JOURNAL OF GEOPHYSICAL
RESEARCH,
VOL. 99, NO. B2, PAGES 3081-3095, FEBRUARY
10, 1994
Constraints on hydrothermal heat flux through the oceanic
lithosphere from global heat flow
Carol
A. Stein
Departmentof GeologicalSciences,Universityof Illinois at Chicago
Seth Stein
Departmentof GeologicalSciences,NorthwesternUniversity,Evanston,Illinois
A significantdiscrepancyexists between the heat flow measuredat the seafloor and the higher values
predictedby thermalmodelsof the coolinglithosphere.This discrepancyis generallyinterpretedas indicating that the upper oceaniccrust is cooled significantlyby hydrothermalcirculation.The magnitudeof this
heat flow discrepancyis the primary datum usedto estimatethe volumeof hydrothermalflow, and the variation in the discrepancywith lithosphericage is the primary constrainton how the hydrothermalflux is
divided betweennear-ridgeand off-ridge environments.The resultingestimatesare importantfor investigation of both the thermal structureof the lithosphereand the chemistryof the oceans.We reevaluatethe
magnitudeand age variationof the discrepancyusinga globalheat flow data set substantiallylarger than in
earlier studies,and the GDH1 (Global Depth and Heat flow) model that betterpredictsthe heat flow. We
estimate
thatof thepredicted
globaloceanic
heatflux of 32 x 1012W, 34% (11 x 1012W) occursby
hydrothermal
flow. Approximately30% of the hydrothermal
heat flux occursin crustyoungerthan 1 Ma,
so the majority of this flux is off-ridge. Thesehydrothermalheat flux estimatesare upper bounds,because
heat flow measurements
requiresedimentat the site and so are made preferentiallyat topographiclows,
whereheat flow may be depressed.Becausethe watertemperature
for the near-ridgeflow exceedsthat for
the off-ridge flow, the near-ridgewater flow will be even a smallerfractionof the total water flow. As a
result, in estimatingfluxes from geochemicaldata, use of the high water temperaturesappropriatefor the
ridge axis may significantlyoverestimatethe heat flux for an assumedwater flux or underestimatethe water
flux for an assumedheat flux. Our data also permit improvedestimatesof the "sealing" age, defined as
the age where the observedheat flow approximatelyequalsthat predicted,suggestingthat hydrothermal
heat transferhas largely ceased.Although earlier studiessuggestedmajor differencesin sealingages for
differentoceanbasins,we find that the sealingagesfor the Atlantic, Pacific,and Indian oceansare similar
and consistent
with the sealingage for the entiredataset,65 + 10 Ma. The previousinferenceof a young
(-20 Ma) sealingage for the Pacific appearsto have biaseddownwardseveralprevious estimatesof the
global hydrothermalflux. The heat flow data also provide indirect evidencefor the mechanismby which
the hydrothermalheat flux becomessmall, which has often been ascribedto isolation of the igneouscrust
from seawaterdue to the hydraulicconductivityof the interveningsediment. We find, however, that even
the leastsedimentedsitesshowthe systematicincreaseof the ratio of observedto predictedheat flow with
age, althoughthe more sedimentedsiteshave a youngersealingage. Moreover, the heat flow discrepancy
persistsat heavilysedimented
sitesuntil -50 Ma. It thusappearsthat -100-200 m of sedimentis neither
necessarynor sufficientto stophydrothermalheat transfer. We thereforeconcludethat the age of the crust
is the primarycontrolon the fractionof heattransported
by hydrothermalflow and that sedimentthickness
has a lessereffect. This inferenceis consistentwith modelsin which hydrothermalflow decreaseswith age
due to reducedcrustalporosityand hencepermeability.
INTRODUCTION
The thermal evolutionof the oceaniclithospheregovemsits
propertiesas a functionof age and hencethe style and natureof
plate tectonics. Following the realizationthat seafloorheat flow
is highestat mid-oceanridges and decreaseswith distance[Von
age of the geotherm in the lithosphere,since the bathymetry
dependson the temperatureintegratedover depth and the heat
flow dependson the temperaturegradient at the seafloor. The
key featuresof the data, the decreasein heat flow and increase
in seafloor depth with age, are describedby models in which
lithosphereformed at high temperaturecools conductivelyas it
Herzenand Uyeda,1963; Langsethet al., 1966], the systematic
spreads
awayfromtheridge[McKenzie,1967;DavisandLister,
variationof oceandepthandheatflow with agebecamethepri- 1974; Parsons and Sclater, 1977].
mary constrainton models of the thermal evolutionof the lithosphere. The two setsof data joinfly reflect the evolutionwith
Copyright1994 by th• AmericanGeophysical
Union.
Pap,r numl•r 93JB02222.
0148-0227/94/93 JB-02222505.00
3081
A principal failing of such conductive models is that the
observedheat flow for ages 0-70 Ma is significantlyless than
predicted. This heat flow discrepancyis thought to reflect the
transportof significantamountsof heat at the seafloorby water
circulation [Lister, 1972; Williams et al., 1974; Anderson and
Hobart, 1976], rather than the conductivecooling assumedin
the models. The circulation is thought to be divided into two
3082
STEm AND STEIN: CONSTRAINTSON HYDROTHERMALHEAT FLOW
major stages[Lister, 1982; Fehn and Cathles, 1986]. Near the
ridge axis, "active" circulation occurs, during which water
cools and cracks the rock, and heat is extracted rapidly by
high-temperature
water flow [Pattersonand Lowell, 1982; Fehn
et al., 1983]. Once crackingceases,"passive" circulationtransportslower-temperature
water on the ridge flanks.
The discrepancybetween the observed and predicted heat
flow is the primary constrainton the volume and age distribution of the heat transferredby water flux [Wolery and Sleep,
1976; Sleep and Wolery, 1978; Andersonand Skilbeck,1981].
Wolery and Sleep [1976] consideredother thermaleffects,such
HEAT FLOW ANOMALY
DUE
TO HYDROTHERMAL
FLUX
active
near-ridge
ssiveoff-ridge
as chemical reactions between the water and crust, and con-
cluded that they were small enough that the heat flow
discrepancycould be treated as essentiallyall due to water circulation. As a result, the heat flow discrepancyis usedto estimate the water flux. This discrepancy(Figure 1) can be shown
COOLING
MODEL
as either a difference or the heat flow fraction, the ratio of the
observedto predictedheat flow. The observationthat the heat
flow discrepancyis largestat the ridgesand decreases
with age
is interpretatedas indicating that the hydrothermalwater flux
decreases with age until a "sealing" age, defined by the
observed and predicted heat flow being comparable,by which
hydrothermalheat transferhas largely ceased.
These data are used to addresstwo issues:how large are the
hydrothermalheat and water fluxes as functionsof age, and
what causesthesefluxesto decreasewith lithosphericage? The
volume of hydrothermal circulation has profound implications
for the chemistry of the oceans, becauseseawaterreacts with
the crust, giving rise to hydrothermal fluid of significantly
different composition[Wolery and Sleep, 1976, 1988; Rona et
al., 1983]. The primary geochemicaleffects are thought to
result from the high-temperaturewater flow observedat ridge
axes [e.g., Corliss et al., 1979; Macdonaldet al., 1980; Von
Datum et al., 1985; Rona eta/., 1986]. Nonetheless,the persistenceof the heat flow discrepancyto ages of about 70 Ma
indicates that much of the hydrothermalheat flux occursaway
from the ridge axis (ages greater than •-100,000-1,000,000
years) by passive low-temperaturecirculation in older lithosphere [Wolery and Sleep, 1976, 1988; Morton and Sleep,
1985]. The effects of this off-axial flow have been observed
[Langsethand Herman, 1981; Abbott et al., 1984; Williamset
a/., 1986; Fisher et al., 1990], and it is thoughtto have a much
smaller geochemicaleffect than the near-axisflow, basedon the
major elementchemistryof the fluid [Bakeret al., 1991].
Estimatesof the hydrothermalwater flux derived from heat
flow data are used for comparisonof the water fluxes inferred
with other techniques. These other techniquesinclude direct
measurementsof near-ridge hydrothermal systems[e.g., Green
eta/., 1981; Baker and Hammond, 1992], inference of water
fluxes from ocean chemistry [e.g., Wolery and Sleep, 1976,
1988; Edmond et al., 1979; Craig and Lupton, 1981], and
modeling of geophysical observables such as the depth to
magma chambersor seismicitywhich reflect the coolingof the
ridge axis by hydrothermalflow [Morton and Sleep, 1985; Lin
and Parmentier, 1989; Purdy et al., 1992].
The heat flow data are also crucial to investigating the
processeswhich cause hydrothermalheat flux and thus presumably water flow to decrease with age. The "sealing" age
estimated from the heat flow data shows when hydrothermal
heat transfer at the seafloor has becomeminor but offers only
indirect information about how this occurs.With hindsight,the
term "sealing" age is not ideal for several reasons.First, this
age is estimated from heat flow data, given the difficulty in
--
OBSERVED
i
i
.1-1
Ma
f
sealing
AGE
___OBSERVED/PREDICTED
HEAT
ß
FLOW
!
!
