Download The Heat Flow Through Oceanic and Continental Crust and the Heat

REVIEWS OF GEOPHYSICS AND SPACE PHYSICS, VOL. 18, NO. 1, PAGES 269-311, FEBRUARY
1980
The Heat Flow Through Oceanicand ContinentalCrust
and the Heat Loss of the Earth
J. G. SCLATER, C. JAUPART,AND D. GALSON
Departmentof Earth andPlanetarySciences,
Massachusetts
Instituteof Technology,
Cambridge,
Massachusetts
02139
Simple thermal modelsbasedon the creation and coolingof the lithospherecan accountfor the observedsubsidenceof the ocean floor and the measureddecreasedin heat flow with age. In well-sedimented areas, where there is little loss of heat due to hydrothermal circulation, the surface heat flow
decaysuniformlyfrom valuesin excess
of 6 !•cal/cm2 s (250 mW/m2), for crustyoungerthan4 Ma (4
m.y.B.P.),to closeto 1.1/wal/cm• s (46 mW/m•) throughcrustbetween120and 140Ma. After200 Ma
theheatflowis predicted
to reachan equilibriumvalueof 0.9!•cal/cm
• s (38 mW/m2).The surfaceheat
flow on continentsis controlledby many phenomena.On the time scaleof geologicalperiodsthe most
importantof theseare the last orogenicevent,the distributionof heat-producingelements,and erosion.
To better understandthe effectsof age, each continent is separatedinto four provinceson the basis of
radiometric dates. Reflectingthe preponderanceof Precambriancrust, two of theseprovincescover the
Archean to the middle Proterozoic, and the third coversthe late Proterozoic to the Mesozoic. The mean heat
flowdecreases
froma valueof 1.84/wal/cm
2s(77mW/m2)fortheyoungest
province
toa constant
value
of 1.1 pcal/cm• s (46 mW/m•) after 800 Ma. The nonradiogenic
component
of the surfaceheat flow
decaysto a constant
valueof between0.65and0.5 !•cal/cm• s (25 and21 mW/m2) within200-400Ma.
Usingtheoreticalmodels,we computethe heat lossthroughthe oceansto be 727 x 10Iø cal/s (30.4 x
10I2 W). The comparison
betweenthe theoreticaland measured
valuesallowsan estimateof 241 x 10Iø
cal/s (10.1 x 10• W) for the heatlostowingto hydrothermal
circulation.We showthat the heatflow
throughthe marginalbasinsfollowsthe samerelation as that for crustcreatedat a midoceanspreading
center.Thesebasinshavea corresponding
heatlossof 71 x 10lø cal/s (3.0 x 10I• W). The heat loss
throughthe continents
is calculatedfrom the observations
and is 208 x 10Iøcal/s (8.8 x 10I2 W). Our
estimateof thevaluefor theshelves
is 67 x 10•øcal/s(2.8 x 1012W). The totalheatlossof theearthis
1002x 10•øcal/s(42.0x 1012W), of which70%is throughthedeepoceans
andmarginalbasinsand30%
throughthe continentsand continentalshelves.The creationof lithosphereaccountsfor just under 90%
of the heat lost throughthe oceansand henceabout 60% of the worldwideheat loss.Convectiveprocesses,which includeplate creationand orogenyon continents,dissipatetwo thirdsof the heat lost by the
earth. Conductionthrough the lithosphereis responsiblefor 20%, and the rest is lost by the radioactive
decay of the continentaland oceaniccrust.
We placeboundsof between0.6 and0.9 !•cal/cm• s (25 and 38 mW/m•) for the mantleheatflow beneathan oceanat equilibriumand between0.40and0.75!•cal/cm
• s (17 and31 mW/m2) for the heat
flow beneathan old stablecontinent.The computedrange of geothermsfor an equilibrium ocean overlaps the rangeof stablecontinentalgeothermsbelow a depth of 100 km. The mantle heat flow beneatha
continentdecayswith a thermal time constantsimilar to that of the oceaniclithosphere.The continental
basins subside with the same time constant. These observations are evidence that there is no detectable
differencebetweenthe thermal structureof an equilibrium ocean and that of an old continent.Thus the
conceptof the lithosphereas a combinationof a mechanicaland a thermal boundarylayer can be applied to both oceansand continents.We evaluatethe constraintsplacedon modelsbasedon this concept
by seismological
observations.
In the absenceof compellingevidenceto the contrarywe favor thesemodels becausethey provide a single explanation for the thermal structureof the lithospherebeneath an
equilibrium ocean and a stable continent.
CONTENTS
Introduction ..........................................................................................
Thermal structureand thicknessof the lithosphere...........................295
269
Heat flow throughthe oceanfloor.......................................................
270
Introduction ......................................................................................
270
Introduction
......................................................................................
295
Comparisonof the 'equilibrium'oceanand old continent
geotherm....................................................................................
295
Comparisonwith geothermometry
and geobarometry
data .........296
Relation betweenreducedheat flow and age.................................
297
Data analysis.....................................................................................
270
Thermal modelsof the lithosphere
..................................................
270
Subsidence of continental basins ..................................................... 297
Hydrothermalcirculation................................................................
271 Convection in the mantle and the thermal structure of the
Reinterpretation
of oceanicheatflowmeasurements
....................
272
lithosphere.....................................................................................
299
Marginalbasinheatflow..................................................................
277 Conclus•on• ...........................................................................................
300
Mantle convection and thermal structure ....................................... 279
AppendixA: Relation betweenarea and agefor oceaniccrust........301
Continental heat flow ........................................................................... 281
Magnetic Anomaly Identifications..................................................
301
Introduction ......................................................................................
281
Deep Seadrilling sitesand bathymetriccontours..........................301
Geologicalmodelsfor continentalformation................................
281
Continental heat flow measurements .............................................. 283
Heat flowand age.............................................................................
284
Heat flow and surfaceheatproduction...........................................
286
Thermal models ................................................................................
Heat loss of the earth ............................................................................
Introduction ......................................................................................
291
292
292
Heatlossthroughtheoceans...........................................................
292
Heat lossthroughthe continents
.....................................................
293
Total heat loss of the earth ............................................................... 294
This paper is not subjectto U.S. copyright. Published in l q80 by
the American GeophysicalUnion.
Paper number 9R1283.
269
Time scale ..........................................................................................
301
Why specificisochronswere chosen................................................
301
Position of the isochrons ..................................................................
302
Area versusage for the oceans.........................................................
303
AppendixB: Relationbetweenareaand agefor continents.............303
Appendix C: The modifiedplate model..............................................
305
INTRODUCTION
In the past 15 years our understandingof the earth has
changed. Rather than regard the oceans and continentsas
static and unrelated, we now think of them as mobile and in-
270
SCLATER
ET AL.: OCEANIC
AND
terconnected.The theory of plate tectonicsaccountsfor the
major featureson the surfaceof the earth by the motion and
interaction of a finite number of rigid plates.These plates are
defined tectonically and include both oceansand continents.
The oceanic crust is younger than 180 Ma (180 m.y.B.P.),
whereas parts of the continents have existed throughout the
whole geological.time span: the oldest continental crust is
Archean
and older than 3800 Ma.
The mechanisms
of heat
transfer beneath continentsand oceansmay be different, and
we considerthe oceansand continentsseparatelyrather than
studyinga singleplate.
In the past 10 years many new heat flow measurements
have been reported in the geophysicalliterature. They have
been assembledunder the auspicesof the International Heat
CONTINENTAL
HEAT
FLOW
ory of plate tectonicsare havingsomesuccess
in accounting
for the subsidence of continental
basins.
(For our computationsand presentationof the data we use
calories. These units permit comparisonwith previous reviews.Also, we presentthe data in SI units.They follow those
in caloriesand are enclosedby parentheses.)
HEAT
FLOW
THROUGH
THE
OCEAN
FLOOR
Introduction
We superimposedall the heat flow valuesupon an isochron
chart of the oceans(Plate 1). A detailed accountof the methods usedto determine the age of the ocean floor can be found
in Appendix A. The data include the compilationof Jessopet
al. [1976]aswell aspaperspublishedsincethis compilationby
Flow Commission
of the International
Association of SeisHerman et al. [1977], Langsethand Hobart [1976], Langseth
mology and Physicsof the Earth's Interior. In 1976,Jessopet and Zielinski [1976], Andersonand Hobart [1976], Andersonet
al. publishedan updated and revisedversionof the previous al. [1976a, b, 1977] and Sclater et al. [1976a].
compilations of Lee and Uyeda [1965] and Simmons and
For purposesof comparisonwe separatedthe data set into
Horai [ 1968]. In our analysiswe use this compilationand in- six groups;North and South Pacific, North and South Atlandude additional data published since then but before June tic, the Indian Ocean, and the marginal basins.We define as
1977. Our approach differs from previous work [Lee and 'marginal'all basinsisolatedfrom activespreadingcentersby
Uyeda, 1965; Simmonsand Horai, 1968; Von Herzen and Lee, clearly defined tectonic barriers. For example, in the western
1969; Chapman and Pollack, 1975a], principally becausewe Pacific all the basinsto the west of the major trench system
concentrate on examining the oceanic and continental values are included. They extend from the Tasman and South Fiji
with local geologicvariablesin mind. Only when theselocal Basin in the south to the Bering Sea and Arctic Basin in the
variables are understoodis it possibleto separatedeep-seated north. Our definition also encompassesthe Caribbean, the
thermal propertiesfrom superficialnoise.
Mediterranean, the Black and Caspian seas,and the Scotia
Our objectiveis to increaseour understandingof the large- Sea togetherwith the Andaman and Sunda seasin the Indian
scalemechanismof heat transportwithin the earth. We sepa- Ocean.
rate this review into two parts.
Unfortunately the 1: 10,000,000scalethat we used was not
In the first section, which is almost totally empirical, we sufficientlylarge. Hence in our averagingwe may have omitpresent a general synthesisof oceanicand continental heat ted a few values,especiallyon youngeroceancrust.A careful
flow data and examine both sets of data within the framework
double check of these areas with the original references
of the theory of plate tectonics.Care is taken in the oceansto showedthat the errors introducedwere insignificant.
account for hydrothermal circulation, and on the continents,
considerationis given to the relation between heat flow and Data Analysis
surface heat production. We use our understandingof geologic perturbationsto establisha relation between heat flow
and age for both continentsand oceansand accountfor this
relation by modelsof oceanicand continentalheat flow which
are compatiblewith the theory of plate tectonicsand uniformitarian in principle. We compare the heat lossthrough continents and oceans,estimate the amount of heat dissipatedby
the creation of the oceanic lithosphere,and compute the total
heat loss for the earth.
Given the success
of the plate theory in accountingfor geophysical observations from the oceans, attempts are now
being made to apply this quantitative approachto the continents.The success
has not been overwhelming,but a productive line of researchhas been to relate the past geologicrecord
to processeswhich are active today. In the secondsectionwe
usethis approachand the data and modelsfrom the preceding
section to examine
the thermal
structure of the oceanic and
continental lithospheres.In particular, we investigatewhether
or not it is possibleto extend the simple thermal models for
the oceans to the continents.
The approach that we take is similar to that used in an earlier paper by Sclater and Francheteau [1970]. The present
analysisplacesmore emphasison removing the effectsof local
geology and has the benefit of three advances in the field.
These are (1) that the scatterin the oceanicheat flow is now
understood,(2) that continental heat flow and radioactive
data are more extensive,and (3) that modelsbasedon the the-
We computed the mean and standard deviation for all data
lying betweentwo isochrons.Throughoutthe studywe usethe
term age province to define the area between two consecutive
isochrons.In particular, the youngestprovince covers crust
created between the present and 4 Ma, and the oldest, crust
created prior to 160 Ma.
