructsucha tem-
poralvariationof seafloor
spreading
rate fromany geological
evidence. This is because the ancient seafloor itself has sub-
We can calculate transportation of K and Ar between various reservoirs using a simple box model composedof three
potassium
reservoirs
(mantle,oceaniccrust,continental
crust)
and of four argonreservoirs(mantle,oceaniccrust,continental
crust,atmosphere).The massbalanceequations
for argonand
ductedinto the mantle. Because
the seafloor
spreading
rate
playsa dominant
rolein transfer
ofinternalheat[e.g.,Turcotte
potassium are as follows:
and Schubert,1982],we may obtain the evolutionof seafloor
D
•(4øK)ma,
, = -• Tk'40
K,}mant-- KK(4øK)ma,t+(1-AK)tr-X(4øK)
spreading
rate by studyingthe globalgeochemical
cyclecou-
d
pled with the thermal evolution of the mantle.
In this paper, we try to infer the temporalvariationof
seafloorspreading
rate, usinga newdegassing
modelof 4øAt
coupled
withthermalhistoryof themantlein whichtemporal
variationof degassing
rate is assumed
to dependon changes
in seafloorspreading
rate and melt generation
depthin the
•t(4øK)oc
=--AT(4øK)oc
+KDK(4øK)m•,t
--tr-X(4øK)oc
(2)
+
dt
d 40
•( Ar)m•,t
= A•(4øK)m•,tK•"(4øAr)m•,t(4)
mantle.
Models
dt
We use4øAtasa tracerfor the mantledegassing.
4øAxis
-dtd
consideredto be the best tracer for the degassing
history of the
mantle amongvariousvolatile components.This is because
d -4o -
(1) 4øAtis a decayproductof potassium,
andsoverylittle
amount of 4øAt existed at the time of formation of the Earth.
This meansthat 4øAtmay not haveexperienced
impactdegassingwhichis considered
to haveoccurredduringaccretion
of the Earth [e.g.,Matsuiand Abe, 1986].(2) The existence
of 4øAtin the presentatmosphere
suggests
the occurrence
of
subsequent
continuousdegassing
overthe historyof the Earth
[e.g.,Turekian,
1964;Hamano
andOzima,1978].And(3)4øAt
probablyhas not experiencedany regassinginto the mantle,
which meansthat we can only considerthe degassingprocess
for the caseof 4øAt. In theserespects,4øAtis considered
to
be an adequateindicatorto constrainthe degassing
historyof
the Earth
after its accretion.
4øAtis produced
by potassium
decayas 4øK+e- -,4øAt,
wherethe decayconstantis ;•e=5.85x10
-n yr-•. 4øAtproducedin the mantle degasses
to the atmospheremainly through
the mid-oceanridge volcanismaccompanied
by the formation
of oceaniccrusts. Sincepotassiumis an incompatibleelement,
=
-
=
-
=
(5)
D,cck
wheretr is the residence
time of seafloor(=area of seafloor/
seafloor
spreading
rate), K}) ia thecoefficient
ofdegassing
rate,
and),T is thetotal4øKdecayconstant
(= 5.305x 10-•øyr-•).
ß
Subscriptsrepresent as follows: mant = mantle, oc = oceanic
crust, cc = continental crust, and arm = atmosphere,respectively. A•½is the accretionratio of potassium,which is a free
parameter in this model. The fraction A•½ of potassium in
the subducting oceaniccrust is assumedto be transported to
the continentswith continental growth. A•½is iteratively determined so that the amount of potassiumin the continental
crust at present may be equal to the observedamount. We
consideredvariousmodelsof continentalgrowth. However,the
continentalgrowth model did not affect the numericalresults
seriously(Table2), andthenwe usethe modelwith a constant
growth rate as a standard.