Z
passive off-ridge
.4
active
near-ridge
.1-1
Mo
f
sealing
AGE
Fig. 1. Schematicillustrationof estimationof hydrothermal
flux from
the heat flow anomaly.The anomaly,or differencebetweenthe heat
flow predicted by a lithosphericcooling model and that observed
(shaded),is presumablytransportedby water flux. The flux is thought
to be divided into a near-ridge,high temperature,"active"flow and an
off-ridge, low-temperature,"passive"flow. At a sealing age, the
observedand predictedheat flow approximatelycoincide.The data
can be presentedeither (top) in raw form or (bottom)as the fraction
of the predictedheat flow that is observed.
determining water flow directly. Second, the reduction in
hydrothermalheat transfer could occur in severalways. The
porosity and permeability of the igneous crustal rocks may
becometoo small, due to hydrothermaldepositionof minerals,
such that the rocks themselves"seal". "Sealing" could also
reflect the igneouscrust's being cappedby thick hydraulically
nonconductive sediments which isolate it from the seawater,
such that convectioncould continueat depth but heat transferat
the seafloorwould be conductive.Becausethe sealingage is an
average value estimated from heat flow data, some water circulation may persist beyond it, but it does not, in general,transport significantamountsof heat.
Analysis of these issuesto date has reflected the limitations
of both the global heat flow data available and the conductive
STEIN AND STEIN: CONSTRAINTSON HYDROTHERMALHEAT FLOW
3083
HEAT FLOW DATA and MODEL
model againstwhich the measurementswere comparedto estimate the hydrothermalheat flux. In particular, assessment
of the
consistencyor inconsistencyof variousestimatesof near-ridge
and off-ridge hydrothermal heat and water flux is difficult.
Similarly, althoughit has been proposedthat the sealingage for
hydrothermal circulation varies between ocean basins and primarily reflects the effect of isolationof the crust from seawater
by thick sediment,these propositionsremain largely untested.
Our goal here is to addresstheseissueswith the large heat flow
data set now available and a model which better predicts the
We use a global heat flow data set (Figure 2) [Stein and
Stein, 1992] significantlylarger than that available to the earlier
studies. We include only good quality experimentaldata and
exclude data from marginal basins, whose thermal evolution
may differ from that of larger oceanic plates [Uyeda, 1977].
Severalof the individual valueswere obtainedby averagingthe
resultsof detailed surveyson crust youngerthan 6 Ma to avoid
biasing the data toward these sites' values. This averaging
conductive
reduces the 5539
heat flow.
In doing so, it is useful to bear in mind the strengthsand limitationsof approacheslike ours, which use heat flow data averaged over lithosphereof a given age range. Such studiesgive
global averageestimatesof the hydrothermalflux, which occurs
by flow whose details presumablydependon local conditions.
This approachhas the advantagethat the estimatesof heat and
water fluxes should average the local flow effects at the sites
sampled [e.g., Langseth and Herman, 1981]. (They are, however, vulnerableto biasesintroducedby where samplingis possible, as discussedlater.) The correspondinglimitation of using
averagedheat flow data is that the results say little about the
flow at specificsites and the physicalconditionsgiving rise to
it. For example, knowledgeof the aggregateoff-axial flux gives
no insightinto how the flux is localized(many small sourcesor
a few large ones) and the relevant water temperatures. Similarly, althoughwe can identify the sealingagebeyondwhichlittle heat is transportedby hydrothermalflow, we can make at
best indirect inferencesabout the processescausingthis effect.
GLOBAL
data to 4458.
The data were comparedto a new model for the thermal evolution of the lithosphere,GDH1 (Global Depth and Heat flow)
[Stein and Stein, 1992]. GDH1 (Figure 3), derived by joint
inversion of depth and heat flow data, fits the variations of
depth and heat flow with age significantlybetter than either a
half-spacemodel or a plate model with the parametersused by
Parsonsand Sclater [1977] (PSM). In particular,GDH1 reduces
the systematicmisfit to the depth and heat flow in older (>70
Ma) lithosphere,where PSM predicts depthsdeeper and heat
flow lower than generally observed. An F ratio test indicates
that the improved fit to the data, an 80% misfit reduction,is
significant at the 99.9% level. The improvementin fit going
from PSM to GDH1 is comparableto that obtainedusing PSM
relative to a half-spacemodel.
This improvementin fit resultsfrom the fact that relative to
PSM, GDH1 has a thinner (95 + 15 versus 125 + 10 km) thermal lithosphere with a higher basal temperature(1450 + 250
versus 1350 + 275øC). The thinner lithospheregives a steeper
HEAT
FLOW
DATA
>1
lOO
80
la.I
rm
60
40
2o
o
0
50 AGE
{Uo)100
•
:'-;:"
.:.....:::,....
"•:'i:•!:.•'-..'..
':' :: ß:.'":.::-::..
150
.:......':'.
.•4•.•'-.
ß : ..•-..;.}.•... .: ..:::..'::..•...•.
-60
-.;:.-...•.'::
ø
0ø
60 ø
120 ø
180 ø
240 ø
300 ø
Fig. 2. Locationsof the heatflow datausedandtheir distributionas a functionof age.
360 ø
3084
STEINANDSTEIN:CONSTRAINTS
ON HYDROTHERMAL
HEATFLOW
DEPTH
AND
HEAT
FLOW
DATA
4
200
150
_•b
HEAT
FLOW _
100
14
7O
12
8O
.3 10
50
9O
0
50
1 O0
150
lOO
AGE(Myr)
-0.3
11o
c
GEOIDSLOPE
-0.2
1250
1300
1350 1400 1450
-0.1
13o
1500
1550
Basal
Temperature
(oc)
I
0
50
100
150
AGE (Myr)
Fig. 3. (a) Depth and (b) heat flow data invertedto derivethe GDH1 model,plottedin 10-m.y. bins, comparedwith the
predictionsof the GDH1, PSM, and half-space(HS) models.All the depthsand the heat flow for agesolderthan 50 were
used. In Figme 3b the HS and PSM curvesoverlapfor agesyoungerthan -120 Ma. (c) Geoid slopedata acrossfracture
zones [Cazenave, 1984] which were not usedin derivingGDH1, averagedin 10-m.y. bins, comparedwith the predictionsof
the three models. (d) Misfit surfacefor the depthand heat flow dataas a functionof plate thermalthicknessand basaltemperature,showingthe positionsof the GDH1 and PSM models. Valuesare normalizedto the GDH1 misfit, and the contour
interval is 0.5. The misfit for PSM is 5 times that for GDH1. The surfaceis plottedfor the GDH1 coefficientof thermal
expansion,
3.1x10
-5 øCq,soPSMwhichhasa different
value(3.28x10
-5 øCq)plotsslighdy
above
thesurface.
Thefitting
functionis discussed
by Steinand Stein[ 1992].
geotherm, higher temperaturesat depth, and higher heat flow.
The asymptoticheat flow for old lithospherefor GDH1 is 48
mWm-2, approximately
40% higherthanthe 34 mWm-2 value
for PSM. Similarly, the thinner lithosphereresultsin less subsidence and hence shallower depths. The improved fits reflect
the predicted higher temperaturesthat result largely from the
thinner plate and would occur even if the basal temperature
were not somewhathigher than in PSM.
Several points about the GDH1 model are worth noting for
our applicationhere. It is a plate model, in which the "flattening" (varying more slowly with age than for a half-space)of
the depth and heat flow for older lithosphereare ascribedto the
additionof heat from below. Becauseheat flow data for young
lithosphereare thoughtto be biasedby hydrothermalcirculation,
the primary constraintson such thermal models are the depth
and heat flow for old lithosphere. As a result, whether to
exclude a priori the depthsof shallow areassuch as swells and
hotspottracks is crucial. The choice is not clear-cut;exclusion
of shallow areas inserts an a priori bias about what is
"anomalous" and forces the model toward deeper values,
to hotspots
appearsgenerallysmall,lessthan10 mW m-2 [Stein
and Stein, 1993].
The depth data usedin derivingGDH1 were taken from studies basedon the from the NOAA DBDB5 digital bathymetric
data set. Although this data set, which is typically used for
depth-agestudies,has biasesdue to inadequatesampling,these
biases do not appear excessivefor depth-age studies in the
Pacific [Phipps Morgan and Smith, 1992; Stein and Stein,
1993].
Because the goal of thermal models is to constrainthermal
structureusingpropertiesobservableat the surface,a usefulway
to comparemodels is to examine their predictionsfor data sets
not used to derive the models. GDH1, thoughderived using
data from the North Pacific and northwest Atlantic, fits heat
flow and sediment-correcteddepth data for the Indian Ocean
basinbetter than PSM whetheror not swells and hotspottracks
are excluded [Shoberg et od., 1993]. Similarly, it better fits
basementdepths for Deep Sea Drilling Project (DSDP) and
Ocean Drilling Program(ODP) drill sites[Johnsonand Carlson,
1992; Stein and Stein, 1993]. An additionalindependentconwhereas inclusion of these areas forces the model toward shalstraint on the thermal structurecomesfrom geoid slope data
low depths.By not excludingsuchshallowareasin developing acrossfracture zones (Figure 3c). As for the depth and heat
GDH1, we have a referencemodel for averagethermalstructure flow, the geoid slope's deviation from the predictionsof a
and the average addition of heat from below, relative to which halfspacemodel providesan estimateof the thermalthicknessof
hotspottracks are perturbations.The heat flow perturbationdue the lithosphere[Cazenave,1984]. Althoughthe data for ages
STEINANDSTEIN:CONSTRAINTS
ONHYDROTHERMAL
HEATFLOW
less than about 30 Ma appear to be biased by local effects of
the fracture zones, the remainingdata are better fit by GDH1
than by PSM. Hence althoughthere is no uniqueor best solution to the inverse problem of inferring thermal structure and
different data sets,uncertaintyassignments,and fitting functions
yield different results, a wide variety of data favor a thin lithospheremodel like GDH1.