In all the oceans we observe the same distribution
of heat
flow (Table 1 and Figure 1). For the young crustthe mean is
high, rangingfrom 2 to 6/•cal/cm2 s (84 to 251 mW/m2), and
is associatedwith a large scatterof about 2/•cal/cm 2 s (84
mW/m2). Beyond60 Ma the meanheat flow hasa relatively
constantvalueof around1.2/•cal/cm2 s (50 mW/m2), and the
associated
scatteris small,lessthan 0.5/•cal/cm2 s (21 mW/
m2). The abnormally high scatterin the youngertwo provincesof the Indian Ocean is a direct consequence
of the high
but very variable heat flow observedin the Red Sea. The marginal basinheat flow has the samedistributionas the oceans.
ThermalModels of the Lithosphere
The oceanic crust is created at a spreadingcenter by intrusion of magma. The magma coolsand annealsitself to the recently createdcrustand movesaway from the spreadingcenter as more magma is intruded. The oceanic crust increasesin
age, losesheat to the seawater,and contracts.This model explains qualitatively the decreasein heat flow with age and the
subsidenceof midocean ridges. The raw heat flow data are
highly scattered.Hence more emphasishas been placedupon
$CLATER ET AL.: OCEANIC AND CONTINENTAL HEAT FLOW
TABLE
1.
Oceanic
Heat Flow
271
Data
Age, Ma
0--4
4-9
9-20
20-35
35-52
52-65
65-80
80-95
North Pacific
36
57
1.48
1.34
95-110
110-125
125-140
140-160
35
1.16
33
1.11
72
1.12
19
1.23
12
1.29
0.37
0.85
14
N 268
rn 4.04
207
2.49
214
1.90
126
1.59
57
1.21
23
1.35
o 3.57
1.74
1.26
0.89
0.76
0.52
0.35
0.46
0.22
0.42
24
1.30
0.41
10
1.16
0.26
19
0.96
0.32
49
1.28
0.75
35
1.32
0.46
34
1.45
0.90
42
1.16
0.39
0.63
>160
N 87
rn 3.01
o 2.03
64
2.49
2.11
99
1.82
1.30
47
1.15
0.74
51
1.10
0.83
South Pacific
7
13
6
1.12
0.93
1.27
0.53
0.66
0.85
N 70
rn 2.86
o 1.85
71
5.23
9.9
67
1.22
1.04
42
1.07
0.67
50
1.49
0.72
122
1.61
0.86
N 56
78
63
65
62
82
85
65
43
30
45
47
rn 3.31
2.13
1.80
1.56
1.62
1.43
1.23
1.19
1.28
1.31
1.29
1.13
1.11
o 2.69
1.68
1.55
1.06
1.04
0.66
0.50
0.31
0.27
0.36
0.30
0.40
0.22
N 25
rn 2.61
o 2.25
24
1.31
1.27
37
1.23
0.73
24
1.45
1.02
32
1.32
0.53
31
1.35
0.53
27
1.35
0.35
56
1.32
0.46
55
1.36
0.36
N 506
444
470
304
252
265
204
193
162
178
66
26
Indian
Ocean
96
1.57
0.86
North/ttlantic
South/ttlantic
47
1.26
0.53
/tll
Oceans
277
m 3.55(149) 2.80(117) 1.69(71)1.43(60) 1.36(57) 1.49(62) 1.37(57) 1.28(54) 1.28(54) 1.31(55) 1.16(49) 1.16(49) 1.19(50)
o 3.01(126) 4.30(180) 1.24(52) 0.92(38) 0.83(35) 0.73(31) 0.68(28) 0.48(20) 0.40(17) 0.51(21) 0.38(16) 0.39(16) 0.59(25)
N
rn
122
2.14
46
1.92
402
1.92
48
1.54
Marginal Basins
32
118
1.28
1.43
141
101
o
1.46
1.16
0.72
0.66
0.74
0.71
0.43
N isthenumber
ofheatflowstations,
misthemean
heatflowin/•cal/cm
2 s (mW/m2),
ando isthestandard
deviation
in/,cal/cm
•s
(mW/m:).
the study of ocean floor topographyin developingquantitative models for the creation of the oceanic lithosphere.
Sclateret al. [1971]have shownthat mostmidoceanridges
are createdat a depthof 2500 m and subsideto depthsgreater
than 6000 m (Figure 2a). For crustyoungerthan 80 Ma the
depthincreases
linearlywith the squareroot of age[Davisand
Lister, 1974].For older oceanfloor this relationbreaksdown,
and the depth increasesexponentiallyto a constantvalue of
6400m (Figure2b) [Parsons
andSclater,1977].This two-stage
relation betweendepth and age can be explainedby the formation of a thermal boundary layer. The magma coolsand
solidifiesas it movesaway from the spreadingcenter,and the
thicknessof the rigid layer thuscreatedincreases(Figure 3a).
Parker and Oldenburg[1973] predicted from a one-dimensionalcoolingmodel that the layer thicknessshouldincrease
asthe squareroot of time. This upperlayerbehavesasa rigid
bodyand is knownas the lithosphere.
After it reachesa certain thicknessat about 80 Ma, it doesnot thicken any further.
This representsthe basicjustificationfor modelingthe thermal boundary layer as a plate of constant thickness
[McKenzie,1967](Figure3b).ParsonsandSclater[1977]demonstratedthat for crust younger than 80 Ma both the plate
and the boundarylayer modelsare essentiallyidentical,and
they usedthe two differentapproachesto computefirst-order
relationswhich match the topographicdata (Table 2).
From thesemodelsit is possibleto computethe heat flow
throughthe oceanfloor.Lister [1977]predicteda simplerelation betweenheat flow and 1/t •/2. Parsonsand $clater [1977]
showed that this relation should break down at about 120 Ma
and that the heat flow should then follow an exponential
In order to compare the observationswith thesemodels we
averagedthe heat flow valuesfor all the oceans.As is the case
for the individual oceans, the mean and scatter decrease with
age (Figure 4a). In the older provincesthe mean values fall
close to those predicted by the plate model, although the
scatter prevents the interpretation of the results unambiguouslyin terms of exponentialflattening.For crustyounger
than 50 Ma
the mean values fall well below the theoretical
(Figure 4b). In order to explain both the topographyand the
heat flow it is necessaryto accountfor the high scatterand the
low mean values for young ocean crust.
HydrothermalCirculation
/lnderson and Hobart [1976], in their analysis of the Gala-
pagosspreadingcenter,have presentedan excellentexample
of the characteristicdistribution of heat flow near a spreading
center (Figure 5). The valuesare highly scattered,and many
low values are observedon crust between 3 and 4 Ma. Beyond
5 Ma the values show less scatter and fall close to the theoreti-
cal. This change in the heat flow distribution is associated
with a sudden increase in sediment thickness. Davis and Lister
[1977] have presenteda remarkably similar distribution over
the Juan de Fuca Ridge.
The oceanic crust is created by the intrusion of basaltic
flows and dykes. Where the intruded magma comesinto contact with seawater, it cools rapidly, horizontal and vertical
cracks are created on both a large and a small scale, and active convection of seawater occurs.Independently, Talwani et
al. [1971] and Lister [1972]suggested
this model to explain the
high scatterin heat flow valuesnear a spreadingcenter. The
decayto a valueof around0.9/zcal/cm
• s (38 mW/m2) (Table high water temperaturesassociatedwith suchconvectionhave
2).
been observedby conventionaltechniquesin Iceland [Palmas-
272
SCLATER ET AL.: OCEANIC
AND
8O
HEAT
FLOW
80
- 300
7O
60
CONTINENTAL
NORTH
PACIFIC
-300
70
SOUTH
60
5O
200
PACIFIC
50
200
40
4O
•0
30
IO0
2O
•0
I00
20
10
' ' ' ' "'"1do"140
"'
60
50
40
6O
NORTH
ATLANTIC
200
5O
3O
30
20
20
10
10
SOUTH
ATLANTIC
I i I ,,t,
i•it
60
80
I•
100 •40
-300
70
60
60
INDIAN
OCEAN
200
5O
40
40
30
30
20
20
•0
2oo
80
70
50
180
t
MARGINAL
300
./ BAS
INS]200
I00
•0
o '1
•'1•0 •' 1'"40
+ •'180
AGE
IN
MA
Fig. 1. Mean heat flow and standarddeviationas a functionof age for five major oceansand the marginalbasins.
son, 1967] and over the Galapagos spreadingcenter [Williams
et al., 1974].Extremely hot water at oceanicspreadingcenters
has been observedduring dives of the submersibleR/V Alvin
at the Galapagosspreadingcenter and East Pacific Rise [Corliss et al., 1979; J. Edmond, personal communication, 1979].
Lister [1977] has proposed a two-stage model for seawater
convectionthrough oceaniccrust. In the active stagethe seawater penetrates into the newly erupted rock, which then
cools, contracts, fractures, and hence permits further penetration. The crust coolsto a depth where active penetration is
halted by the overburdenpressureor volume alteration of the
intruded mafic rock. These systemsare thought to have a lifetime of a few hundred years over a penetration depth of 6-8
km [Francis et al., 1978]. In the passivestage,hydrothermal
circulation continuesto occur becausethe permeable watersaturatedcrustis heated from below as the lithospheremoves
away from the spreadingcenter. This passivesystemexistsas
long as the permeabilityand temperaturegradientsare large
enough.
Lister [1972], Sclater et al. [1974], and Davis and Lister
[1977] have shown that the pattern of heat flow over a midocean ridge can be explained by this model (Figure 6). Most
deep-seasedimentshave a low permeability(J. Crowe and A.
Silva, unpublisheddata, 1979) and in sufficientthicknessare
impermeable to seawater.Where the permeable crust is not
covered,water circulatesfreely. A highly variable heat flow
results,and the mean is lower than is predicted becauseconventional techniquescannot measurethe heat lossby advection. When the crustis coveredby a thick blanket of sediment,
circulation still occurs,but no heat is lost by advection because the thick sediments are impermeable to seawater. In
these areas the measured mean flux is a reasonable estimate of
the heat flow at depth.
It is not our purposein this paper to review the subjectof
hydrothermal circulation of seawater through the oceanic
crust. An exhaustive investigation is presented by Lister
[1974].Anderson[1979]has reviewedthe temperaturegradient
observationswhich may indicate seawaterflow in thin sediments overlying permeable ocean crust. Corliss [1971] and
Bottinga [1974] have analyzed the effect that this circulation
has on the compositionof the oceaniccrust. Readers should
consultthesepapersto obtain more detailed information concerningthis rapidly expandingscientificfield.
Reinterpretation
of Oceanic
Heat Flow Measurements
Recognizing the importance of hydrothermal circulation,
Sclateret al. [1976a] reanalyzedall publisheddata on the Pacific. They characterizedthe environment accordingto sediment thicknessand topographicroughness.Each station was
assignedan environmental quality factor grading from A
through D (Figure 7). Only the grade A stationswhere the
SCLATER ET AL.: OCEANIC
AND
A
2000
HEAT
FLOW
277
and Table 4), and the mean values lie closeto the theoretical
-
[3
NORTH
ATLANTIC
0
NORTH
PACIFIC
i?:'•.:..
(Figure 11). We reexamineddata in the Norwegian Sea by
plotting them on an isochronchart of the area (Figure 12). As
there were not enough data within a given age province to
compute a reliable mean, we consideredeach of the grade A
stationsindividually. The valueswhich are all on young crust
fall closeto the theoreticalexpressionfor the heat flow (Fig-
PLATE
MODEL
4000
6000
CONTINENTAL
ure 11).
At an active spreadingcenter near the zone of intrusion the
relation appears to break down. For example, Lawver et al.