The degassing
processof Ar is modeledas follows:4øAt
Copyright
1993by theAmericanGeophysical
Union.
in a certain volume Vo of the mantle degasto the atmosphere
when oceanicplates are formed at the mid-oceanridge. This
volume Vo probably dependson the seafloorspreadingrate Sr
and the melt generationdepth d,• in the mantle. Assuminga
Paper number93GL00731
first orderrate process
(i.e., assuming
a homogeneous
mantle),
0094-8534/93/93GL-00731503.00
the degassing
rate Fo of 4øAtfromthemantleis expressed
by
•Nowat Geological
Institute,Universityof Tokyo
851
852
Tajika and Matsui: Evolutionof SeafloorSpreadingRate
rv -
'ß
(8)
whereK• r is thecoefficient
ofdegassing
rateofargon.
In the previousstudiesof degassing
history[e.g.,
Turekian,1964;Hamduoand Ozima, 1978],the coefficient
of
degassingrate was given as an adjustableparameter for the
degassinghistory and called "degassingconstant". However,
in this study, we define the coefficientof degassingrate as
follows[e.g.,TajikaandMatsui,1992]:
Forsythand Uyeda(1975)suggested
that platemotionmay
be driven by the forcesacting on the downgoingslab and that
drag force on the bottom of oceanic plates may be less important. If this were the case, the oceanichthospherewould
couple weakly with the' underlying flow becauseof lower vis-
cosityof asthenosphere
[Forsythand Uyeda, 1975]. This is
consistentwith the numerical result of thermal history of the
mantlewith variableviscosity[Christensen,
1985]. According
to Christensen
(1985),the Rayleigh-Nusselt
exponent/•should
be nearlyzerounderthe conditionof the mantleconvection,
K•V(t) -=far' VD(t)IVM-- far' St(t). dm(t)/VM (9)
and in sucha caseseafloorspreadingrate becomesto be constuntin spiteof drasticchangein convective
vigor. Therefore
whereVM is the volumeof the mantle,VD(t) is the volumeof
mantle material from which degassing
occursin an unit time,
weconsider
anothermodelin which/• is setto be zero("the
modelB"). In this model,the seafloorspreading
rate is con-
St(t) is theseafloor
spreading
rate,anddin(t)is themeltgen- stant at the presentvalueoverthe historyof the Earth.
We needto knowthe total amountof potassiumto calculate
erationdepth in the mantle. Here we assumethe degassing
of4øAtproduced
bythepotassium
decay.
Because
volumeVt>= Sr x din, whichis time-dependent
in this case. theamount
it is difficultto estimatepotassium
contentin the presentmanJAr is the degassing
fractionof argonwhichrepresents
the
massratio of argonpartitioninginto the gasand melt phases tle, we useits upperestimateof 400 ppm and lowerestimate
to the total amountoriginallyincludedin the degassing
volume of 100 ppm derived from the discussionof surfaceheat flow
[TajikaandMatsui,1992].Theeffectofprocesses
suchasmelt
generation,
partitionofvolatileelements
to themelt,andbub-
[HamduoandOzima,1978].Recentgeochemical
estimates
on
ble formationunder the mid-oceanridge are includedin this
theabundance
ofmantlepotassium
[e.g.,Jochum
et al., 1983],
however,
agreewellwith the average
of the two(= 250ppm).
factor. far can be estimatedfrom observation
and physical
We thereforeregard250ppmasthe mostprobablevaluein this
quantitiessuchas partition coefficient,solubility in the sihcate
study.Theinitialaverage
mantletemperature
Tø•issimplyas-
melt and so on. [Tajikaand Matsui, 1992].For concentration sumedto be in the range of 2000-3000K.
of potassium
into melt,we usef•c and (4øK)mam
insteadof
far and (4øAt)main.
The valuesof JArandf•c areestimated
Numerical
Results
to be 0.93and0.99,respectively
[Tajika,1992].It isnotedthat
Figure 1 shows the temporal variations of the seafloor
the coefficientof degassingrate in this model has a physical
spreading
rate, the melt generation
depthin the mantle,and
meaning(not an adjustableparameter)and varieswith time
(not constant)sincethe seafloorspreadingrate and the melt
generationdepth changewith the mantle cooling.
100
•
The melt generation depth is defined by the depth where
the ascendingmantle material intersectsthe mantle solidus,
thus extensivemelting and melt segregationoccurat this depth.