The new data and model provide a better basisfor estimation
of the heat flow anomalydue to hydrothermalcirculation.Previous estimatesfaced the difficulty that the PSM (or the other)
thermal models used underpredictedthe heat flow data for old
ages.The new data have greaterareal coverage.Comparisonof
the data to the GDH1 predictions(Figure 4) suggeststhat the
heat flow fraction is approximately0.5 in young(0-5 Ma) lithosphereand increaseswith age to -1 by 65 + 10 Ma, by which
essentiallyall heat transfer is conductive.The sealing age ts is
estimatedby fitting a least squaresline to the heat flow fractions
for agesless than 50 Ma (Figure 4, bottom). This approachhas
the advantagethat it is not biasedby the heat flow discrepancy
in young lithosphere,becauseheat flow data for ages< 50 Ma
were not used in deriving GDH1. Moreover, the GDH1 model
is also constrainedby the depth data, which even without the
heat flow data yield the samethermalstructure[Steinand Stein,
1992]. Thus the agreementof the heat flow data with the model
predictionsat old ages and the discrepancyat young ages are
not artifacts
3085
and Sleep [ 1976] and Sclater et aL [1980]. We divide the ocean
basins into age intervals, with the ith age interval extending
from ti_] to ti, whereto is zero. We then find the meanobserved
global heat flow data for each age interval,qi, and its standard
deviation,
The averagepredictedheat flow for this intervalis
q'i= I q'(t)
dt / (ti - ti_•)
ti_1
where q'(t) is the predicted heat flow for age t. For the GDH1
model,
q'(t)= 510t-1/2
t<55Ma
= 48 + 96 exp(-ct)
t>55 Ma
wherec=0.0278
Ma4, ageis in Ma, andtheheatflowis in mW
m-2. Theseexpressions
areeasilyintegrated,
giving
I q'(t)
dt= 1020
(tiu2- ti•2)
ti<_5S
Ma
ti_]
I q'(t)
dt= 1020
((55)
u2- ti•2)+48(ti - 55)
of the data used to derive the model.
ti_•
HYDROTHERMAL
HEAT FLUX
- 3543 [ exp(-cti)- exp(-c(55))]
We use the heat flow data and model to reassessthe hydrothermal heat flux, using an approachsimilar to those of Wolery
GLOBAL
HEAT
I
FLOW
I
250,
-I
I
_
^. -
5oL ' '..-"-'..'-.
I q'(t)dt
=48(ti -ti_•)-3543
[ exp(-cti)exp(-cti_•)
]
DATA
GDH1-
ti4<_55Ma; ti>55 Ma
ti_•>55Ma
where the integralis in mW m-2 Ma. Althoughthe predicted
heat flow at the axis (t=0) is infinite, integrationremoves the
singularity. Thus we obtain a finite value for the averageheat
flow in young lithosphere quite simply. The result is almost
identical(within 0.4%) to that obtainedusingthe seriessolution
for the GDH1 plate model with a modified boundarycondition
at the ridge that conservesenergy [Sclateret al., 1980].
If the area of crust with ages betweenti_• and ti is Ai, the
cumulativepredicted and observedheat fluxes for agesless than
tn are
0
50
100
150
Q'n=•'q'i
OBSERVED/GDHI'GLOBALDATA
• 1.5[N= 4•58oO' oo o 'ot
<•
O.
•
"
01'
0
,
50
AGE(Mo)
i=l
Thus the cumulative heat flux due to hydrothermalflow is the
difference
fa = 65
+ 10 rn.y,-J
,
, I
100
Qn=•'qi.
i=l
Qn
h=Q'n
- Qn
=• Ai(q'i-qi)'
i:l
150
The uncertainty in the cumulative observedheat flux can be
found using linear propagationof errors
Fig. 4. Observedheat flow versusagefor the globaldata set (Fig. 2)
and predictionsof the GDH1 model, shownin (top) raw form and
(bottom)fraction. Data are averagedin 2-m.y. bin•. The discrepancy
for ages < 50-70 Ma presumablyindicatesthe fraction of the heat
Qn= i=l
transported
by hydrothermalflow. The fractionsfor ages< 50 Ma
(solid circles), which were not used in deriving GDH1, are fit by a
assumingthe errors in the different age bins are independent.
least squaresline. The sealing age, where the line reachesone, is
65 + 10 Ma.
We also treat this quantity as the uncertaintyin the cumulative
3086
STEINANDSTEIN:CONSTRAINTS
ONHYDROTHERMAL
HEATFLOW
hydrothermalheat flux. This assumesthat the uncertaintyin the
hydrothermalheat flux estimateis due to the uncertaintyin the
observedflux and neglectsboth uncertaintiesin the area-age
relationand thermalmodel, and a possiblesamplingbias. Thus,
as discussedshortly, the uncertaintywe estimatefor the cumula-
CUMULATIVE
HEAT
FOR OCEANIC
i
i
i
PREDICTED
30
OBSERVED
tive hydrothermalheat flux is a lower bound.
For calculations,we use the area-agevalues from Sclater et
al. [1980]. Becausetheir youngestbin is 0-4 Ma, we add 0-1
and 0-2 Ma bins, assumingthat their area is a quarterand a
half, respectively,of that of the 0-4 Ma bin. Table 1 andFigure
5 show the results. For each age range, the differencebetween
the average predicted and observed heat flow gives the
estimatedaveragehydrothermalheat flux. The resultingcumulative hydrothermalheat flux increasessteadilyuntil about50 Ma
and then levels off as the observedheat flow becomesapproximately that predicted.The slight variation with age about the
10
HYDROTHERMAL
0
0
asymptotic
valueof 11+ 4 x 1012W is an artifactcaused
by the
fact that the observedheat flow slightlyexceedsthe predicted
value for someof the older age bins.
The two primary quantifiesof interestfrom suchcalculations
are the estimatesof total hydrothermalheat flux and the nearaxial heat flux. We thusdiscusseachof thesequantifies.
LOSS'
LITHOSPHERE
50
I
I
1 O0
1 50
AGE(Ma)
BY HYDROTHERMAL
15L
i
FLOW
I
10
Net HydrothermalHeat Flux
We find that of the predicted global oceanic heat flux of
32x 1012W, 11+ 4 x 10•2 W or 34 + 12% occursby hydrother-
66%
mal flow. This estimateis in good agreementwith the value of
10x 1012W determined
by Sclateret al. [1980].Our estimate
is
10% higher, becauseour predictedheat flow is for the GDH1
33%
thermal model, whereas theirs was for the Parsons and Sclater
0
TABLE 1. HeatFlow DataandModelResults
Assuming
Only UncertaintiesDue to Observations
AverageHeat Flow, mW m-2
Age,Ma
Area,106km2
0-1
0-2
0-4
4-9
9-20
20-35
35-52
52-65
65-80
80-95
95-110
110-125
125-140
140-160
160-180
3.5
7.1
14.2
19.7
31.8
42.6
37.0
29.7
37.3
27.9
24.8
15.2
16.7
8.3
3.4
Age, Ma
Predicted
1020
721
510
204
136
98
77
66
60
56
53
51
50
49
48
Observed
131 +
136 +
128 +
103 +
82 +
64 +
' 60 +
62 +
61 +
59 +
57 +
53 +
52 +
51 +
52 +
93
99
98
80
52
40
34
26
27
43
20
13
20
14
10
Cumulative
HeatFlux,10•2W
Predicted
Observed Hydrothermal
1
2
4
9
20
35
52
65
80
95
110
125
3.6
5.1
7.2
11.3
15.6
19.8
22.7
24.6
26.9
28.5
29.8
30.6
0.4 +
1.0 +
1.8 +
3.8 +
6.5 +
9.2 +
11.5 +
13.3 +
15.6+
17.3 +
18.7 +
19.5 +
0.3
0.7
1.4
2.1
2.7
3.2
3.4
3.5
3.7
3.9
3.9
3.9
3.2 __+
0.3
4.1 + 0.7
5.4 + 1.4
7.4 + 2.1
9.1 + 2.7
10.5 + 3.2
11.2 + 3.4
11.3 + 3.5
11.3 + 3.7
11.2 + 3.9
11.1 + 3.9
11.1 + 3.9
140
160
180
31.5
31.9
32.0
20.4+ 3.9
20.8 + 3.9
21.0 + 3.9
11.1 + 3.9
11.1 + 3.9
11.0 + 3.9
20
i
i
40
60
AGE (Ma)
Fig. 5. (top) Cumulativepredicted,
observed,
andinferredhydrothermal heat fluxesas a functionof age. Data are listedin Table 1. The
linesconnect
thepointswhosevalueswerecomputed.
For clarity,the
1 Ma point is not plotted,and the observedvaluesare offset. Error
bars are one standarddeviationof the data. (bottom)Cumulative
inferredhydrothermal
heatflux for 0-65 Ma. Data are from Table 1,
except
forthe1 Ma point(2.9+ 0.5 x 10•2W) whichis fromTable
2. Thisestimatereflectsthe greateruncertainty
in thenear-axial
value
resulting from incorporatinguncertaintiesin the thermal model and
crustal area.
[1977] (PSM) model. BecauseGDH1 predictsheat flow about
10% higher than PSM, the hydrothermaldiscrepancy
predicted
for the sameobservedheat flow is about10% higher.