.
I
I
40
I
810 I
AGE
IN
I
I
120
•.l•
160
I
MA
B
2000
:5:..
o
::iii:•iq:i::
'
0 NO
RT
H PA
CIFIC
C
::•iiiii
":'
":i•i::i•i•::._
:.."::"
NORTH
ATLANTIC
-- PLAT
E M0DEL
UNDARY
LAYER
[1975] have measuredthe heat flow through the very young
but well-sedimented Guyamas Basin in the Gulf of California. They found that in crustlessthan 2 million years old the
mean heat flow falls below the theoreticalvalue. A likely explanation is the discontinuousnature of the intrusionprocess
[Lister, 1977], which is not adequately representedin present
thermal models. Fortunately, the effect of the initial conditions on thesemodelsis small (cf. Appendix C) and only important for ageslessthan 5 Ma. It doesnot affect significantly
our estimates of heat loss.
4000
From
6000
.....•:...
......!!i!ii'"'
'..::::.:?
....
ß
ß
-..•..
-:....•
.:.....
H.
'
0
'•:::i:i:::
==========================
•
•
•
I
I
I
I
2
5
I0
25
50
I00
AGE
IN
......-...:.:v
•,
I
200
this reexamination
of the heat flow data we have es-
tablished that for crust older than 2 Ma and covered by a
thick layer of impermeable sedimentsthere is a simple relation between heat flow and age. This relation is very closeto
that given by the modelswhich accountfor the subsidenceof
the midocean ridges.
Marginal Basin Heat Flow
MA
Fig. 2. (a) Relation between mean depth and age for the North
Atlantic and North Pacific.The shadedarea representsan estimateof
the scatterin the original pointsusedto determinethe mean data. The
solid curve is the theoretical elevation from the plate model. The
dashedcurve is the elevationcalculatedby assumingthat the lithospherethickenswith time. (b) Plot of depth versusthe squareroot of
age,emphasizing
thet•/2depen'dence
of depthfor crustyoungerthan
80 Ma. Note that the boundary layer model breaks down at 80 Ma
and that a much better fit in older crustis given by the plate model.
basementis completelycoveredby sedimentwere assumedto
give reliableheat flow values.Using thesestations,Sclateret
al. [1976a]found that the scatterwas reduced(Figure 8 and
Table 3) and that the mean valuesfall closeto the theoretical
value (Figure 9). Further surveyson the Juan de Fuca Ridge
[Davisand Lister, 1977]and in the vicinity of anomaly 13 on
the Reykjanes Ridge yielded identical results [Sclater and
Crowe, 1979](Figures8 and 9). Two well-sedimentedareasin
the Pacific,the equatorialsedimentbulge and the Guatemala
Basin, fall well below the theoretical heat flow. No detailed
surveyhas been carried out over the Guatemala Basin.But J.
Crowe and R. P. Von Herzen (personalcommunication,1979)
Watanabe et al. [1977] have recently reviewed the heat flow
through the back-arcbasinsof the westernPacific.They emphasizedthat though the volcanic zone has a highly variable
heat flow, there is still a detectabledependenceon age in the
back-arc basins.Rather than follow the strictly empirical approach of these authors we examined the data which include
these back-arc areas,using our understandingof the heat loss
through normal ocean floor. We consideredeach basin individually and calculateda mean and a standarddeviation for
the heat flow (Tables 5a-5c). They vary significantlyfrom one
basin to another.
We found it difficult for two reasonsto follow the procedure
developed in the deep oceansto establisha convincingrelation between heat flow and age. First, the age of most marginal basinsis unknown, and second,where it is known on the
basis of magnetic lineations or deep-seadrilling holes, there
are few heat flow measurements.The Scotia Sea is an example
of such a basin. It has well-identified
lineations
flow values. We found six basins with reliable
but no heat
heat flow mea-
surements(environmentalquality grade A) and age estimates.
These basinsinclude the Tyrrhenian Sea and Balearic Basin
have shown that the low and variable heat flow values on the
equatorialsedimentbulge are associated
with extremebasement relief and unusually permeable sediments.
Partially as a result of the above analyses,authors now
show or describe the local environment
of all heat flow sta-
tions. We examined thesenew data and found, particularly in
the Indian Ocean [Andersonet al., 1977] and the Norwegian
Sea [Langsethand Zielinski, 1974],a large number of measurements
on well-sedimented
basement.
TABLE 2. SimpleRelationsBetweenDepth, Heat Flow, and Age
[after Parsonsand Sclater,1977]
Age
Depth
0-70
>20
d(t) = 2500+ 350t•/2
d(t) ---6400- 3200e
½-'/6•'8)
0-120
>60
q(t)-- 11.3/t•/• (473/t•/•)
q(t)-- 0.9+ 1.6e
•-'/6z8)(37.5+ 67e•-'/62'8))
A few measure-
mentsare reportedfor the Pacific[Andersonet al., 1976b]but
are too widely distributedto justify our replotting them. We
averagedthe grade A stationsfrom the Indian Oceanwithin
variousage provincesand also,where the age was unknown,
by individualbasin.The scatterin the data is low (Figure 10
Relation
Heat
Flow
Here t is in millionsof years,d(t) is in meters,and q(t) is in pcal/
cm2 s (mW/m2). The decayof the radioactive
elementscontributes
0.1/•cal/cm
2 s (4 mW/m2)to theheatflow.
278
SCLATER ET AL.: OCEANIC AND CONTINENTAL
SEA
HEAT
FLOW
SURFACE
MIDOCEAN
RIDGE
• 5
5
•00
•00
Fig. 3a. Schematicmodelfor a thermalboundarylayer showingthe materialflow (dashedlines)and the conceptof a
thickeninglithosphere.
The solidustemperature
Tsseparates
solidandpartiallymoltenstates:
thesolidlithosphere
above
is coolerthan Ts,and the asthenosphere
belowis hotter.The solidlinesindicateisothermalsurfaces
within the cooling
lithosphere.AH is the subsidenceof the ridge crest.
in the Mediterranean, the Parece Vela and the West Philip-
pine basinsin the PhilippineSea, and finally, the Coral and
Bering seas.The sourcesfor the age and heat flow data can be
found
in Tables
5a-5c.
The two basins in the Mediterranean
have been correctedfor recentsedimentaccumulation(Table
6). In each of thesebasinsthe mean heat flow is closeto the
theoretical value predicted by the thermal models for normal
ocean crust (Figure 13). This supportsthe ideas of Karig
[1970] and others that marginal basinsare formed by extensional processes
similar to thoseoccurringat active spreading
centers.
In order to compare the marginal basins with the deep
oceanswe wishedto separatethe data into the sameage provincesand plot the mean and standarddeviationversusage. As
the age of many marginal basins is unknown, this is not as
straightforward as it first appears. For those basins where
magnetic lineations have been identified or where deep-sea
drilling holeshave been sited,agescan be assignedin a fairly
straightforwardmanner. For the othersthis in'formationis not
available, and a different approach must be taken. Various
authors [Sctater et at., 1976a; Louden, 1976; Watanabe et at.,
SEA
0
SURFACE
1977]haveobservedthat the PareceVela and West Philippine
basinsare about 0.5-1 km deeperthan oceancrustof the same
age. Thus the relation betweendepth and age for the deep
oceansis not a reliable indicator of age for the marginal basins. In contrast, the 'reliable' heat flow values from these ba-
sinsfit the relationbetweenheat flow and age found in wellsedimentedareasof the deep-oceanfloor. Where the heat flow
has been measured in a well-sedimented basin, we use this re-
lation to determinethe age(Tables5a-5c). In light of the high
sedimentationrate of thesebasins,suchagesshouldbe treated
with caution. The agespredicted in this manner for four basins in the western Pacific are of particular interest. The
Ryukyu Trough is Mioceneor younger,and the Japan,China,
and Okhotsk seasare Oligocene.For basinswhere no magnetic, deep-seadrilling, or heat flow information is available
we estimatedthe age from the surroundinggeology.
Having assignedagesto all the marginal basins,we separated the data into age provincesand plotted the mean and
standarddeviationversusage (Figure If). In the youngregionsthe mean value is high, and the scatterlarge. With increasingage both the mean and the scatter decrease.This dis-
A
B
....
0
MIDOCEAN
RIDGE
•
5 --
X2=a --
f
LITHOSPHERE
jOo(I-(•T)
• oo •
•
'ls
'
Ts
too
X2=0
ASTHENOSPHERE
Fig. 3b. Platemodel.Theelevation
AH is calculated
by assuming
thatcolumns
A andB of unitareamusthaveequal
massesabove a common level x2 -- 0.
SCLATER ET AL.: OCEANIC AND CONTINENTAL
HEAT FLOW
279
8.0
300
7.0
• ALL
OCEANS
6.0
,":
MARGINAL
PLATE
5.0
---
BASINS
MODEL
BOUNDARY
LAYER
2002
4.0
;5.0'
4oo
2.0
t.0
I
i
20
40
60
80
`100
4GE
IN
120
140
't60
'•80
M4
Fig. 4a. Mean heat flow and standarddeviationfor all the oceansand for the marginalbasinsas a functionof age.Also
shown are the expectedheat flows from the plate and boundary layer models.
tribution of values is remarkably similar to that for normal
ocean floor (Figure 4a).
Mantle
Convection and Thermal
Structure
A variety of geophysicalobservations,including mean heat
flow, bathymetry,and velocityof surfacewaves,dependupon
the age of the oceaniccrust.Forsyth[1977] has reviewed these
and shown that all reflect changesin the thermal structureat
depth. He concludedthat all the data were compatible with
the model of a cooling plate 125 km thick in a periodotitic
mantle. As an alternative to the plate model, Parker and Oldenburg [1973] suggestedthat the bottom boundary increased
in depth with age. Crough [ 1975] and Oldenburg[ 1975] have
shown that by including an input of heat from below, this
model gives the exponential decrease in depth of the old
ocean floor.
The thickeningboundary layer model and constanttemperature plate model approximate each other [Parsons and
20.0
F
t0.0
•
r
-
8OO
PLATE
MODEL
5OO
•
BOUNDARY
LAYER
5.0
tO0•
50 •
t.0
t
2
5
t0
AGE
20
IN
50
100
200
MA
Fig. 4b. Log-logplot of the mean heat flow and standarddeviationas a functionof age for the oceans.Note that for
crust younger than 50 Ma the mean values fall below the expectedheat flow.
280
SCLATER ET AL.: OCEANIC
AND
CONTINENTAL
HEAT
FLOW
8OO
-
,.
16
E•
600
--
o
•:
o
oøo
• •oO•
o•
I •
In
•
I•, n
z
o
•o
- 400 --
;o
o •8o
•
I
I o•
0
o
• oo
• %•• Y• o •
O•
2
o
o
i
o
I
4
-oo
oi
I
6
AGE
IN
,
8
I
i
I0
MA
Fig. 5. Heat flow valuesplottedas a functionof ageon the Galapagosspreadingcenter.Only thosevalueswhich are
on oceaniccrustof well-definedage were usedfor this plot. Circlesrepresentheat flow values.Plusesare l-m.y. means.
The long-dashedcurveis the heat flow expectedfrom the thermalmodel of Parsonsand Sclater[1977],and the shortdashedcurve connectsthe mean of the observeddata [after •lndersonand Hobart, 1976].