We assume that mantle volatile componentsare released effectively with the melt segregationat this depth. Temporal
variation of the melt generationdepth can be calculatedfrom
that of the averagemantle temperature and the mantle sohdus
I ' I ' I , ! ,
(a) MODEL A
if.:::.'
..........
profile[TajikaandMatsui,1992].On the otherhand,temporal
variation of the seafloorspreadingrate is related to the mantle
heat flow. Both the mantle heat flow and the averagemantle
temperature are obtained by solvingthe thermal evolution of
the mantle [Tajikaand Matsui, 1992].
We use the parameterized convectionmodel to calculate
0.1
m
I
I
I
I
I
m
I
•
100
,
•
,
•
,
•
,
,
,
the wholemantleconvection
[e.g.,Schubertet al., 1980;Chris-
(b) MODEL B
tensen, 1985; McGovern and Schubert, 1989; Tajika and Mat-
sui, 1992]. In this model,we trace the temporalvariationsof
averagemantle temperature Tm and heat flow q from the mantle which is parameterizedin terms of the Rayleighnumber Ra.
The equation of conservationof energyis given by
atto- -3R•q+ (RS•
•Q
pC•(
RS•
- R•S)-•--•_ Rc)
..
VD, dm
(10)
wherep is the density,Cp is the specific
heat at constantpressure,and R, and Rc are the outerand innerradii of mantle, respectively.Q is the energyproductionrate by decay
of radiogenicheat sourcesin the mantle. Mantle heat flow
q is parameterized
in termsof the RayleighnumberRa as,
0.1
I
0
i
2
I
I
3
I
I
4
I
5
q ock(Tm- Ts)/(Rm- Rc)Ra
Is,wherek isthethermal
con-
TIME
(Ga)
ductivityand Ts is the surfacetemperature.The factor/• is a
Rayleigh-Nusselt
exponent,
usuallytakenas0.3 [e.g.,Schubert
Fig. 1. Temporalvariationof the seafloorspreadingrate St,
the melt generationdepth in the mantle din, and the mantle
degassing
volumeVD (fromwhichthe degassing
is assumed
to
et al., 1980].Because
q ccv/• [e.g.,Turcotte
andSchubert,
1982],
wecanestimate
Sr fromqbyusing
arelation
ofSr ccqa occur)for (a) the modelsA and (b) the modelB. Eachvalue
[e.g.,Christensen,
1985;McGovern
andSchubert,
1989;Tajika
is normalized
by the presentvalue(St* = 2.84x 10iama/Ma,
andMatsui,1992].In thisway,wecanobtainthe average
mantle temperatureandthe seafloorspreading
rate by solvingthe
aboveequations(wecall this "modelA").
temperature is assumed to be 2000-3000 K for the model A
d• = 40x 10am,andV/• = 11.4x 1016mS/Ma).
Initialmantle
and2000-2500K forthe modelB (expressed
ashatchedarea).
Tajika and Matsui: Evolutionof SeafloorSpreadingRate
the mantledegassing
volumefrom whichthe degassing
is assumedto occur. Thesevariationsare closelylinkedwith thermal evolutionof the mantle. In the modelA, averagemantle temperature, mantle viscosity,and mantle heat flow are
shownto be greatly changedthroughoutthe historyof the
Earth. Thesefeaturesare qualitativelysimilarto the results
of previousstudies[e.g.,Schubert,etal., 1980;McGovernand
Schubert,1989;Tajika andMatsui,1992].As a consequence,
the seafloorspreadingrate in Arcbeanis estimatedto be 4-16
timeslargerthan that of todayand the melt generation
depth
at that time to be about 70-100 km (i.e., 2-3 timeslarger
than that of today),resultingin a largemantledegassing
volume about8-45 timesgreaterthan that of todayin the model
853
Table1. 4øAtdegassing
history
forthemodels
A andB (forthe
mantlepotassium
content
250ppm).TOm
is theinitialaverage
mantletemperature.