Our hydrothermal heat flux estimates are, however,
significantly
greaterthanthevaluesof 5-7 x 1012
W obtained
by
Wolery and Sleep [1976] and Sleepand Wolery[1978]. Their
estimatesare lower in part due to the limited heat flow data then
available.At the time, it was assumedthat the sealingage for
hydrothermalflow was -20 Ma, whereasour larger data set
indicatesthat hydrothermalheat flux continuesto about 65 + 10
Ma. Assuminga lower sealingage omits a significantamountof
hydrothermalheat flux. For example,on a globalbasis,-33% of
the hydrothermalheat flux occursfor ages greaterthan 9 Ma
(Table 1). Wolery and Sleep's [1976] estimatewas also lower
becausethey used a cooler temperaturemodel, a 100-km-thick
plate with a 1200øC basal temperature,which predictsasymp-
toticheatflow for old lithosphere
of 30 mWm-2, 38% lessthan
for GDH1. The thermal model and the sealing age are not
independent,
in that the coolermodelimpliesa youngersealing
age. As discussedshortly, the choice of a model for young
STEINAND STEIN:CONSTRAINTS
ON HYDROTHERMAL
HEAT FLOW
lithosphereis not straightforward,and we use GDH1 becauseof
its goodfit to the depthsand heat flow for old lithosphere.
Near-AxialHydrothermalHeat Flux
The magnitudeof the hydrothermalheat flux near the axis is
of specialinterestbecausethe geochemicaleffectsof hydrothermal flow are thoughtto be greatestnear the ridge, where water
temperaturesare highest [Staudigelet al., 1981; Alt and Honnorez, 1984; Wolery and Sleep, 1988]. The relative fraction of
near-axial versusoff-axial heat flux is thus an importantconstraint on models.
We compute(Table 1) the cumulativehydrothermalheat flux
for agesof 1, 2, and 4 Ma, and find valuesof 3.2 + 0.3, 4.2 +
1.0, and 5.4 + 1.4 x10•2 W, respectively.These values
correspond
to 29%, 38%, and 49% of the net hydrothermal
heat
flux. They thus support the observation that most of the
3087
TABLE 2a. Near-Ridge0-1 Ma HydrothermalHeat Flux Estimates,
10•2W,for VariousCrustalAreasandThermal
Models
Area,
106 km2
3.55
2.94
Model (Predicted
AverageHeatFlow,mW m-2)
GDH (1020) PSM (945) Sleep(810) SGDHI* (1052)
3.2 + 0.3
2.6 + 0.3
2.9 + 0.3
2.4 + 0.3
2.4 + 0.3
2.0 + 0.3
3.3 + 0.3
2.7 + 0.3
*Sleepmodelwith GDH1 platethickness
andbasaltemperature.
TAB LE 2b. Near-Ridge0-1 Ma HydrothermalHeat Flux Estimates
IncludingAssumedUncertaintiesDue to
Area, Melting Temperature,and Observations
Age,Ma
Area,10ø km2
Melting
Cumulative
Temperature, Hydrothermal
øC
O-1
0-4
3.25 + 0.3
14.0 + 0.3
HeatFlux,10•2W
1450 + 200
1450 + 200
2.9 + 0.5
5.3 + 1.6
hydrothermalheat flux occursin crustolder than 1 Ma. The 0-4
Ma estimate is consistentwith Sclater et al.'s [1980] estimate
that 45% of the hydrothermalheat flux occursin this age range.
kin-thick plate with a 1290øC basal temperature.We evaluate
Becausesuch estimatesof near-axialflux are often compared
the heat flow for this model by differentiatingthe seriessolution
to those inferred from geochemicalarguments,it seemsuseful
for temperaturewith respectto depthand find averageheatflow
to try to assessthe uncertaintyin our estimatesfurther. The
by integratingthe resultantseriesover an age range.The model
uncertaintiesquoted so far come from the standarddeviationof
is even cooler than PSM and predictsan average0-1 Ma heat
the heat flow measurementsin the relevant age range. Addiflow of 810 mW m-2. This modelpredictsan asymptotic
heat
tional uncertaintiesresult from the uncertainty in the area of
flow of 32 mW m-2 andis thustoocoldfor old lithosphere,
but
crust of the relevant age and from uncertaintyin the heat flow
we use it to representan extreme case for young lithosphere.
predictedby the thermal model.
We also use a versionof the Sleepmodel with a 95-km-thick
The 0-4 Ma area from Sclater et al. [1980] is within 3% of
one from a recent area-agecompilation[Stoddard,1989], which
yields 13.8 x10ekm
2. The implied 0-1 Ma age area, 3.55
plate and a 1450øC basal temperature,which combines the
latent heat boundaryconditionand the GDH1 plate thickness
and basal temperature.This model, SGHD1, has a 0-1 Ma heat
x10e km2, however, differs from the 2.94 x106km2 estimated
flow of 1052mW m-2, slightlyhigherthanfor GDH1.
from global spreadingrates [Chase, 1972]. Spreadingrates from
Table 2a showsthe 0-1 Ma hydrothermalheat flux for these
the recent global plate motion model NUVEL-1 yield essentially different models and area values. The individual estimates
the
same
value
as Chase's.
Some
of
the
17%
difference
between these 0-1 Ma area estimatesmay be due to marginal
basin spreading[Parsons,1981].
To assessthe uncertaintyin the predictedheat flow, we consider
alternative
thermal
models.
It is unclear
what
model
is
most appropriatefor predictingthe thermal structureof young
lithosphereif no hydrothermalcoolingwas present.The primary
constraintson thermal models are the depth and heat flow in old
lithosphere,which reflect both the basal temperatureand plate
thickness.For young lithosphere,the depth data are adequately
fit by a cooling half-spacemodel (Figure 3) and so are insensitive to plate thickness. Moreover, becausein young lithosphere
the hydrothermalcirculation preventsthe heat flow data from
being used to constrain the model, the depths alone constrain
only the productof the coefficientof thermalexpansionand the
melting or basal temperature. As a consequence,models are
generallyderived to fit old lithosphereand applied for young
lithosphere,implicitly assumingthat the basal temperaturesfor
old and young lithosphereare the same.Thoughthis approximation has limitations[Steinand Stein, 1992], it hasthe advantage
of simplicity.Following this approach,we use GDH1 becauseit
providesa good fit to heat flow and depthsin old lithosphere.
We compare the 0-1 Ma hydrothermalheat flux predicted
include only the uncertaintydue to the heat flow observations,
and the range of the estimatesillustratesthe effect of different
areas and models.As noted by Sleep and Wolery [1978], the
estimatedhydrothermalheat flux is not very sensitiveto the
thermal model, owing to the large differencesbetweenthe
predicted and observed heat flow. We thus consider the basic
result,that mostof the hydrothermal
heat flux occursat ages
greaterthan 1 Ma, quite robust.
We also approach
this issuein anotherway, by explicitly
considering
the uncertaintyin the hydrothermal
heatflux due to
the three factors. We assumethat the predictedheat flow for
younglithosphere
as a functionof age t is givenby the halfspaceexpression[Davis and Lister, 1974]
q'(t)= kTm(mCt)
-1/2
wherek is thermalconductivity,
Tmis meltingtemperature,
and
•: is thermal diffusivity. The predictedaverageheat flow
betweenthe ridge axis and aget is then
t
1kTm(•lc)
l(t,)_l/2dt,
=cTmt_l/2
•'(t)= -•-1/2
0
wherec = 2k(mc)
-1/:. The corresponding
hydrothermal
heatflux
from GDH1 (Table 1) to those for several other models (Table
2). The Parsons and Sclater [1977] model, which is similar to
GDH1 but somewhatcooler (Figure 3), predictsan average0-1
is then
Ma heatflow of 945 mW m-2, compared
to 1020mW m-2 for
where A is the crustalarea and q is the averageobservedheat
flow. If we treat the area, the melting temperature,and the
observationsas variables and assume linear propagationof
errors,the uncertaintyin the hydrothermalheat flux is
GDH1. The Sleep [1975] model, which includesa ridge boundary condition which takes explicit account of the latent heat
released during magma ascent and crust formation, has a 100-
Qh= A (q'(t)- q)
3088
STEIN ANDSTEIN:CONSTRAINTS
ON HYDROTHERMAL
HEAT FLOW
2
i5{•
h= (•'(t)- q)2
t•A
2+A2t•q2
+(Act-l/2)2
t•Tm
'
observed heat flow within 0.1 m.y. of the axis. If we assume
the same average observedheat flow as for 0-1 Ma (131 mW
Using this expression,we estimatethe near-ridgehydrother- m-2),andusethepredicted
average
heatflow (3326mW m-2)
mal heat flux and associateduncertainty,assuminguncertainties
for 0-0.1 Ma, the averageaxial hydrothermalheat flux would be
in the area of crust, the thermal model (indicated by melting
3095mW m-2, or about3 W m-2. Henceassuming
an areaof
temperature)and the observations.We use an area estimate 0.3 + 0.03 x 106 km2, and a meltingtemperature
of 1450+ 200
midway betweenthe valuesmentionedpreviously,the GDH1 øC yields0.9 + 0.1 x 1012
W or 8 + 1% of the totalhydrother-
meltingtemperature,
and assume
uncertainties
of 0.3x 106km2
mal heat flux within
0.1 Ma of the axis.
in the area and 200øC in melting temperature.These area and
For comparisonwith estimatesderived from measurementsin
melting temperatureranges, and thus the resultingvalues and the water column,it is useful to considerthe hydrothermalheat
uncertaintiesin hydrothermalheat flux, spanthe rangeof values flux per unit ridge length.For a typicalridge with a full spreadconsideredearlier (Table 2a). These values, which include thering rateof 60 mm yr-1, we predictan axial(0-0.1Ma) hydrothmal model and area uncertainties,are quite similar to those
ermalheatflux of 18 MW knl-l. Althoughour calculations
do
which incorporated
only the uncertaintydueto the observations. not include a dependenceof thermal structure(and hence heat
We thus consider the values in Table 2b our best estimates of
the near-axialhydrothermalheat flux. For theseestimates,2.9 +
0.5 x 1012W or 26 + 4% of the hydrothermalheat flux occurs
within 1 m.y. of the axis, again showingthat most of the
hydrothermalheat flux is off-axial.