McKenzie,1978].They differ principallyin their lower boundary condition.In essence,there are two waysof handlingthis
condition:the first is to specifythe heat flux at the baseof the
plate and allow the plate thicknessto vary; the secondis to
keep the plate thicknessconstantand to specifythe temperatureat the base. Two mechanismshave been suggestedto
maintain the constantheat flux at the lower boundary:shear
stressheating associatedwith plate motion [Schubertet al.,
1976]or the heat producedby a uniform distributionof radioactive elementsin the upper 300 km of the mantle [Forsyth,
1977]. In contrast, various authors [Richter, 1973;Richter and
Parsons,1975;McKenzie and Weiss,1975]have suggested
that
small-scale
convection
int•eupper
mantle
canmaintain
the
necessary
verticalheattransport
andthetemperature
nearthe
baseof the lithosphereis maintained at a constantvalue. The
TABLE
3.
lithosphereconsistsof two parts, a rigid mechanicalupper
layer and a viscousthermal boundary layer (Figure 14). As it
cools, both layers increase in thickness.At about 60 Ma the
thermal boundary layer becomesunstable. Small-scale convectiondevelopsand createsa thermal structurecloselyanal)gousto that modeledby a fiat plate [Parsonsand McKenzie,
19781.
We favor the small-scale convection
model for two reasons.
First, as it is generallyacceptedthat convectionoccursin the
mantle, there is no necessityfor shear stressheating or large
heat production rates. Second,the thermal stabilitiesof the
constant heat flux models have not been investigated,and
they are incomplete.The convectionmodel can be approximated by a constanttemperatureat a fixed depth with all the
convectivetransport of heat confined to the origin. This al-
Mean and Standard Deviation of Heat Flow Data in Selected Well-Sedimented
Areas of
Known Age in the Pacificand North Atlantic
Age
Range, Ma
1. Northwestern
Pacific
120-140
2. East of Hawaii
3. North of Hawaii
90-100
80-90
4. Equatorial Pacific, 114øW
5. North of the Galapagos
spreadingcenter
15-20
5-10
6. South of the Costa Rica Rift
7. Combination
of areas 5 and 6
5-10
5-10
8. Southof CarnegieRidge
10-20
9. EquatorialPacific, 130ø-150øW 35-75
10. Explorer Ridge, 49øN
11. Juan de Fuca Ridge, 47øN
12. ReykjamesRidge, anomaly 13
3.5-7
3-4
32-38
N
rn
o
o
0%
30
8
18
7
6
1.13(47)
1.57(66)
1.36(57)
2.40 (100)
4.21 (176)
0.14 (6)
0.15 (6)
0.24 (10)
0.58 (24)
0.51 (21)
0.03 (1)
0.05 (2)
0.06 (2)
0.22 (9)
0.21 (9)
12
9
17
24
13
4
10
9
6
24
4
16
3.97 (166)
4.12 (173)
2.85 (120)
0.92 (39)
5.72 (239)
6.40 (268)
1.98(83)
0.41 (17)
0.46 (19)
0.52 (22)
0.48 (20)
2.30 (96)
2.90 (121)
0.24 (10)
0.21 (9)
0.15 (6)
0.17 (7)
0.20 (8)
0.47 (20)
1.40(58)
0.06 (2)
11
12
18
52
40
45
3
N is thenumberof values,rnis themeanheatfluxin #cal/cm2 s (mW/m2),o is thestandarddeviation
in/•cal/cm2s(mW/m:),• isthestandard
errorin #cal/cm2s(mW/m:),and0%thestandard
deviationas
a percentageof the mean.
SCLATER ET AL.: OCEANIC AND CONTINENTAL
HEAT FLOW
281
paper.We studythe relationbetweenheat flow and age and
estimatethe contributionof the decayof radioactiveelements
withinthecrust.Fromthisanalysis
wedevelop
a coherent
geologicmodel to accountfor the observations.
GeologicalModelsfor ContinentalFormation
Recent compilationsof radiometricagesfor exposedgeologicformationshaverevealedthat the continentsconsistpri,
,
marily of Precambriancrust[Hurleyand Rand, 196911.
More
than two thirds of the crust falls within this age range when
areas covered by more recent sedimentationare added [cf.
Goodwin,1976, Figure 2] On closeinspectionit appearsthat
(b)
much of the Precambrian
crust was created before 2.5 billion
yearsago in what is calledthe Archcan.Detailed mappingof
these terrains reveals that the petrology, geochemistry,and
geologicalassociations
are remarkably similar to moderu examplesof island arc and microcontinentalcollisions[Tarney
et al., 1976; Katz, 1976]. These observationshave led to the
generalacceptancethat the Archeancrustwas producedby
processes
whichare still activetoday.However,thereare conflicting theoriesfor the origin and evolutionof the Continental
(c)
crust.Most of themlie betweentwo extrememodels.In "the
first, most of the presentcontinental masshas differentiated
during late permobile times (3000-2500 Ma). The continents
do not grow much after the Archean but are modified by relatively continuousarc-arc amalgamationand continent-continent collision resulting from highly active plate motions
Fig. 6. (a) Patternof convection
to be expected
neara ridgecrest,
1978].The alternative
concept
is thatthecontinents
wherethe permeablelayer is opento the ocean.(b) Convective
pat- [Winalley,
timeby irreversible
chemical
differentiation
of
tern forcedby topographyin an areaof permeablecrustboundedby a growthrough
thin impermeableblanketof sediment.(c) The caseof permeable the upper mantle and by accretionof newly differentiatedmacrust with a rough boundary,buried by flat-lying sediments.The terial particularly at or near the margins. The accretionary
varyingthermalresistance
of thesediment
blanketoverpowers
thedirect effectof the topography[from Lister, 1972].
lowsa straightforward
comparison
of the heat lost by plate
creationwith that lostby conductionthroughthe plate.With
the constantheat flux conditionthe plateboundarydoesnot
remainat a fixeddepth,and the heatlostowingto advection
fromthe mantlehasto be calculated
continuously
alongthe
processes
are the sameasthosein the firstmodel,i.e, arc-arc
amalgamationand continent-continent
collision.In an ex-
D
CREST
bottom of the plate.
CONTINENTAL
HEAT
FLOW
Introduction
The interpretationof continentalheat flow measurements
is
difficult for many reasons.The continentalcrust has an age
spangreaterthan 3800 Ma and has beenmodifiedcontinuouslyby geologicprocesses.
The interpretationinvolvesmany
c
FLANK
variables whose effects, in particular radioactivity, are not
properlyunderstood.Any reasonablemodelmustincorporate
a numberof independentfactors,and it is necessary
to exam-
ine themeasurements
according
to theirlocalcontextandto
integratethemwithin a geologicframework.We useasa basis
the theoryof plate tectonics.Continentsare modifiedthrough
time by severalprocesses,
the mostimportantbeingislandarc
vulcanism,arc-arc amalgamation [Burke et al., 1976], continental collision [Molnar and Tapponier, 1976], continental
stretching[Artemjevand Artyushkov,1971], and finally erosion.
"•:
Mostof thecontinents
arePrecambrian
in age,andwe have
concentratedon this geologicperiodto investigatethe relation
betweenheat flow and age. A studyof Phanerozoiccontinental crust would require the considerationof the specifictectonic historyof each region and is beyondthe scopeof this
B
BASIN
A
BASIN
Fig. 7. Schematic
diagramof theenvironmental
gradesA-D [from
Andersonet al., 1977].
282
SCLATER ET AL..' OCEANIC
HEAT FLOW
A i 50
15•-•m
Lu
150
B
200
N•DRTH
V(/ESTE
RN'
II
I
IN mW/rn z
I00
PACIFIC
I
D
15
2
5o
I
3
4
I DO
15 0
CONTINENTAL
HEAT
5
FLOW
HEAT
FLOW
INmW/m
z2OO
I00
150
C
5O
I00
15 0
200
IO
5
5
0
o
E
200
HEAT
FLOW
INmW/m
2
50
151
' NOR?H
OF
hAWAII
'1
I0
z
o
15
AND
,
50
I O0
150
200
15
' EQUATORIAL
PACIFIC
I
50
I00
150
20•0
' COSTA"RICA R'IFT
'
I0
z
0
I
2
G
3
4
I00
I
i
150
AND
H
J
i oo
'5i
•oo
'
;oo
'
I00
150
I
200
3
2
I00
5
0
I
K
•oo
EXPLORER
RID(•E
2
,oo
3
•oo
151 '
4
•oo
III
5
400
5
150
200
PACl FI'C
130øW - 150øW
,
I
2
3
/
•oo
'JUAN
lieFUCA'
RIDGE'
4
EQUATORIAL'
••511
' •OUT.
•F"
4
3
50
'
F
•oo
50
OF
i.
2
I
200
COM•II NATIOI{I
E
i i I Ii ß
5
4
50
•
I00
150
200
15
t 'REYKJ•
RIDG
'
60ON-
56ON
2
3
I0
z
5
0
2
4
6
8
I0
12
14
u
HEATFLOWIN p.CAL/CM2S
2
4
6
8
I0
12
HEATFLOWIN p.CAL/CM2S
14
0
I
4
5
HEATFLOWIN p.CAL/CM2S
Fig. 8. Histogramsof the 'reliable'heat flow valuesfrom areasin the North Pacific(Figures8a-8k) and from one areain
the North Atlantic (Figure 8/). The meansand standarddeviationsare givenin Table 3.
treme version the continentsformed in small globular masses
which grow in size through time from a central core [Moorbath, 1977].Obviously,somecombinationof the two models
can explain the observations,and in permobile times they
were identical. At this time the loss of heat due to radioactive
TABLE
4.
Mean and Standard Deviation
of Grade A Environment
Heat Flow Measurementsin Various Age Provincesof the Indian
Ocean
Age
Range, Ma
N
m
Indian
35-52
52-65
65-80
80-95
95-110
110-125
125-140
6
22
!7
19
14
4
14
Somali
'•
12
water and radioactive trace elements such as uranium, tho-
Ocean
1.49(62)
1.64(69)
1.55(65)
1.25(52)
1.17(49)
1.20(50)
1.14(48)
0.15 (6)
0.39 (16)
0.36 (15)
0.22 (9)
0.18 (8)
0.37 (15)
0.21 (9)
Basin
1.34(56)
decay was greater than today [Lambert, 1976] and probably
resultedin the existenceof more plates and a greater area of
young oceanic crust [Bickle, 1978]. However, irrespectiveof
the model favored, it is to be expectedthat Precambrian crust
will exhibit large differencesin age. This is observed,and the
radioactiveagesextendfrom 3800 to 600 Ma.
For our purposesit is not important which model is preferred. Both the reworked or newly created continentsare assignedthe age of the last orogenicevent, and both involve a
vertical and horizontal gradation of the metamorphosedrocks
as is observedtoday. One important consequenceis that the
lower continental crust is depleted in chemically combined
0.16(7)
N is the numberof values,rn is the meanin/zcal/cm•-s (mW/m•),
and o is the standarddeviationin/•cal/cm•-s (mW/m•).
rium, and potassium.
Reworking or accretionof continentalcrust has probably
occurredover short inte_rvalsof time (200 m.y.) at specificpehods in the past [Moorbath, 1977; Windley, 1978].There were
two major pulsesin the Archean,one at the beginning,38003700 Ma, the other at the end, 2900-2700 Ma. In the Pro-
terozoic pronounced pulsesoccurred between 1900 and 1700
Ma and around
1500 and 1000 Ma.
A series of distinct
oro-
genieshave taken place almost continuouslythroughoutthe
Phanerozoic.
SCLATER ET AL.: OCEANIC AND CONTINENTAL
A
8.0
-- 300
•.0
-
-•oo •
•4.0
these measurements
-
.x,,
•
_ •oo ,,•
I
40
•
I
80
•
I
t20
AGE
IN
MA
I
I
t60
283
are less than 20% and fall well within
the
range of variations associatedwith geologicand environmental causes.