The superscript
ß represents
the present
valueand the overlinerepresents
the time averageoverthe
history of the Earth. X is the ratio of the amount of 4øAr
degassed
to the atmosphere
to the totalamountof 4øArproducedby potassiumdecay.
model Tøm(K)St/St* dm/d• V•v/v• 4øArt X
3000
2500
2000
2500
2000
2500
A (Figurela). Thisstrongly
suggests
thevigorous
degassing
duringthe Hadeanand Arcbeanperiods,and thus the total
amount
of 4øAtdegassed
to theatmosphere
wouldbelarger.
In the modelB, however,degassing
from the mantlewouldbe
8.69
5.48
3.72
1.0
0.5
2000
lesseffectivecompared
to the modelA (Figurelb) because
the mantledegassing
volumevariesonlywith melt generation
depthin thiscase.The numerical
resultson 4øAtdegassing
2500
2000
2.0
1.93
1.73
1.52
2.33
1.50
2.04
30.75
11.12
6.44
2.33
1.50
1.02
13.30
13.30
12.90
8.42
6.61
4.96
0.70
0.70
0.67
0.44
0.35
0.26
1.25
0.62
3.53
0.18
2.93
1.89
5.87
3.78
13.30
11.60
0.70
0.61
history are summarized in Table 1.
Figure2 showsthe total amountof 4øAtdegassed
to the
atmosphere
as a consequence
of eachcorresponding
degassing
history (the error bars representuncertaintiesof the mantle
potassiumcontent,100-400ppm).In the modelA, compared
to the observed
value,4øAthasdegassed
too muchto the atmosphere
for any initial average
mantletemperature
(Figure
2a). As shownin Table 1, the degassing
fractionX, which
represents
the ratio of the amountof 4øAtdegassed
to the atmosphere
to the totalamountof 4øAtproduced
by the potassium decay, is about 0.7. These results reflect more effective
degassinghistory of the model A. On the other hand, in the
modelB, theamountof4øAtdegassed
to theatmosphere
shows
a goodagreement
with the presentobserved
value(Figure2b).
The degassing
fractionX is about0.35forthismodel(Table1).
This meansa mild degassinghistory of the model B. Figure 2c
$ axnountof 4øAtdegassed
to the atmosphere
in 1016kg at
t=4.6 Ga (cf. theobserved
valueis 6.6x 1016kg).
and 2d show the results for the cases with different
constant
seafloorspreadingrate (larger and smallerthan the present
one)for comparison.In the casehigherthan the presentvalue,
the amountof 4øAtdegassed
to the atmosphere
is muchlarger
(Figure2c), whereasin the caselowerthan the presentvalue,
the amountis muchsmaller(Figure2d). This resultstrongly
suggests
that the seafloorspreadingrate may not havechanged
greatly from the present value over the Earth's history. It is
alsosuggestedthat volatile degassingrate from the mantle may
have been as same as that of today, with possiblevariations of
at most 2-3 times larger than that of today.
Discussion
25
a
A
•o
•'
MODEL
A
b
MODEL
B
( Sr,= 1.0x Sr* )-
20
15-
5 -
2O
.
amountof 4øAtin the atmosphere.
In thisrespect,the parameterized convectionmodel with fl = 0 is more reasonablethan
the usual model with fl = 0.3. This would be, in turn, consistent with the idea that the oceaniclithospherewould couple
weakly with the underlying asthenospherebecause of lower
viscosity of the latter. The plausibility of constant seafloor
spreaaqng
rate werediscussed
by Christensen(1985) basedon
c ( Sr=2.0xSr* ) d ( Sr.=0.SxSr* )
A
The seafloorspreadingrate is suggestedto have been almost constantduring the Earth's history to explain the present
.
theoretical considerationsand geologicalevidence.
The numerical results, however,include somesort of ambiguities becauseof simple assumptionsfor the model and also
uncertaintiesin physicalparameters.Therefore,we performed
sensitivityanalysiswith respectto the standardmodel(model
.
B: TOm
=2000 K, (K)•ant =250ppm)whichgivesa proper
amountof 4øAtdegassing
to the atmosphere.