All of our estimates,however,do not includea possiblesystematicdata samplingbias, which is difficultto assessbut may
be significant.Becauseheat flow measurements
requireabout10
m of sedimentfor the probe to be emplaced,measurements
in
young lithosphereare made in sedimentponds.Suchmeasurements [Langsethetal., 1992] suggestthat water is flowing
downward in the sediments,in accordwith modeling [Lowell,
1980] indicatingthat in thinly sedimentedregions,water should
descendat low points and upwell at high ones. As a result,
isothermswould be depressedat low points,giving lower conductive heat flow and raised at higher elevations,giving higher
conductive heat flow [Lister, 1972]. The observationsare thus
biased to lower conductive heat flow, and hence tend to overes-
timate the discrepancybetweenthe predictedand observedheat
flux. As a result, our estimates of the uncertainties are lower
bounds, and our estimates of the hydrothermal heat flux are
upper bounds.
ComparisonWith OtherAxial Estimates
Comparisonof these estimatesof hydrothermalheat flux with
estimatesfrom other techniquesis not straightforward.The primary issue in comparingestimatesis the age range over which
they treat the heat flux. In particular, much attentionhas been
directed to estimates of axial or near-axial hydrothermalheat
loss, both in terms of its effects on the tectonicsof the ridge
axis and in terms of its geochemicaleffects.
The literature on this issue is complicated by the fact that
terms such as "axial,"
"near-axial,"
and "off-axial"
are often
not defined. This ambiguity may be in part unavoidablein geochemical discussion,becauseit may be unclear over what age
range various rock-water interactionsextend. Our study has the
advantage that for any age, the predicted and observedheat
flow, and hence the hydrothermal heat flux, age can be easily
estimated. We thus use "axial"
for the interval 0-0.1 Ma,
"near-axial" for 0-1 Ma, and "off-axial" for agesgreaterthan
1 Ma. These divisionsare, of course,somewhatarbitrary.
One commonlycited estimate[Morton and Sleep, 1985] is
that 10-20% of the total hydrothermalheat loss occurs in the
axial region. This value is basedon modelingthe hydrothermal
cooling within 50,000-100,000 years of the ridge axis sufficient
to yield a magma chamber at the depthswhere one is suggested
by seismic data. This estimate is consistentwith ours. Given the
uncertaintiesin determiningthe ages of heat flow sites and the
position of the ridge axis, it is difficult to reliably estimatethe
flow) on spreadingrate, an effect which is greatestcloseto the
axis, the spreadingrate here simply scalesthe age range into a
distance.This estimateof about 10 MW km-l for average
spreading rates is consistentwith those from other thermal
models [Morton and Sleep, 1985]. Comparisonwith estimates
from other techniques,however, is more difficult [Dymondet
al., 1988]. Estimatesfor the Juan de Fuca Ridge derivedby
samplingvents at the seafloorare about an order of magnitude
lower, about 1 MW km-2 [Bemisetal., 1993]. This discrepancy
may reflect underestimation
of the heat loss,becauseboth some
vents and the possibly-commonlow temperatureflow are
missed. Studies of hydrothermalplumes estimate their heat
content at - 1000 MW [Baker and Massoth, 1987]. Assuming
the plumesrepresentabout 10 km of ridge length,the estimated
flux per unit ridgelengthis about100 MW kin-2, an orderof
magnitudehigher than our estimate.Thus plumes appearto be
transportingmore heat than the total steadystatesurfaceflux for
the cooling lithosphere. The discrepancyappearsnot to be an
artifact of the age interval sampled,as the plume studiesextend
to distancesof a few km off-axis, comparableto the age interval
we assume. Hence if both the thermal and plume calculations
are appropriate,the plumes observedmay be intermittent,in
accord with the observationthat only a fraction of the ridge (20% for the Juan de Fuca) presentlydischargesplumes[Baker
and Hammond, 1992].
We thus believe, becauseof this comparisonand the comparisonof our estimateswith thoseof $clater etal. [1980], that
our estimates of the total, near-axial, and axial hydrothermal
heat fluxes are reasonablyrobust.Uncertaintiesin thesequantifies remain, however, due to the uncertainties in both the data
(including the samplingbias toward sedimentedsites) and the
thermal
model.
Water Flux Estimates
Comparison with heat and water fluxes inferred from geochemical data is significantly more complicated.Geochemical
estimates[e.g., Edmondetal., 1979; Mottl, 1983] infer hydrothermal heat flux rates via calculationsassuminga mass of fluid
and its temperature. Because the inferred water flux rate
F = H/T%is relatedto the hydrothermal
heatflux H via the
watertemperature
T andthe specificheatof waterCp,thewater
temperature and specific heat assumed are significant. The
specific heat depends on both temperatureand composition.
Sleep and Wolery [1978] show that the inferred water flux
varies by a factor of almost7 betweeninferredwater temperatures of 100-400øC.
Although little is known about the temperaturesof off-axis
upwelling water, these temperaturesare probably much lower
than the high temperatures(-350øC) of the axial flow. Fehn and
STEIN AND STEIN:CONSTRAINTS
ON HYDROTHERMAL
HEAT FLOW
3089
crest, becausethe cessationof hydrothermalflow may reflect, at
least in part, decreasedporosity of the basaltic crust due to
temperatureflow with temperatures
less than -100øC. As a hydrothermal deposition of minerals [Jacobson,1992]. Because
result, the water flux shouldbe even more dominantlyoff-axial direct measurementsof off-axial water flow are rare compared
than the heat flux, becausea larger volume of low temperature to heat flow measurements,most water flow is generally
water is neededto transportthe sameheat. Considera simple assumed to cease at approximately the sealing age, where the
casewherethe 0-1 Ma hydrothermal
heatfluxof 3 x 1012
W has observed and predicted heat flow are approximatelyequal
an averagewater temperatureof 250øC,and the remainingoff- [Wolery and Sleep, 1976; Andersonand Hobart, 1976; Anderaxial heatflux of 8 x 1012W hasan averagewatertemperature son eta/., 1977; Sleepand Wolery, 1978]. Beyondthis age, heat
of 50øC. Using for simplicity specificheats for pure water of transfer through the sedimentsimmediately below the sea floor
4.5 and4.1 x103J kg-1 s-l [Helgesonand Kirkham,1974] gives is thought to be primarily conductive,althoughsome water cira near-axialwaterflux of 8.5 x1013
kg yr-1 andan off-axialflux culationmay continuein the basementrock underlyingthe sediCathles' [1986] modeling predictsthat within 25 km (-1 m.y.)
of the axis, high-temperatureflow will give way to low-
of 1.2 x1015kg yr-1. Thusthe near-axial
flux transports
27% of ment [Andersonand Skilbeck, 1981].
Estimation of the sealing age from the heat flow discrepancy
theheat,but only7% of thetotal(1.3 x1015
kg yr-1) water.For
comparison,
assumingaveragewatertemperatures
of 300øCand depends on both the data available and the thermal model
75øCyieldsnear-axialandoff-axialwaterfluxesof 6.6 x1013
kg against which they are compared. Using the data set here and
yr-1 and 8.2 x10TMkg yr-1, with essentially
the samefraction the GDH1 model, we find important differencesfrom some of
the sealing ages inferred previously. It has been assumedthat
(8%) of thetotal(9 x10TM
kg yr-1) waterfluxbeingnear-axial.
Thus becausemost of the hydrothermalheat flux occurs at
agesgreaterthan 1 Ma, it is probablynot appropriateto usethe
high (-350øC) water temperaturesobservednear the axis for
describingprocessesthat extend beyondvery young ages. Calculationsusing these temperatureswill underestimatethe water
flux for a given heat flux or overestimatethe heat flux for a
given water flux. For example,assumingthat all the hydrothermal heat flux occurredvia 300øC water would predict a much
lowerwaterflux, 2.4 X1014
kg yr-1.
These examplesillustrate the difficulty in developingcoupled
estimatesof hydrothermalheat and water fluxes.First, both heat
flow and geochemicalestimatesare limited by our knowledgeof
the primary quantityfor the calculation,hydrothermalheat flux,
or water mass. For example, due to the low hydrothermalheat
flux assumedfrom the then available data, Wolery and Sleep's
[1976]estimateof the totalhydrothermal
waterflux, 2 x10TM
kg
yr-1, and Mottl's [1983] estimateof near-axialwater flux, 2
x1013kg yr-1, are lowerthanours.Othergeochemically
based
water flux estimates are biased downward by the assumption
that all water flow occursat high axial temperatures,as noted
by Mottl [1983].
Resolution of these difficulties may be some time in coming.
Formulation of an appropriatemodel to relate water flux and
heat flux is challenginggiven that the off-axial flow is rarely
sampled and poorly understood. Ideally, one would like a
model with appropriatetemperatures
for the relative amountsof
near-axial and off-axial flow, coveringthe age range where the
relevant reactions are thought to occur. Such a model would
permit comparisonof the geochemicallyinferred hydrothermal
heat flux rates to those inferred
from
heat flow
and use of the
relative amounts to infer the age range for the geochemical
interactions.Until the temperaturedata are availableto constrain
such a model, estimatesinvolving water fluxes have considerable uncertainties because different temperatures give quite
different fluxes. In addition, the variation in specificheat with
fluid temperatureand composition,and thus its variation as the
flow changeswith age, provides additional uncertainty.Given
this challenge,we happily restrictour scopehere to heat flowbased estimates.