In 1968, Polyak and Smirnov suggestedthat the average
heat flow decreasedwith orogenic age. Later, Sclater and
Francheteau [1970] and Chapman and Pollack [1975a] confirreed this rough relation. The heat flow is generally high and
very scattered in young regions and decays to a value of
_
,
FLOW
and erosion.The principal environmentalproblemsare largescalewater circulation and past climatic changes.In addition,
there are difficultieswith early thermal conductivity determinations.Many were made on unsaturatedsamplesand are too
low [Simmonsand Nur, 1968],and othersconsistof a few values supplementedby a relation between conductivity and
rock type. Fortunately, in general the errors associatedwith
•
SIMPLE COOLING MODEL
PLATE
MODEL
HEAT
,
200
around 1.0/•cal/cm2 s (42 mW/m 2) in the early Proterozoic.
-
3OO
Estimatingthe contribution of the radioactivedecay of U,
Th, and K to the surfaceheat flow was a formidable problem
until Birch, Roy, and their co-workers[Birch et al., 1968; Roy
et al., 1968] establishedthat the heat flow and the surfacera-
-200
-•00
,?zz'•_•..7.•
•l•
50
INDIAN OCEAN 'A' S TATIONS
5
Fig. 9.
•0
AGE//V
20
MA
50
•00
200
35-
(a) Mean heat flow as a function of age for the well-sedi-
•o
50
52-65
Solid rectanglesrepresentthe errors in heat flow and age. The solid
curve is the theoreticalheat flow from the plate model, and the dashed
curve that from the boundary layer model. The hatched area representsthe value from the equatorial Pacific. (b) Log/log plot of heat
flow as a function of age for the averagevalues from the well-sediareas.
•oo
•
mented areas in the North Pacific and one area in the North Atlantic.
mented
52
HEAT FLOW mW/m 2
5
0
t.0
2.0
65•o
1.0
80
i
2.0
80 - 95
I
i
[t.63
pulsebetween1900and 1700Ma. The secondgroupextends
from 1700 to 800 Ma and covers the entire Helikian
•oo
I •-t.65
I
5
0
We decidedto separatethe continentsinto four age groups.
The first comprisesall continentswith agesgreaterthan 1700
Ma including the Archeart,the Aphebian, and the orogenic
50
I to
I
-t.24
and the
first portion of the Hadrinian. The third group is from 800
Ma, the early Hadrinian, to the start of the Mesozoicat 250
Ma. Finally, the fourth group is the Mesozoicand Cenozoic.
It encompasses
the presentepisodeof plate motion and creation of sea floor. All the relevant information documenting
our estimatesof the age of cruston individual continentscan
t.o
2.0
95-
t .o
2.0
tt0-125-
tt0
to
140
I
be found in Appendix B.
A detailed discussionof the philosophyfundamental to our
approachin determiningthe age of the basementcan be
5
t.30
found in the work of Hurley and Rand [1969]. In essence,we
have tried to assignthe age of the last thermal event rather
than the primary age.Thesetwo agesare sometimesquite different. As we separate the continents into only four age
groups,the error introducedin the heatlosscalculations
is not
large. However,thesedifferencescould presenta problemto
the interpretation of the relationship between heat flow and
age,especiallyin the late Proterozoicand Phanerozoic.We return to this questionat the end of our discussionof continen-
t.0
ARGO
•o
2,0
ABYSSAL
oLJl-J
4.0
PLAIN
SOMALI
ABYSSAL
to
•t08
2.0
PLAIN
I
1.33
5
5
tal heat flow.
Continental
Heat Flow Measurements
o
0
The variation
of heat flow on continents
is a function
of a
variety of geologicfactorsand a suite of environmentaland
measurementproblems. The major geologicfactors include
orogenic history, the amount of radioelementsin the crust,
t.o
2.0
t.0
2.0
HE4T FL 0 Wt• ca//crn •s
Fig. 10. Histogramsof the reliable heat flow valuesfrom the Indian
Ocean. The means and standarddeviationsare given in Table 4.
284
SCLATER
ET AL.: OCEANICAND CONTINENTAL
HEAT FLOW
- 300
7o[
• INDIAN
OCEAN
o
NORWEGIAN
PLATE
50
---
•L
250
SEA
MODEL
BOUNDARY
LAYER
MODEL
o
•
-t50•
•3o-
o oo
20 -
-t00•
or
,ø
10
.5
20
I
I I
.4
.3
I
•
.2
50
t00150
I
] I
.1
MA "-.
0
Fig. 11. Meanheatflowandstandard
deviation
fromtheageprovines
in theIndianO•an plotted
against
l/t •/•.
Alsopresented
aregradeA enviro•entstations
fromtheNo•egianSea.Theexpected
heatflowsfromtheplateand
bounda• layer models are shown.
diogenicheat productionwerelinearlyrelatedwithin tectoni- Thereis,however,a greatdealof controversy
aboutthe matcally definedregionswhichthey calledheat flow provinces. ter [$asset al., 1971].Both factorscan lead to underestimates
Lachenbruch
[1970]suggested
that the upwardmigrationof of the heat flow; their combined effects could amount to 30%
the radiogenic elementscould account for this relation.
The validity of isolated heat flow measurementshas been
questionedby LewisandBeck[ 1977]andLachenbruch
and$ass
[1977]. These authors have demonstrated that the slow circu-
Heat Flow and.4ge
lation of water affectsmany measurements
in westernNorth
America. The climatichistoryalso perturbsthe heat flow at
upon a world map with each continentseparatedinto four
ß
of the actual value.
_
We superimposed
the land data from Jessop
et al. [1976]
provinces
(Plate2). We considered
thecontinents
individually
depth.Horai [1969],Jessop
[1971],andBeck[1977]havesug- andconstructed
a histogram
of thevaluesfor eachageinter-
gestedthat in North America the last glaciationcan reduce val (Figure 15).
the near surfacetemperaturegradient_byas much as 20%.
We didnotapplyanyselective
criteriabasedonqualityand
30øW
30øE
GREENLAND
11
\
68/
/ 2 03
/
40
/
098
60øN
60øN
Fig. 12. Grade
A environment
stations
ona polarprojection
chart
ofthemagnetic
lineations
intheNorwegian
Sea[after
Langsethand Zielinski, 1976].
SCLATER ET AL.: OCEANIC
TABLE
5a.
Marginal Basin
Arctic Ocean
Bering Sea
KamchatkaBasin
Seaof Okhotsk
Seaof Japan
Ryukyu Trough
Shikoku Basin
Mariana Trough
PareceVela Basin
West Philippine
Basin
South China Sea-•
Carolina Basin
Andaman Sea
Sulu Sea
CelebesSea
AND
CONTINENTAL
HEAT
FLOW
285
Age, ObservedHeat Flow, and Area for the Arctic Ocean and Northwest Pacific Marginal Basins
Age,* Ma
N
rn
o
Area, 106km•-
65-80
125-140
9-20
20-35
20-35
9-20
9-20
0-4
20-35
35-52
52-65
20-35
9-20
20-35
35-52•:
0-9
9-20
20-35
47
7
1.58(66)
1.16(49)
0.40 (17)
0.30 (13)
80
191
10
12
11
29
28
18
8
2
6
3
5
8
8
2.01 (84)
2.20 (92)
2.97 (124)
1.20(50)
1.22(51)
1.42 (59)
1.45 (61)
1.18(49)
1.74(73)
2.04 (85)
1.57(66)
2.33 (98)
2.45 (103)
1.94(81)
1.64(69)
0.81 (34)
0.56 (23)
1.59(67)
1.03 (43)
1.02(43)
1.01(42)
0.77 (32)
0.92 (39)
0.80 (33)
0.01
0.09 (4)
0.28 (12)
1.67(70)
0.61 (26)
0.49 (21)
2.27
0.81
0.10
0.20
0.44
0.02
0.57
0.36
1.40
1.81
1.00
1.24
0.24
0.75
0.80
0.15
0.04
0.23
Basisof Age Estimate
heat flow, thispaper
Cooperet al. [1976]
guess
heat flow, thispaper
heat flow, this paper
heat flow, this paper
Wattset al. [1977]
Karig [1971]
Fischeret al. [1971]
Louden[1976]
Louden[1976]
heat flow, Watanabeet al. [1977]
Bracey[1975]
Bracey[1975]
Bracey[1975]
Lawyeret al. [1975b]
heat flow, this paper
heat flow, this paper
N is thenumberof values,rn is themeanin/mal/cm2 s (mW/m2),ando is the standarddeviationin/•cal/cm:s (mW/m:).
*Assigned age province.
-•New values[Andersonet al., 1978]give a higher mean and lessscatterand indicate an age closerto 25 Ma.
$Partssouthof the equator.
TABLE 5b. Age, ObservedHeat Flow, and Area for the Mediterraneanand Caribbean Marginal Basins
Age,* Ma
N
rn
o
Area, 106km2
Basisof Age Estimate
1.12(53)
0.68 (28)
1.19(50)
0.48 (28)
0.87 (25)
1.24(52)
0.72
0.31
0.18
0.40
0.41
0.42
Barberi et al. [1978]
Hsu et al. [1978]
Bayer et al. [1973], Hsu et al. [1978]
heat flow, this paper
heat flow, as above
heat flow, this paper
Mediterranean
Tyrrhenian Sea
North Balearic Basin
South Balearic Basin
Eastern Mediterranean
Black Sea
Caspian Sea
6-10
20-35
20-35
110-140
old
old
13
13
19
33
51
20
2.69 (113)
1.75(73)
1.42(59)
0.75 (31)
1.04 (44)
1.95(85)
0-4
2
2.19(92)
0.12(53)
4-9
3
1.99(83)
0.34 (14)
3
3
11
37
27
50
7
3
1.72 (72)
1.59(67)
1.45 (61)
1.36(57)
1.30 (54)
1.13(47)
1.66 (70)
1.10(46)
0.55 (23)
0.47 (20)
0.18 (8)
'0.50 (21)
0.20 (8)
0.63 (26)
0.35 (15)
0.84 (35)
Caribbean
Cayman Trough
9-20
20-35
35-52
50-65
65-80
65-80
110-140
20-35
20-35
Yucatan Basin
Columbia Basin
Venezuela Basin
Gulf of Mexico
Grenada Trough
Tobago Trough
0.23
0-35
Scotia Sea
Total
J. Morgan (personalcommunication, 1979)
0.22
0.64
0.50
0.64
0.13
heat flow, this paper
heat flow, this paper
heat flow, this paper
heat flow, this paper
guess
sameas Grenada Trough
Barker and Burrell [ 1977]
1.54
5.69
N is thenumberof values,rnis themeanin/•cal/cm2 s (mW/m:), ando is the standarddeviationin/•cal/cm2 s (mW/m2).
*Assigned age province.
TABLE 5c. Age, ObservedHeat Flow, and Area for the SouthwestPacific Marginal Basins
SolomonSea
WoodlarkBasin
WestCoral Sea
New HebridesBasin
Fiji Plateau
Lau-KermadecTrough
SouthFiji Plateau
TasmanSea
BandaSea
Age,* Ma
N
rn
o
Area, 106km2
Basisof Age Estimate
9-20
0-20
35-52
20-35
0-9
0-4
20-35
53-65
65-80
35-52
2
12
14
13
45
31
22
3
7
1.73(72)
1.97(82)
1.53(64)
1.48(62)
2.53 (106)
1.70(71)
1.13(47)
1.26(53)
1.21(51)
0.17 (7)
1.01(42)
0.35 (15)
0.50 (21)
1.60(67)
1.51(63)
0.78 (33)
0.15 (6)
0.69 (29)
0.06
0.46
0.42
0.87
1.42
0.60
1.26
0.83
1.46
0.56
Luyendyket al. [1975]
Luyendyket al. [1974]
Burnset al. [1973]
Burnset al. [1973]
Chase[1971]
Weissel[1977]
Weisselet al. [1977]
Weisseland Hayes[1977]
Weisseland Hayes[1977]
guess
Total for southwest Pacific
Total for all west Pacific
7.94
20.37
Total for all marginal basins
26.06
N is the numberof values,rnis themeanin/•cal/cm2 s (mW/m2),ando is the standarddeviationin/•cal/cm2 s (mW/m2).