The resultsare
summarized in Table 2. As shown in Table 2, the ambiguities causedby uncertainties of the model parameters and assumptionsmay not drastically changethe results. Even if we
take into account the effectsof hot spot volcanismand mantle
plumeson the 4øAtdegassing,
we do not needto changeour
Fig. 2. Totalamountof 4øAtdegassed
to the atmosphere
for
the modelsA and B as the consequence
of eachdegassing
his-
tory (figuresb, c, d correspond
to the modelswith constant
seafloorspreadingrate once,twice, and half of the present
value,respectively).
The presentpotassium
abundance
in the
mantleis assumedto be 100-400ppm (rangeof changein the
resultsdue to potassiumabundances
is representedby error
bars),and the initial mantletemperature
is assumed
to be
2000K (circles),
2500K (diamonds),
and3000K (stars),respectively.
The brokenlinerepresents
the observed
amountof
4øAtin thepresentatmosphere
(6.6x1016
kg).
conclusions. This is simply becausemuch larger amount of
4øAtmusthavedegassed
in this case.
The assumptionsof homogeneousmantle, constant partition
coefficient
under the variable
conditions
from the melt
generationdepth to the surface,and the definitionof the mantle degassingvolumewould provideanothersourcesfor uncertainties. Becausethe extent of mantle heterogeneityand the
change in partition coefficientshave not been known, there
remain ambiguities due to these assumptions. Although the
mantle degassingvolume is defined as Sr x dm in this study,
the studiesof flow patterns of ascendingmantle materials and
854
Tajika and Matsui: Evolutionof SeafloorSpreadingRate
Table 2. Summaryof sensitivityanalysis
parameters/asumptions
accretion ratio AK
continental
degassing
rate K D,cc
ar
mantle solidusprofile
continentalgrowth model
degassinghistory
"
uncertainties
errorst
0•1.0
+50%
+50%
-5.0% • 6.2%
+3.c%
+30%
(nocontinental
growth)
(growthafter2.5GaBP)
(nodegassing
for the first1.0Ga)
-5.0%
-3.3%
-6.0%t
Difference
between
theresult
ofdegassed
4øAtforthestandard
case
(model
B' Tø•:2000K,
=250ppm)
andthatforsensitivity
analysis
(values
areshown
relative
tothestandard
result
in %).
Relative to the result of the model A.
melts below the spreadingcenter might suggestmore complex
geometryof mantle degassing
volume[e.g., Spiegelmanand
McKenzie, 1987].Here we modifythe definitionof the mantle
degassingvolume by introducing the geometricalfactor • as
VD ----St. drn/•. In order to explainthe observedamountof
4øAtby the modelA, • •20 is required.This seems
to be too
large for consideringmodification due to the flow pattern. Although someof the problemsstill remain unknown, the model
B seems much more reasonable
than the model A.
Sleep(1979) has alsoattemptedto constrainthe seafloor
spreadingrate and the amount of mantle potassiumby usinga
simpleanalyticformulation
of the 4øAtdegassing
andthermal
evolutionmodels. Accordingto his result, the averageseafloor
spreadingrate during the last 3 bilhon years is no more than
twice the present value. The differencebetween his and our
results would be partly becausehe did not take into account
the effect of temporal variation of melt generationdepth on
the degassingrate. As shown in Table 1, the faster constant
seafloorspreadingrate model(twicethe presentvalue)restfits
in deeperaveragemelt generationdepth(about 2-3 timesthe
presentone), whichmeansthe averagemantledegassing
volume is about 4-6 times the present one. In such a case, as
described
earher(Fig. 2c), muchmore4øAtdegasses
to the
atmosphere. This suggeststhat more reahstic treatment of
temporal variation of melt generation depth is required to constrain the seafloorspreadingrate. It is noted that the temporal
variation of melt generationdepth is an inevitable result as far
as the mantle has been coohngover the history of the Earth.
Acknowledgments. This researchwas partially supported
by the grants-in-aidfor ScientificResearch(No. 02804023)of
the Ministry of Education of Japan.
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T. Matsui,Department
of Earth andPlanetaryPhysics,
Facultyof Science,
University
of Tokyo,Tokyo113,Japan.
E. Tajika,Geological
Institute,Facultyof Science,
University of Tokyo,Tokyo113, Japan.
(ReceivedDecember15, 1992;
revised March 8, 1993;
acceptedMarch 17, 1993.)