SEALING AGE FOR HYDROTHERMAL
FLOW
The age at which hydrothermalflow ceasesto be significant
is important for the thermal evolution of the oceanic crust. In
addition, it may be important for the physical evolutionof the
significant differences exist between the sealing ages for
different ocean basins. Figure 6 compares our data to the
widely cited results of Anderson and Skilbeck [1981]. For the
Pacific,Andersonand Skilbeckshowthe flux anomalyendingat
-20 Ma, whereas our data show it persistingto -70 Ma. For
the Atlantic, their data showed lower heat flow than we observe
for the -10-60 Ma range, presumablybecauseof the limited
data then available. The Indian Ocean data show a sealing age
similar to their estimate.These data alsoreflect the anomalously
high heat flow for Cretaceous age lithosphere in the Central
Indian Ocean [Stein and Weissel, 1990], possibly associated
with the diffuse plate boundary between the Indian and Australianplates[Wienset al., 1985; Steineta/., 1990].
We estimate the sealing ages and test for differencesbetween
oceansby fitting a least squaresline to the heat flow fraction in
2-m.y. bins for ages less than 50 Ma (Figures4 and 7). The
sealingage t• is the age at which the line reachesone. The data
are somewhatscatteredbut are adequateto define lines. By this
measure, the sealing ages for the different oceans are comparable, with at most a suggestionthat the Atlantic seals at a
slightly younger age. We thus regard all three ocean basinsas
sealingat an age consistentwith that of the entire data set (Figure 4), 65 + 10 Ma.
This exerciseillustratesthe utility and limitationsof the sealing age concept. Clearly, there is an age range for which the
heat flow fraction increasestoward one and beyond which the
heat flow fraction is approximatelyone. The precise transition
between these two ranges is not well defined, becausethe data
are scattered and relatively sparse. As a result, the linear fit
yields an estimate of the sealing age with considerableuncertainty. Presumably,this uncertaintyreflectsboth the uncertainty
in the heat flow measurements
and the variation
in heat flow for
a given age range. One can thus think of the sealingage as an
age range beyond which most heat transfer at the seafloor
occursby conduction.
Becausethe heat flow fraction measuresonly heat transferat
the seafloor, the observation that it is close to one indicates that
the expectedheat loss is occurringby conductionat the seafloor.
This does not preclude water circulation at depth. In some areas,
water flow may maintain the basementrock at a constanttemperature, such that conductionthrough the sedimentgives surface heat flow measurementscorrelatedto basementtopography
[Davis et al., 1989, 1992]. The global data set we use doesnot
address such fine-scale variations, in that the sites are either iso-
lated or areal averages.
3090
STEIN AND STEIN: CONSTRAINTSON HYDROTHERMALHEAT FLOW
250] •
•-, 200
t
•
• ] 250] •
Anderson
and
Skilbeck
[1981]
t 200
•
Pacific
Ocean
_
• 150
I•••,[]Aflanfic
xGalapagos
]J
150
I+\\• PSM
o ,n,on
O/
I
0
"•
. ,
•0
!
I
100
1 s0
!
,
,
/•X
•
GDH1
I I + +
I
o
/
___
I•- •,•••
0/
0
I
50
O/
-
[
I
100
150
AGE(Ma)
I
I
I
so
1 oo
1 so
,
I
,
,
I X•
•
GDH1
,
___
I• oo ••o
/
0
O O
_
o I
50
-
o Oooo
o _oo
I
100
O
I
150
AGE(Ma)
Fig. 6. Observedandpredictedheatflow versusagefor the oceanbasins.(topleft) Summaryof resultsfrom earlierstudy
[Andersonand Skilbeck,1981]. In their figure,the predictedcurveis schematic.Otherpanelsshowresultsfor our larger
data set, comparedto predictionsof referencemodelsGDH1 and PSM [Parsonsand Sclater, 1977]. We find that the seal-
ing age for the Pacificis comparable
to that for the otheroceanbasins,in contrastto the earlierresultshowinga much
youngersealingage.
The linear fitting approachcharacterizessimply the presumably complex age and site dependenceof the heat flow fraction.
The scattereddata appear inadequateto characterizethe age
dependencebeyonda linear trend. The heat flow fractionmight
be expectedto increasemost rapidly for the younger(0-4 Ma)
ages and more slowly near the sealingage, as perhapssuggested
by the data.
Our Pacific sealing age differs from that of Anderson and
age. Some of the scatter presumablyreflects the noise in the
data, both from measurement uncertainties and topographic
effects [e.g., Lachenbruch,1968; Noel, 1984]. There also appear
to be sites in relatively old lithospherewhere heat flow studies
indicate the water circulation occurs, such as the 80 Ma site dis-
cussed by Ernbley et al. [1983]. The limited number of
sufficientlydenseheat flow surveyson old lithospheresuggest
that such water flow is not common. Considerablymore such
Skilbeck [1981] because their data were comparedto the surveys would be required for any meaningful generalization
predictionsof a thermal model with an 80-km-thick lithosphere, about water flow. The heat flow data presentlyavailableindicate
a 1200øC basal temperature,and a thermal conductivityof 6.15 only that any water flow in older lithosphereis not transporting
x10-3 cal *C-I cm-I s-l' This modelpredictstoolow heatflow in significantamountsof heat throughthe seafloor.
older lithosphere,which was not apparentbecausethey had only
data for 0-50 Ma lithosphere [Andersonand Hobart, 1976],
MECHANISM OF SEALING
whereas our data extend to older ages. As a result, their model
at 20 Ma predictsheatflow -29 mWin-2 lowerthanGDH1 and
The mechanismswhich causethe heat flow discrepancy,and
hence implies a younger sealing age. Thus global hydrothermal hence presumably hydrothermal circulation, to decrease with
heat flux estimatesusing this young sealing age [Wolery and lithosphericage have long beenof interest.Two primaryeffects,
Sleep, 1976, 1988; Andersoneta/., 1977; Sleep and Wolery, both of which may be present,are thoughtto contribute.Ander1978] are significantlylower than ours.
son and Hobart [ 1976] proposedthat the heat flow fractionwas
It is not clear how much significanceto ascribeto the scatter low for young, unsedimented,crust and rose to about one once
in the heat flow fractionfor agesexceedingthe nominalsealing the basementrock was covered by 150-200 m of sediment.In
STEIN AND STEIN:CONSTRAINTS
ON HYDROT.I•V•L
OBSERVED/GDHI'ATLANTICOCEAN
DHI'
0OBSERVE ½/g
1O0 OCEAN150
INDIAN
50
1 O0
3091
this model, the sediment isolatesthe crustal convectivesystem,
which no longer exchangeswater with the ocean.A secondpossibility, suggestedby the thinning of, and seismic velocity
increasein, the uppermostlayer 2A of the crust [Houtz and
Ewing, 1976], is that the vigor of hydrothermalcirculationis
reduced with age by decreasedporosity and hence permeability
of the crust due to hydrothermaldepositionof minerals [Anderson et al., 1977]. For this mechanism,the reductionin hydrothermal
heat
flow
should
correlate
with
variations
in
Often
it is assumed
that both increased
sediment
1 50
for sites with different sediment thicknesses. Of the 5539 sites,
Fig. 7. Heat flow fractionsversusagefor the threeoceanbasins.Data
are shownin 2-m.y. bins. The fractionsfor ages< 50 Ma (solidcircles), which were not used in deriving GDH1, are fit by a least
squaresline. The sealingages,wherethe line reachesone, are similar
for the three oceansand consistentwith the globalaverageof 65 +_10
sediment
thickness
has been determined
at 1494 from
Open
'passive
:ir iation' hydrothermal
u
of sediment.
Closed
'passive
hydrothermal
Thermal
conduction
circulation'
circulation'
0:2
Sediment
Magma
Chamber
seismic
reflection profiles. Sedimentthicknessesare given in secondsof
two-way travel time in 0.05-s increments.Assumingan average
seismicvelocity in sedimentof 2 km/s, 1 s correspondsto 1 km
Ma.
'Active
cover
and reduced crustal permeability contribute to decreasingthe
hydrothermalflow and henceheat transfer(Figure 8) [Anderson
and Skilbeck, 1981; Jacobson, 1992]. In such models, it is
assumedthat for ages older than the sealing age inferred from
the heat flow, some passivehydrothermalcirculationmay still
occur within the crust but is largely isolatedfrom the seafloor
by the integratedpermeabilityof the sedimentcolumn.
The questionis whether the increasein heat flow fraction to a
sealing age is due primarily to the overlying sedimentor agedependentproperties of the crust. The two possible effects
appearsimilar in the data, becausesedimentthicknessgenerally
increaseswith age. In the hopeof discriminatingbetweenthese
effects, we examine the heat flow fraction as a function of age,
AGE(Ma)
hydrothermal
crustal
seismic velocity, as both reflect the physical evolution of the
crust.
0
HEAT FLOW
Abyssal
Hills
'
Crust
-/ k,,,,
Fig. 8. Schematicmodelfor the evolutionof the hydrothermal
systemin the oceaniccrust[Jacobson,1992]. In this model,
the heatflow fractionreachesone oncesedimentis thickenoughto sealoff the crustfrom the ocean.This ageis considered
to be thetransition
from "openpassivehydrothermal
circulation"to "closedpassivehydrothermal
circulation."Beyondthis
age,hydrothermal
flow maycontinuein the crust,butit is isolatedfrom the seafloorandhenceproduces
no heatflow anomaly. Our resultsare consistent
with the generalfeaturesof this model,with the exceptionthatthe sealingappearsto reflect
crustalage primarily,and sedimentthicknessonly secondarily.