*Assigned age province.
286
SCLATER ET AL.: OCEANIC AND CONTINENTAL
TABLE 6.
Marginal Basin
N
rn
HEAT
FLOW
Marginal Basins'Reliable' Heat Flow Estimates
o
Reference
Age, Ma
Reference
TyrrhenianSea*
BalearicBasin-•
8
6
3.275(137)
2.17õ(91)
0.375(15)
0.25õ(10)
6-10
18-32
PareceVela Basin
West Philippine Basin
6
6
2.15 (90)
1.72 (72)
0.16 (7)
0.16 (7)
Ericksonet al. [1977]
Ericksonet al. [1977]
Hsu et al. [1978]
$clateret al. [1976b]
$clater et al. [1976b]
18-32
38-50
Barberiet al. [1978]
Hsu et al. [1978]
Bayer et al. [1973]
Fischeret al. [1971]
Louden[1976]
West Coral Sea
BeringSea
11
7
1.64(69)
1.16(49)
0.32 (13)
0.30 (13)
thispaper
thispaper
45-55
110-125
Karig et al. [1974]
Burnset al. [1973]
Cooperet al. [1976]
N is the numberof values,rn is the meanin/zcal/cm2 s (mW/m2),and o is the standarddeviationin/zcal/cm2 s (mW/m:).
*All values thought to be closeto basementoutcropshave been neglected.
-•The two valueson the Rhone Fan havebeenneglected.
SHeatflowis3.43+ 0.37/zcal/cm:
s (144+ 15mW/m:) whenit isincreased
by5%to account
for recentsedimentation
[Erickson
etal., 1977].
õHeatflowis2.66+ 0.30/zcal/cm:
s(111+ 13mW/m2)whenit isincreased
by22%to account
forrecentsedimentation
[Erikson
etal., 1977].
treated all the data. The heat flow stationsare not randomly
distributedon the continents,and many of them are locatedin
closely spacedgroups. In order to reduce the bias which this
introduceswe averagedall values which differed by lessthan
10% and lay within a radius of 30 km. These figures cover
most closelygroupedvaluesand were chosenintuitively. For
groups with a large deviation all values were considered.For
Lake Superior and Europe we examined histogramsof individual clustersto checkthat the data were not biasedby this
approach.
We computed the mean, standard deviation, median, and
meandeviationaboutthe medianfor eachprovince(Table 7).
evidencethat the heat flow is approachingan equilibrium
value in provincesolder than 800 Ma. We explainthe remaining scatterlater in this section.
The equilibrium value is higher than previous estimates
(Table 7). This increaseprobably resultsfrom a better treatment of the environmental
and instrumental
factors in the
newer values. For example, Lewis and Beck [1977] have
shown that the variation of heat flow values in a Precambrian
greenstonebelt in Ontario can only be explainedby slowcirculation of water at depth and rejectedthe lower valuesmeasured.
An important feature of the histogramsis the distribution of
The use of the median and the mean deviation about the me-
heat flow valuesbelow 0.6/.tcal/cm2 s (25 mW/m2). In the
dian reduces the bias created by erroneousand anomalous
older two provincesoutside of Africa there are almost no val-
values. There is no reason to believe that the values are nor-
uesbelow0.6/.teal/era2 s (25 mW/m2). This cutoffis alsoobservedfor the youngerprovincesbut is not so obviousowing
mafly distributed, and the standard deviation and mean deviation about the median give only estimatesof the scatter.
Certain simpleconclusionscan be drawn from this analysis.
to the flatness of the distribution.
Heat Flow and SurfaceHeat Production
The Eurasian and North American values have almost identi-
cal distributions.In the youngestprovincethe mean heat flow
The distributionof the main radioactiveheat-producing
is high (about2.0/zcal/cm:s, or -•80 mW/m :) and is associ- elements, U, Th and K, has received much attention and sevated with a large scatter.For all continentsin provincesolder eral of its featuresare now well documented.The radiogenic
than 800 Ma the heat flow tends to a constantvalue lying in heat productionis a scalarquantitywhich is highly variable
the range 1.0-1.2/zcal/cm:s (42-50 mW/m:). Both the mean on the surfaceof a continent,on both small and large scales.
Continuous belts enriched in uranium and thorium have been
and the scatterdecreasewith age (Figure 16). This behavioris
5.0
MARGINAL
--
PLATE
-
BASINS
200
MODEL
BOUNDARY
LAYER
MODEL
5.0
-too
2.0
50
t.o
t0
20
50
100 450 MA
x..
I
.2
.'1
0
Fig. 13. Mean heat flux and standarddeviationfrom the marginalbasinsplottedagainstl/t 1/2.The expectedheat
flowsfrom the plateand boundarylayermodelsare alsoshown.T and B, the dashedbars,representthe valuesfrom the
Tyrrhenian Sea and BalearicBasin,respectively.
SCLATER ET AL.' OCEANIC
AND
0
50
I00
I
I
I
CONTINENTAL
HEAT
FLOW
150
-
287
Age,rn.y.B.
P
I
Onset of
the instobility
I Viscøu$
I
Therrnol
structure
of pleteend
smoll-scele convection epproech eqmlibrium
Fig. 14. Schematicdiagram showingthe division of the plate into rigid and viscousregionsand the occurrenceof an
instability in the bottom viscouspart [after Parsonsand McKenzie, 1978].
reported in Norway [Killeen and Heier, 1975], in Australia
[Heier and Rhodes, 1966], in the United States [Phair and
Gottfried,1964],and in the SuperiorProvincein Canada (P.
G. Killeen, personalcommunication,1978). A general trend
of decreasewith depth has been shownin a seriesof plutons
in Idaho [Swanberg,1972],in a vertical sectionof the eastern
Alps [Hawkesworth,1974], and in several deep boreholes
[Lachenbruchand Bunker, 1971;Lubimovaet al., 1973].
The radiogenic heat production can be correlated with
magmaticdifferentiation,accordingto a relationshipwhich is
not unique and differs for different magma series[Tilling et
al., 1970].It can also be correlatedwith a metamorphicindex.
High-grade metamorphicrocks are significantlylower in Th
and U than theft counterpartsin lower metamorphic grades
[Lambert and Heier, 1967; Heier and Adams, 1965; Rybach,
1976]. Typical lower crustal rocks have low heat production
for by an upward concentrationof the heat-producingelements in the crust combined
with lateral concentration
differ-
ences.
Detailed seismic studies, using reflection and refraction,
have revealed that the crust has a complicated structure,heterogeneousto the depth of the Moho. The crustal thicknessis
highly variable, both on a small scale, for a given tectonic
unit, and on a large scale,from one unit to another [Mueller,
1978; Berry, 1973; $ollogub et al., 1973]. Also, Padovani and
Carter [1977] have shown from petrologicalstudiesthat the
continental crust varies horizontally. This complexity extends
throughoutthe whole crust,as deep seismicsoundings[Smithson, 1978] have revealed variations at depth comparable to
thoseobservedfrom geologicalobservationsat the surface.As
a consequencethe picture of a layered crust must be either
abandonedor, at best, acceptedonly as a crude average.This
rates,rangingfrom0.2 to 1.5x 10-• cal/cm• s (0.08to 0.62 x complexitypreventsthe direct estimationof either the amount
10-6 W/m•). In summary,all availabledata canbe accounted or the distribution of the radiogenicelementsin the crust.
TABLE 7. Heat Flow Statisticsfor the Continental Age Provinces
Age
Province, Ma
Mean Deviation
N
rn
o
Median
About Median
0.93 (39)
1.34(56)
1.10(46)
0.64 (27)
0.10(4)
0.31 (13)
1.22(51)
0.19 (8)
1.07(45)
0.79 (33)
0.33 (14)
0.38 (16)
1.84(77)
1.40 (59)
1.20(50)
1.05 (44)
0.64 (27)
0.59 (25)
0.24 (12)
0.26 (11)
0.91 (38)
1.50(63)
1.79(75)
0.97 (41)
0.51 (21)
0.62 (26)
0.17 (7)
0.29 (12)
1.53(64)
1.48(62)
1.10(46)
1.00(42)
0.70 (29)
0.32 (13)
0.12 (5)
0.21 (9)
1.67(70)
1.46 (61)
1.17(49)
1.05(44)
0.76 (32)
0.34 (14)
0.22 (9)
0.29 (12)
250-800
800-1700
>1700
19
6
39
Africa and Madagascar
1.15 (48)
0.82 (34)
1.36(57)
0.11 (5)
1.14(48)
0.52(22)
0-250
19
1.31(55)
South America
0.22 (9)
North
America
0-250
250-800
800-1700
> 1700
164
44
50
216
1.97(82)
1.53 (64)
1.26(53)
1.11 (46)
0-250
250-800
800-1700
>1700
18
17
10
14
0-250
250-800
800-1700
>1700
197
420
72
106
1.09(46)
0.76 (32)
1.81(76)
0.78 (33)
1.76(74)
0.27 (11)
1.14(48)
0.44 (18)
Europe and Asia
1.81(76)
1.24(52)
1.50(63)
0.44 (18)
1.07(45)
0.15 (7)
1.05(44)
0.31 (13)
0-250
250-800
800-1700
>1700
398
500
138
375
1.82(76)
1.50(63)
1.20(50)
1.10(46)
Australasia
All
Continents
1.26(53)
0.51 (21)
0.24 (10)
0.38 (16)
N is the numberof values,rn is the meanin/•cal/cm2 s (mW/m2), and o is the standarddeviationin
/•cal/cm:s (mW/m:).
288
SCLATERET AL.: OCEANICAND CONTINENTALHEAT FLOW
SCLATER
ETAL.;OCEANIC
ANDCONTINENTAL
HEATFLOW
289
(B)
N. AMERICA
3.0
EURASIA
3.0
•oo
2.0
2.0
I
I
1.0
4.0
I
I
• 000
2000
{000
I
2000
(D)
(c)
ALL CONTINENTS
AUSTRALIA
and
AFRICA
I
I
'
•000
5O
I
2000
'1000
AGE-/N
2 000
M•
Fig.16. Heat
flow
asafunction
ofagefor(a)North
America,
(b)Eurasia,
(c)Australia
andAfrica
(dashed
lines),
and
(d) all continents.
andPollack,1975;Kutas,
However,withincertainspecific
areasthereis a simplelin- al., 1974;Raoet al., 1976;Chapman
to be reliablearelistedin
earrelationship
between
heatflowandsurface
radioactivity: 1977]andthosethatweconsider
Table8. Thegeneralfeatures
of theseprovinces
arefor a maQo-- Qr+ D ' Ao
(1) jorityofvalues
tolieona linedefined
byQrandD anda cer-
whereQoand,40arethe surface
heatflowandradioactive tain numberof valuesto be offsetfrom the line. Theseoffset
definea 'heatflowsubprovince'
wherethere
heatproduction.
Q,, the 'reduced'
heatflow,andD arecon- valuessometimes
is
a
similar
relationship,
with
the
same
Qr
and
a
differentD
stants[Birchet al., 1968;Royet al., 1968].The relationship
[Blackwell,
1971].
When
the
number
of
data
points
is small,
holdsfor largeareaswheretheheatproduction
ratesandrathe
uncertainty
in
the
determination
of
the
parameters
Qrand
diometric
agesvaryconsiderably.
Theinterpretation
of thereto select
themostreliableones
lationis ambiguous
andimpossible
withouta certainnumber D isgreat,andit isnecessary
any interpretation.
We useda criterion
of assumptions.
In particular,
thereisconsiderable
discussionbeforeattempting
basedon thenumberof datapointswhichactuallydefinethe
andtherangeof heatproduction
ratesrepThesimplest
interpretation
is thatD represents
thethick- linearrelationship
In particular,we considered
a valueof Qr to be
nessof a slabof uniformradioactivityand that Qr is the heat resented.
asto the physicalmeaningof both Qr and D.
onlywhenlowvaluesof crustalheatproduction
fluxthrough
thebase[Royetal., 1968].
Anotherinterpretationmeaningful
is that D is the inverseof the decrementfor an exponentially were reported.
and Sass[1977],for the United
deCreasing
rateof radiogenic
heatproduction
[Lachenbruch, Recently,Lachenbruch
States,andRaoandJessop
[1975],for all stations
in the Pre1970]. In this case,
A(z) -- Aoe-z/D
(2)
cambrian,haveexaminedthisrelationship
in moredetail.In
the United States,for stationswestof the Great Plains,i.e.,
sections
of the country,
Lachenbruch
andSass
where,40is theheatproduction
at thesurface.
Suchan inter- the younger
in thevalues
andlittleobvious
corpretation
hassome
justification
ongeochemical
grounds
and [1977]finda largescatter
haslimitedsupportfrom observations.
Lachenbruch
[1970] relation betweenheat flow and surfaceradioactivity(Figure
17).However,
withinindividual
orogenic
beltsandin particu-
demonstrated
that with thisdistributionthe linearrelationis
preserved
if differential
erosion
occurs
withintheheatflow lar for the SierraNevada there is still evidencefor a correlaof theNorthAmerican
continent
the
province
considered.
In thismodel,
D characterizes
thedegree tion.Forolderportions
relationship
is
well
established.
Elsewhere
in
the
world,
Rao
of upward
migration
of theradiogenic
elements,
andQrisapandJessop
[1975]havefoundthattherelationbetween
heat
proximately
theheatflowat thebaseof thecrust.
heatproduction
hasanoverall
significance.
Equation
(1)hasbeenusedtodefine
heatflowprovinces
in flowandsurface
theyhaveshown
thatthereisa general
correlamanypartsof theworld[RaoandJessop,
1975;Swanberg
et Forexample,
290
SCLATER ET AL.: OCEANIC AND CONTINENTAL
HEAT
FLOW
TABLE 8. Age and ParametersDefining the Linear Relation BetweenHeat Flow and Age for SeveralContinentalHeat Flow Provinces
Province
Age, m.y.
N
Q
Qr
D, km
Reference
Basinand Range (North America)
Sierra Nevada (North America)
Eastern Australia (Australia)
EasternUnited States(North America)
United Kingdom (Eurasia)
Central Shield (Australia)
Ukranian Shield (Eurasia)
Western Australia (Australia)
Canadian Shield (North America)
65-0
125-0
65-0
400-100
600-300
2000-600
2500-1900
2000
3000-2000
86
9
9
14
10
9
12
7
11
2.20 (92)
0.93 (39)
1.72 (72)
1.36 (57)
1.40 (59)
1.98(83)
0.87 (37)
0.93 (39)
0.93 (39)
3000-2000
5
0.86 (37)
9.4*
10.1
(11.1)*
7.5
16.0
11.1'
7.1
4.5
14.4
13.6'•
8.5*
Sassand Lachenbruch[1978]
Sassand Lachenbruch[1978]
Sassand Lachenbruch[1978]
Sassand Lachenbruch[ 1978]
Richardsonand Oxburgh[ 1978]
Sassand Lachenbruch[1978]
Kutas [ 1977]
Sassand Lachenbruch[1978]
Jessopand Lewis[1978]
Baltic Shield (Norway)
1.41 (59)*
0.40 (17)
1.37 (58)*
0.79 (33)
0.56 (24)
0.64 (27)*
0.60 (25)
0.63 (26)
0.50 (21)
0.67'•
0.53 (22)
Swanberget al. [1974]
N is thenumberof values,Q is themeanheatflowin/•cal/cm2 s (mW/m2),Qristhereduced
heatflowin/•cal/cm2 s (mW/m2),andD isthe
characteristicdepth.
*Unreliable
estimate.
•'Qo and D valuesallowing for Pleistoceneglaciation.
tion betweenthe heat flow and the surfaceheat productionin
the Precambrian (Figure 18). The large number of stations
where the radioactivity is low constrainsthe reducedheat flow
to lie between0.5 and 0.7/•cal/cm2 s (21 and 29 mW/m2).
Work done since 1975 confirms these values (see Table 8).
Rao and Jessop [1975] have also examined the heat flow
through Precambriangreenstonebeltsand find a range of val-
Proterozoic
and Achean.
These observations
are evidence that
steadystate conditionsare reachedand that the scatterin the
heat flow is almost solely due to differencesin the concentration of heat-producing elements.
As we have shown above, the values of the reduced heat
flow Qr obtained in all the old continental provincesare in
striking agreement(Table 8). In most of theseprovincesthe
ues from 0.69 to 1.18/•cal/cm: s (29 to 49 mW/m •) with a heat flow which is actually measured at the surfaceis closeto
meanof 0.90/•cal/cm• s (38 mW/m •) (Table 9). Thesevalues Qr for low valuesof the rate of heat production.Thus Qr must
lie between the intercept heat flow and the mean value for the
have a general geophysicalsignificancefor old continental
early Proterozoicand Archean (Table 7). Where the valuesof
crust. On the other hand, the complexity of both the crustal
radioactivity are consistentlylow in Precambrianregions,for structureand the behavior of U, Th, and K in geologicenviexample, the Superior Provinceof Canada [Jessopand Lewis, ronments prevents any simple interpretation of the relation1978], the heat flow has little scatter, and the mean value is ship between heat flow and radioactivity. In particular, neicloseto 1.0/•cal/cm• s (42 mW/m2). Where the valuesare ther D nor Qr is knowa with certainty. D varies significantly
high, suchas the Central Australia Shield, the heat flow is varfrom placeto place and haslittle obviouscorrelationwith any
iable, and the mean higher than elsewhere.However, the rephysical phenomena. Also, Richardsonand Oxburgh [1978]
duced heat flow is very similar to that through other areasof
and C. Jaupart and G. Simmons(unpublisheddata, 1978)
the Precambrian. Clearly, there is no obviousrelation between have shown that metasedimentaryand metamorphic terrains
age and either heat flow or surfaceradioactivity in the early surroundingthe granitic plutons exhibit the same relation between heat flow and surfaceradioactivity as the plutons. The
reasonfor this similarity is unknown, but it doesimply that
HœA T PRODUCTION 10-6W/rn $
:•.õ
õ.0
7.õ
the relation
IO
200
5.0[I oI I I"
4.o•o
_
-
/ oooo
z.o- ••
o •
•
_
cannot
be attributed
to crustal
fractionation
alone. At best, the empirical relation is an indication that
heat-producingelementfractionationin granitesand metamorphic and recrystallizedclasticsare on related Scales[Richardson and Oxburgh, 1978]. At worst, as it has as yet no sound
physicalexplanation,it could be entirely fortuitous.However,
it is still the single quantitative piece of information which
gives any indication of the variation of radioactivity with
depth. The relationship can only be valid if the radioactive
elementsare concentratednear the surface.At present, Qr is
the best estimate that we have of the nonradiogenic component of heat flow, and to a first approximationit is the heat
flow at the base of the crust.
The distributionof crustalradioactivitydistortsthe relation
between
heat flow and tectonic age. For example, the heat
HE4 • •OOEC T/O• /O-/•ca//cm•s
flow through the Precambrian rocks in Central Australia and
Fig. 17. Observationsof heat flow and radioactiveheat producIndia [Rao et al., 1976] is much higher than is predictedfrom
tion from crystalline rocks in the United States; linear regression
curvesare from Roy et al. [1968] for the Basin and Range (dashed the grossrelation betweenheat flow and age.However,the re-
o 5'
o
I
I
I
I
5
IO
15
20
25
curve), easternUnited States,and Sierra Nevada provinces.Solid circlesrepresentpoints eastof the Great Plains, and crossedcirclesrepresent points interior to the Sierra Nevada physiographicprovince.
Vertical arrowsrepresentcorrectionsfor the finite sizeof plutons [Roy
et al., 1968]. Three of the open circles on the eastern United States
curveat about I /•cal/cm• s are from the KlamathMountainsin
northern California [from Lachenbruchand Sass, 1977].
duced heat flow is consistent with that from other shields. In
contrastwith decreaseof surfaceheat flow versusage (Figure
16) the reduced heat flow drops within 300 Ma to a constant
value of 0.6 +_0.2/•cal/cm: s (25 + 8 mW/m :) (Figure 19).
The sharp decreaseoccursover a time span slightly longer
than that for the oceans,and the equilibrium value of 0.6 +_
SCLATER ET AL.' OCEANIC AND CONTINENTAL
2
I
3
I
4
•
75
50•
2O
i,,, 0.5
centrate
I
I
4
I
I
6./3
8 ..
/-/œ47'•œ/Vœ/• 7'/O/Vx/•
291
In general, intrusion and erosionalprocessesare dominant,
and the heat flow, though scattered,has a high mean value.
With time, tectonic activity terminates, magmatic sources
cool, and the rate of erosion decreases.Thus the heat flow
tends to equilibrium. In areaswhere the heat flow is initially
low, there is an increasedheat input from below, and low values are no longer observed. Sometime between 250 and 800
Ma theseperturbationsbecomenegligible(Figure 16). To obtain a better estimateof this time scale,it is necessaryto con-
ß 1.o
2
HEAT FLOW
10
½•//½m'•$
Fig. 18. Heat flow and heat generation for stations in the Precambrian shields[after Rao and Jessop,1975].
on the Phanerozoic
and to take into account
varia-
tions in surfaceheat production.From our preliminary plot of
reducedheat flow versusage we suggestthat the time constant
is of the order of 200-300 m.y. (Figure 19). At presentit is not
possibleto give a more precisefigurebecauseof the large scatter in the data. Assuminga thermal diffusivityof 0.01 cm2/s,
the associatedthermal diffusion length scale lies betwen 100
and 200 km.
0.2/tcal/cm'•s (25 +_8 mW/m') is closeto the predictedequilibrium heat flux of 0.8 +_0.1 /tcal/cm'•s (33 +_4 mW/m')
through the oceans.The two values could be even closer.
Most of the continental values are from high northern lati-
tudesandmay haveto be raisedby asmuchas0.2/tcal/cm2 s
(8 mW/m') to allow for the effectof the last glaciation.
Thermal
Models
The aboveobservationscan be integratedwithin the framework of the new ideas on continental
formation.
Continents
In the early Proterozoic and Archcan crust there is still
some scatter in the heat flow. This is probably due to variations in the surface radioactivity. These variations can have
two causes.On a large scale(100 km or more) they can be directly associatedwith horizontalchangesin the geologicenvironment. On a small scale(within an individual pluton) they
can be createdby weathering[Lachenbruch,1970]and hydrothermal mobilization of the radioactive elements [Killeen and
Heier, 1975].
One of the areas which does not apparently fit this simple
are deformed or modified either continuously or discontin- model is the Sierra Nevada. The Sierra Nevada are in western
uouslysincepermobiletimes.Greenstonebeltsare essentially North America. Presumablythey were on the continental side
collapsedmarginal basins[Tarneyet al., 1976],and the gran- of a trench in the Late Cretaceousand early Tertiary. The
ite-gneissterrain on either sideof thesebeltsis deformedcal- heat flow distribution in this area (Figure 21) is little different
calkaline tonalitic batholithic rocks [Tarney and Windley, from that observed in Japan (Figure 20). Hence Roy et al.