3092
Sl•I•
AND STEIN: CONSTRAINTSON HYDROTHERMALHEAT FLOW
Figure 9 shows the heat flow fraction as a functionof age,
for groupsof siteswith different sedimentthicknesses.
The data,
thoughscattered,permit sealingage estimates.The sealingage
decreaseswith increasingsedimentthickness,being 98 + 79 Ma
for sites with less than 0.05 s (-50 m), 83 + 32 Ma for sites
with 0.05-0.2 s (-50-200 m) sediment,and 51 + 17 Ma for sites
with 0.2 s (-200 m) or more sediment.The sealingages are
sufficiently poorly determinedthat differencesbetweenthem are
not formally significant. The data suggest, however, the
expected pattern of the more sedimentedsites "sealing" at a
younger age. It is striking, however, that even those siteswith
less than -50
m sediment
show the increase of heat flow frac-
tion with age. It thus appearsthat 100-200 m of sedimentis not
required for the measuredheat flow to approachthat predicted.
Moreover, the fact that sites with more than -200 m sediment
show the increasein heat flow fraction with age indicatesthat
this amount of sedimentis not in itself enoughto causethe heat
flow
fraction
to rise to one.
OBSERVED/GDH
1: "A" SEDIMENTARY
ENVIRONMENT
1.5
øø
0
2.,, o
o =1=
fs = 52
21 m.y.
•
50
0
o
o
oo oo oooo
ß
•' ' " . .
•
1 O0
150
OBSERVED/GDHI'"B" SEDIMENTARY
ENVIRONMENT
z
1.5
0
•-
41:
N = 430
ø
øo
%
o øø
o
ß oo
øooo•:o
.00
oooo
1
ß
C'
eeee
o
o Ooo
= 59:1:18
a:0.5•.
0
t
50
0
oø
o
ß . .•..r,.o,•'-ooø
øø j,,,,
,.
Ors
o
m.¾.
t
1 O0
150
OBSERVED/GDH
1: "C" SEDIMENTARY
ENVIRONMENT
An alternativeway to examine the effects of sedimenton the
heat flow is to use the sedimentaryenvironmentclassificationof
Sclater et al. [1976]. The best sedimentedsites,classified"A",
have fiat or rolling hills with more than 150-200 m of continuous sediment
N=415
1 '
cover within
18 km.
"B"
1.5
o o'O
368.
o20%ø
00ooooo oO_Ooo_O
o
lt.[ N=....
oo_o
/
o.51ß4 '.
sites have flat or rol-
0½
ling hills with generally continuoussedimentcover, with either
an outcroppingbasementhigh or thin sedimentarycover. Poorly
0
ß
's - "'"'+ 11 m.y,
50
1 O0
150
OBSERVED/GDHI'"D" SEDIMENTARY
ENVIRONMENT
OBSERVED/GDH
1'
• 1.5 N=.502" oo
ALLOCEANS;<0.05 (S 2W'l-r)
z
1.5tN=.2.,,31
'o o ' o ø '
o øø
o
1/ /
/
/e
0.5
/
ß
ß
ß
ß
,4k.•
Q
o
ß
•-
o
="'
"0
..,.
..•(:•;o•
---,,•,
o
-,-
0
o•,
,..
"
50
0
m.y.
i
150
1 O0
1.5
0.5
N = 305
I/
'-
ßß
%
oo o o o
--oo0
I
I
I
50
1 O0
150
ALLOCEANS;_•0.20 (S 2WTr)
z
1.5
o
---I
1 O0
..o,:j
::f: ? m. o
150
increaseof heat flow fraction with age to a sealingage does not
requiresignificantsedimentary
cover.
•$ = 83 + 32 m.y.
0
,,
00000
%
Fig. 10. Heat flow fractions versusage for different sedimentary
environments,ranging from the best "A" to worst "D" (sediment
ponds) sedimented. There is little difference between the behavior
with age of the different environmenttypes, indicatingthat the
o oC
o o oooøo.•O,,o o
,/. e.._ee
50
:...
oO
AGE
ALLOCEANS;0.05-<0.20 (S 2W'l-r)
z
1/ ..
0
OOo
•' •r..,."*-' ß " ooors=98 :E79
0
L,_
o
ß - o,•
sedimentedsites are classifiedas "C," rolling hills or rough
topographywith a thin or variable sedimentcover, or "D," sediment ponds next to outcroppingbasementhighs. It has been
assumedthat heat flow at A sites will be the least affectedby
hydrothermalcirculation, whereasmeasurementsat C or D sites
may be significantlyaffected.
We thus examine (Figure 10) the heat flow fraction as a function of age for the sites with different sedimentaryenvironments, and find little difference. There is a slight suggestionof
older sealingagesfor the assumed-poorer
environments.These
plots further suggestthat the phenomenonof heat flow fraction
increasingwith age to one does not require significantsedimen-
N=958 o o ooOooOo
oooøøoo--]
1
ß
ß
0.5
0
0
ß
.=..,,•.
u - _o •
e l.ff j.--be-oo
,
50
u 0
"',.',.'
_
u
1 O0
-
O-
u
"
o
0
I
'
150
1
(Mo)
Fig. 9. Heat flow fractions versus age for groupsof sites with
different sedimentthicknesses.Data are shown in 2-m.y. bins. The
least squaresline fit to the fractionsfor ages< 50 Ma (solidcircles)
givesthe sealingage. All threegroupsshowtheincrease
in heatflow
fractionwith age, indicatingthat -200 m of sedimentis neithernecessary nor sufficientto sealthe crust. (top) Data for siteswith lessthan
0.05 s (-50 m) sediment. (middle) Data for sites with 0.05-0.2 s
(-50-200 m) sediment. (bottom) Data for sites with more than 0.2 s
(-200 m) sediment. Some of the scatter results from the limited
numberof sites for lithosphereolder than 50 Ma (top) and 100 Ma
(middle).
tary cover.
Additional insight can be obtained by consideringthe variation of sedimentthicknesswith age at the heat flow sites.Figure
11 showsthe median sedimentthicknessin 2-m.y. bins for the
global data. As expected, sediment thicknessincreaseswith
age. The scatterfor a given age is large, becausesites in very
different settings are averaged. We characterizethe average
sediment thicknessat sites with ages less than the sealing age
by fitting a least squaresline to the data for 0-50 Ma. The line
STEINANDSTF_•:CONSTRAINTS
ONHYDRO•
ALL OCEANS
OBSERVED/GDH1HEATFLOW
HEATFLOW
3093
tinued evolutionof crustalproperties.It is also intriguingthat
the ratio of the standarddeviationto the predictedheat flow is
roughlyconstant
with age.This constancy
reflectsthe ratioof
two quantities
thatbothdecrease
withage,perhaps
because
the
predicted
heatflow (thenear-surface
gradient
in theabsence
of
water flow) indicatesapproximately
the temperature
difference
available to drive water convection and the standarddeviation in
0
50
1 O0
1 50
THICKNESS
(S 2wmm)
Z
'"
o
1
(/) 0 -"m•
•ø I
50
oI
00
part reflectsthisconvection.
The latter issuesbear out the challengein relating heat flow
as a functionof ageto the mechanisms
controlling
watercirculation. M6st statementsabout water flow which are based on
heat flow dam are at most plausible inferencesrather than
demonstratedfacts. It is thus useful to distinguishgeneralizations about the heat flow dam from inferencesabout hydrother-
oOO
mal circulation, Our results show that the heat flow fraction
I /
depends
primarilyon crustalageandonlysecondarily
on sediment distribution. These results are consistent with the idea that
50
ALL
Fig. 11. Comparison
of (top)theheatflowfractionversusagefor the
globaldatasetto (bottom)the mediansediment
thickness
at thesites
versusage. The increase
in heatflow fractionwith agecontinues
for
(>- 30 Ma) ageswheresediment
thickness
exceeds
-200 m.
•
lOO
I
•=
ure 9 shows that the heat flow fraction increaseswith age even
for ageswith sedimentthickerthan-200 m.
Figures9-11 togethersuggest
thatthe primarycontrolon the
80
o
60
'"
40
•
zo
z
I
0
•
0
heat flow fraction, and thus the amount of hydrothermalheat
I
sediment, and those with the poorest (D) sedimentary
environment,show the heat flow fraction increasingwith age.
cate that 100-200 m sedimentis neither necessarynor sufficient
for the heat flow to reachthat predicted.
65
'"
•
urements and the ratio of the standard deviation to the mean
value were higherfor age rangeslessthat the sealingage and
1 oo
150
1 O0
150
0.2
lation betweensedimentthicknessand heat flow [e.g., Anderson
and Hobart, 1976; Davis and Lister, 1977] and regional average
studiessuggestingthat sites with lower relief seal at younger
[1981] noted that both the standarddeviationof heatflow meas-
I
z
havingan effect comesfrom derailedsurveysindicatinga corre-
chemistry
of the waterin the sediment.
Anderson
and Skilbeck
I
I
Ma
0.6
• 0.4.
ties inferredfrom the temperaturegradientsand variationsin the
150
----- 0.8
sedimentedsites. Other evidence in favor of sedimentarycover
detect heat flow variations and correlate them with water veloci-
1 O0
>.
The effect of overlyingsedimentappearsinsteadto be secondary, as suggested
by the youngersealingagesfor the heavily
ages[Abbottet al., 1992].Theseresultsareconsistent
with ours
in that for regionalstudies,wherethe crustalage variesonly
slightly,the heatflow variationsmay reflectsediment
thickness.
The heat flow fraction is only an indirect indicatorof the
presence
or absence
of watercirculation.
Suchcirculation
is best
detectedby the rare heatflow surveyswith sitescloseenoughto
I
50
flux, is the age of the crust.Even siteswith lessthan-50 m of
Thesedam,togetherwith the increaseof heatflow fractionwith
age for the heavilysedimented
and A environment
sites,indi-
i
Ma
E
z
indicatesthat on average,a sedimentthicknessof 0.1 s (-100
m) occursby 10 Ma and0.2 s (-200 m) occursby 33 Ma. Fig-
65
E
OCEANS
I
i
65 Ma
z
•
1
•
0.5
z
0
•
0
5O
AGE(Me)
Fig. 12. (top) Standarddeviationof theheatflow measurements
in 2m.y. bins versusage. (middle)Standarddeviationnormalizedby the
decreasedtoward the sealingage. They interpretedthis change meanin eachbin versusage. (bottom)Standarddeviationnormalized
as reflectingthe slowingof convection.Our dam (Figure 12)
by the predictedheat flow for each bin versusage. The standard
show this decrease,which continuesbeyond the sealing age. deviationand the standarddeviationnormalizedby the meandecrease
with age. This decrease
hasbeeninterpreted
as reflectingthe slowing
Thus althoughthe decreaseis consistent
with convectionlargely of convection.Note that both quantitiescontinueto decreasebeyond
stoppingat the sealingage,thecontinued
decrease
in themeas- the averagesealingage of 65 Ma. The standarddeviationnormalized
urementscattermay reflect the presenceof someflow and con-
by the predictedheatflow is roughlyconstant
with age.
3094
STEL• AND STEIN: CONSTRAINTSON HYDROTHERMAL HEAT FLOW
the heat flow fraction increaseswith age becauseof reduced
flow in the crust due to decreasedcrustal porosity and hence
permeability. Our results do not, however, show evidencefor
the idea that thick sediment is the primary control on the heat
flow fraction approachingone and by implication the cessation
of water flow. Instead, our results suggestthat the overlying
sediment may reduce, but not eliminate, the effects of water
flow. Analysis of samples from drill sites, however, does not
show the expecteddecreasein porositywith age [Johnsonand
Setnyan, this issue], perhapsbecausethe porositymeasuredin
drill coresdoes not samplethe appropriatespatialscales[Becker
Abbott, D. L., C. A. Stein, and O. Diachok, Topographicrelief and sediment thickness: Their effects on the thermal evolution of the oceanic
crust,Geophys.Res.Lett., 19, 1975-1978, 1992.
Alt, J. C., and J. Honnorez,Alterationof the upperoceaniccrust,DSDP
site 417: Mineralogy and chemistry,Contrb. Mineral PetroL, 87,
149-169, 1984.
Anderson, R. N., and M. A. Hobart, The relation between heat flow,
sedimentthickness,and age in the easternPacific,J. Geophys.Res.,
81, 2968-2989, 1976.
Anderson, R. N., and J. N. Skilbeck, Oceanic heat flow, in The Seas,
vol. 7, The OceanicLithosphere,editedby C. Emiliani,pp. 489-523,
Wiley-Interscience,New York, 1981.
Anderson,R. N., M. G. Langseth,and J. G. Sclater,The mechanisms
of
heat transferthroughthe floor on the Indian Ocean,J. Geophys.Res.,
eta/., 1982; Pezard, 1990].
82, 3391-3409, 1977.
Much clearly remainsto be done beforea clear understanding Baker, E. T., and S. R. Hammond, Hydrothermalventing and the
of the hydrothermalflow processis obtained. Such an underapparentmagmaticbudget of the Juan de Fuca Ridge, J. Geophys.
Res., 97, 3443-3456, 1992.
standingshould ideally reconcile models basedon large-scale
of hydrothermal
plumes
averagecrustalproperties,suchas heat flow or seismicvelocity, Baker,E. T., and G. J. Massoth,Characteristics
from two vent fields on the Juan de Fuca Ridge, northeastPacific
with site measurements
of water flow and crustalphysicalproOcean, Earth Planet. Sci. Lett., 85, 59-73, 1987.
perties.
Baker, P. A., P.M. Stout, M. Kastner,and H. Elderfield,Large-scale
lateraladvectionof seawaterthroughoceaniccrustin the centralequaCONCLUSIONS
We examine a large heat flow data set to reassessthe basic
ideas about the magnitudeand distributionof hydrothermalheat
flux that have been derived from smallerandmore spatiallylimited data sets.Our primary resultsare as follows:
1. More than two thirds of the hydrothermalheat flux occurs
at ages greater than 1 Ma. Given that the off-axial flux occurs
via water flow at lower temperaturesthan the axial flux, even a
larger fraction of the water flux will be off-axial. As a result, in
estimatingfluxes from geochemicaldata, use of the high water
temperaturesappropriatefor the ridge axis may significantly
torial Pacific, Earth Planet. Sci. Lett., 105, 522-533, 1991.
Becker, K., R. P. Von Herzen, T. J. G. Francis, R. N. Anderson,J. Hon-
norez,A. C. Adamson,J. C. Alt, R. Emmermann,P. D. Kempton,H.
Kinoshita, C. Laverne, M. J. Mottl, and R. L. Newmark, In situ electr-
ical resistivityand bulk porosityof the oceaniccrustCostaRica Rift,
Nature, 300, 594-598, 1982.
Bemis, K. G., R. P. Von Herzen, and M. J. Mottl, Geothermalheat flux
from hydrothermalplumeson the Juande Fuca Ridge, J. Geophys.
Res., 98, 6351-6365, 1993.
Cazenave,A., Thermalcoolingof the lithosphere:
New constraints
from
geoidheightdata,Earth Planet.Sci. Lett., 70, 395-406, 1984.
Chase, C. G., The n-plate problem of plate tectonics,Geophys.J. R.
Astron• Soc., 29, 117-122, 1972.
Corliss,J. B., J. Dymond, L. I. Gordon, J. M. Edmond,R. P. von Herzen, R. D. Ballard, K. L. Green, D. Williams, A. L. Brainbridge,K.
overestimate the heat flux for an assumed water flux or underesCrane, and T. H. van Andel, Submarine thermal springs on the
timate the water flux for an assumed heat flux.
Galapagosrift, Science,203, 1073-1083, 1979.
2. Our data show no significantdifferencein the sealingage Craig, H. L., and J. E. Lupton, Helium-3 and mantlevolatilesin the
ocean and oceanic crust, STOP in The Seas, vol. 7, The Oceanic
for hydrothermalflow between the major ocean basins,in conLithosphere,editedby C. Emiliani, pp. 391-428, Wiley-Interscience,
trast to earlier studies.In particular,we find that hydrothermal
heat flow in the Pacific extendsto comparableages as for the
other ocean basinsand suggestthat earlier studieswhich found
hydrothermalheat fluxes significantlylower than those we find
were biasedby an assumed-younger
sealingage.
3. Our data do not supportthe traditionalview that the cessation of hydrothermalflow, as inferred from the equality of
observed and predicted heat flow, reflects the isolationof the
basaltic crust from the ocean by -200 m of sediment.Comparison of data from sites with different sedimentthicknesses
indicate that -200 m of sediment is neither necessarynor
sufficient to cause the observed heat flow to equal that
predicted. It appears, instead, that the fraction of heat transportedby hydrothermalflow dependsprimarily on crustalage
and that sediment
thickness has a lesser effect. These results are
consistentwith models in which water flow decreaseswith age
primarily becauseof reducedcrustalporosityand hencepermeability.
New York, 1981.
Davis, E. E., and C. R. B. Lister, Fundamentalsof ridge crest topography, Earth Planet.Sci. Lett., 21, 405-413, 1974.
Davis, E. E., and C. R. B. Lister, Heat flow measuredover the Juan de
Fuca Ridge: Evidencefor widespreadhydrothermalcirculationin a
highlyheattransportive
crust,J. Geophys.Res.,82, 4845-4860, 1977.
Davis, E. E., D. S. Chapman,C. B. Forster,and H. Villinger,Heat-flow
variationscorrelatedwith buried basementtopographyon the Juande
FucaRidge flank,Nature, 342, 533-537, 1989.
Davis, E. E., D. S. Chapman,M. J. Mottl, W. J. Bentkowski,K. Dadey,
C. Forster,R. Harris, S. Nagihara,K. Rohr, G. Wheat, and M. Whiticar, FlankFlux: An experimentto study the nature of hydrothermal
circulationin young oceaniccrust, Can. J. Earth Sci., 29, 925-952,
1992.
Dymond, J., E. Baker, and J. Lupton,Plumes:oceaniclimb of seafloor
hydrothermal
systems,The Mid-OceanRidge-A GlobalDynamicSystem,Proceedings
of the SalishanWorkshop,
NationalAcademyof Sciencespp. 209-231, NationalAcademyPress,Washington,D.C., 1988.
Edmond, J. M., C. Measures, R. E. McDuff, L. H. Chan, R. Collier, B.
Grant, L. I. Gordon, and J. B. Corliss, Ridge crest hydrothermal
activity and the balancesof the major and minor elementsin the
ocean:the Galapagosdata,Earth Planet.Sci.Lett.,46, 1-18, 1979.
Acknowledgments.We thank Keir Becker and an anonymous Embley, R. W., M. A. Hobart, R. N. Anderson,and D. Abbott,
Anomalous heat flow in the northwest Atlantic: A case for continued
reviewer for constructivecomments. This researchwas supportedby
hydrothermalcirculationin 80-m.y. crust, J. Geophys.Res., 88,
NSF grantsOCE-9019572 and EAR-9022476, and NASA grant NAG1067-1074, 1983.
5-1944.
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