1977; Windleyand Smith, 1976].Extra vulcanismis createdby [1972] suggestedthat the low reducedheat flow is the resultof
continent-continent collision and the formation of major
a subduerionprocesswhich terminatedin the middle Tertiary.
granite plutons.Fractional separationof the radioactiveeleAs most of the continents consist of Precambrian basement,
mentstakesplace, and they are preferentiallydistributednear we have concentratedon this port•onof the geologictime
the surface.
The high heat flow in the youngerregionshas four causes:
island arc magmatism,plutonismassociatedwith continentcontinent collision, erosion [England and Richardson,1977],
and crustal thinning [McKenzie, 1978; Lachenbruch, 1979].
The heat flow in theseregionsis not uniformly high, and low
values can be observed.The classicexample (recognized by
Holmes [1965, Figure 730]) is Japan [Uyeda, 1972]. In this
area the heat flow changesfrom lessthan 1.0/tcal/cm'•s (42
mW/m') along the easterncoastto values as high as 10.8
/tcal/cm'•s (452 mW/m') closeto the westerncoast(Figure
scale. In order to handle the large quantity of data we have
followed a simplistic approach to analyzing the relation between heat flow and radioactiveage. It is important to remember the problemsassociated
with this approach.In particular,
our age estimatesare reliable only for the Archcan and some
of the early Proterozoic. We run into problems in areas such
1-5
L
20).
--5O
TABLE 9. Categorization of Data According to General Rock
Type of the Heat Flow Sites [after Rao and Jessop,1975]
Rock Type
N
Range
5
0.50-0.81
(21-34)
(31)
Greenstones
11
0.69-1.18
0.90
Mafic igneous(plutonic
and volcanic)
Granitesand gneisses
11
(29-49)
0.65-1.10
(27-46)
0.59-1.44
(25-60)
(38)
0.90
(38)
1.03
(43)
Sediments
10
Ultramafic
and anorthosites
16
Mean
i
I
I
8
- 25
I
0.74
1.05-1.20
1.12
(44-50)
(47)
N is the numberof values.The rangeand meanare in ttcal/cm2 s
(mW/m2).
I
1000
i
I
2000
AfiE
IN
t
I
3000
HA
Fig. 19. Reduced heat flow plotted againstage. The circlesare
unreliableestimatesfrom the youngerheat flow provinces.The theoretical heat flow (assumingthe plate model) through the ocean floor
with the crustal contribution subtracted is presented as a dashed
calve.
292
SCLATER ET AL.'
OCEANIC
AND
44 ø
CONTINENTAL
HEAT
died out, the scatter about the equilibrium flow is causedby
variationsin surfaceradioactivity and/or erosion.Our global
model is not intended to accountfor local perturbations,and
to get a more detailed picture, it will be necessaryto consider
processessuch as intraplate vulcanism, zones of weaknesses
[Sykes and $bar, 1973], and crustal thinning [Chapmanand
Pollack, 1975b; Lachenbruch, 1979].
HEAT
40 ø
FLOW
LOSS OF THE
EARTH
Introduction
One of the objectivesof this review is to comparethe heat
loss through oceansand continentsand to estimate the total
heat loss of the earth. For the oceans, as the observed mean
values underestimate the heat flow, we have used the theo36 ø
retical heat flux to compute the loss through a province of a
given age. The total heat loss through a single ocean is the
sum of the individual valuesfor eachprovince.For the continents, water circulation is lessimportant. We have assumed
that the actual
observations
are reasonable
estimates
of the
heat flow at depth and have usedthe raw data to computethe
lossthrough each province.
32 ø
Heat Loss Throughthe Oceans
In the young crustmost of the heat is lost by water circulation. Thus to compute the total heat loss through these reFig. 20. Heat flow values on the Japaneseislands. The dashed gions,it is necessaryto usea theoreticalvalue. We cannotuse
linesarethe 1.0and2.0 peal/era2 s heatflowcontours.
Note theband the plate model of McKenzie [1967] becauseon integrationit
of low heat flow along the east coastof Japan.
yields an infinite heat flux at the origin. Davis and Lister
[1974]usedan alternativeboundaryconditionfor the temperature at the origin. They equated the heat brought up by the
as the West Siberian Platform and the sedimentarybasinsof ascendingmagma to the sum of the heat lost horizontally by
western Europe where Proterozoic basement is covered by conductionand that lost vertically by the magma once it is in
Phanerozoic sediments.These sedimentarybasinsare almost place.The conditionimpliesa discontinuitybetweenthe supcertainly the result of a Phanerozoicorogenicevent which is ply temperatureand the temperatureat the origin, but it is a
not reflected in the radioactive dates. The problem becomes reasonablemathematical representationof the discontinuous
extreme in the case of the Sierra Nevada, the belt series of the
intrusionprocess.Though the heat flux at the origin is still innorthern Rocky Mountains, and areas such as the Pannonian finite, the integratedheat lossis finite. We usedthis boundary
Basin,where the heat flow is affectedby orogeniceventsmuch condition to modify the model of McKenzie [1967]. Details
youngerthan the radioactiveage.
The outflow of heat through the continentsis the result of a
suite of factors such as orogeny, the vertical distribution of
heat-producing elements, and erosion. Because continental
creation generally results in a thickening of the crust and
changein the vertical distributionof the heat-producingele132 ø
138 ø
t44 ø
ments, it is not obvious that the decrease in the observed val-
ß
ues is directly related to the thermal time constantof the continental lithosphere [England, 1978]. We suggestthat the
reduced heat flow gives the most reliable estimate and find
*
• lo•
relation between surface heat flow, surfaceheat production,
erosion,and orogenyneedsto be examinedmore carefully for
the Phanerozoic.Such a study requiresan analysison a local
scaleand has not been attemptedin this paper. However, our
analysisyields an upper bound for the time constantof orogenicevents.It is interestingto note that orogeniesthroughout
the geologicrecord occur in pulsesof the sameduration.
In summary, we observethat continental heat flow is high
but variable in young regionsand decaysto a value of 1.05 +_
terozoic and Archean crust (Table 7). The high but variable
heat flow is related to the processesby which continentsare
created or modified. Once the effectsof theseprocesseshave
I
.' I t,Oo
,.4' eoeoe
I?'g
that it is of the order of 300 Ma. To obtain a better value, the
0.29 pcal/cm2 s (44 +_ 12 mW/m :) through the early Pro-
q, }
'•lb J
/
J
//*
J
I• ;l
36 ø
'
':'•:::' .
t
32 ø
122 ø
118ø
112ø
Fig. 21. Contour plot of heat flow for the westernUnited States
showingthe low associatedwith the Sierra Nevada batholith (hatched
area).
SCLATER ET AL.: OCEANIC
AND
and equationsare given in Appendix C. Beyond 1 Ma both
this and the original plate model give exactly the same results
for both heat flow and topography[Lister, 1977].
We comparedfor each age province(1) the theoreticalheat
lossthroughthe upper surface,(2) the theoreticalflow entering the baseof the plate by conduction,and (3) the heat loss
given by the observedvalues (Table 10). The sum of item 1
for all provincesis the theoreticalheat lossof the oceans.The
sum of item 2 is the heat gained by the oceaniclithosphere,
and that of item 3 the measured heat loss of the oceans. Sub-
tracting the heat gained by the lithospherefrom the theoretical heat loss gives the heat releasedby the mantle in plate
creation. The radioactive decay of the heat-producingelementswas included in the calculationof heat gained.The difference between the theoretical loss and that actually observed represents the heat lost by water flow and by
conduction through bare rock.
The total heat lossvariesfrom oceanto ocean.It is largest,
about 30%, in the South Pacific, where the spreadingrate is
fast, and is least, about 10%, in the North Pacific, where the
rate is slow. Almost
50% occurs in the Pacific with about 20%
in each of the Atlantic and Indian oceans, and 10% in the
marginal basins.The total heat lossof the oceansincluding
the marginalbasinsis 727 x 10•øcal/s (30.4 x 10•2W). It is
not uniform with age, as about 50% takes place in the first 20
million years (Table 10). The heat gained by conduction
throughthe baseof the plate and by radioactivedecayin the
crust is small. Over 85% of the heat loss of the oceans occurs
by creation and consequentcooling of the lithosphere.The
difference between the theoretical heat lossand that observed,
241 x 10•øcal/s (10.1 x 10•2W) represents
aboutonethird of
the heat lost by oceans.All of this difference takes place in
crustyoungerthan 50 Ma, and it is causedprincipally by the
advectionof seawaterthrough hot young crust.
Heat Loss Throughthe Continents
In a previoussectionwe have establisheda generalrelation
on continentsbetweenheat flow and age. Here we use this relation and the separationof the continentsinto age provinces
to estimate their total heat loss. Continental
heat flow measure-
ments are considered
than those on the
to be more reliable
ocean floor becausethey are made at greater depth and involve direct inspection of the local environment. Only largescalesteadystatewater circulation remainsundetected[Lewis
and Beck, 1977]. In the younger regionsthe scatterin the heat
flow valuesis high, but the error in the total heat lossis likely
to be minimal becausethe correspondingareasare small. We
calculated the total heat loss for each continent separately,
first by multiplying the observedmean flow by the area of
each age province and then by summingthe resultantvalues
(Table 11). For Antarctica, where there are no observations,
we used the measured
mean value from the rest of the conti-
nents. About one fourth of the continents are shelves. To calcu-
late their heat loss,we assumedthat about one quarter were
created
duringCretaceous
b•eakup
andhaveanaverage
age
of 120Ma and a meanheat flow of 1.1/•cal/cm2 s (46 mW/
m2).For the remainingthreequartersthe shelves
weredivided
into groupsfollowing the ratio of the areas of the age prov-
incesonthecorresponding
continent.
Dividingthetotalh½•t
lossby the area givesthe mean flow through each continent.
The valuesrangefrom 1.19to 1.52/•cal/cm• s (49 to 64 mW/
m2). The Antarctic value is speculative.For the other continentsthe averageheat flow is roughly constantexceptfor Af-
CONTINENTAL
HEAT
FLOW
293
294
SCLATER ET AL.: OCEANIC AND CONTINENTAL
HEAT
FLOW
TABLE 11. Heat LossesThroughthe ContinentalAge Provinces
Age, Ma
Continental
AfricaandMadagascar
Total
Mean
0-250
250-800
1700
> 1700
Shelf
Heat Loss
Heat Flow
0.9
18.6
7.3
13.l
4.9
44.8
I. 19(49)
SouthAmerica
NorthAmerica
Australasia
3.4
11.4
1.0
7.7
5.7
5.2
5.9
4.5
5.8
5.7
11.7
2.1
5.5
10.9
14.5
28.2
44.2
28.6
1.26(53)
1.30(54)
1.52(64)
Antarctica
EuropeandAsia
All continents
Additionof heatlossdue
2.2
31.9
50.8
6.9
28.3
72.4
4.2
27.7
7.2
13.3
53.1
6.6
24.7
67.1
22.9
102.4
271.1
275.1
1.30(54)
1.44(60)
1.35(57)
1.37(57)
to volcanic activity
Mean heatflow*
1.78(75)
1.41(59)
1.31(55)
1.10(46)
1.29(54)
Meanheatflowvaluesaregivenin #cal/cm
2 s (mW/m2).Heatlossvaluesaregivenin l0 iøcal/s(1012W).
*Resultsfrom totalingrowsor columnsmay differslightlyfrom thosegivenowingto rounding.Thesevaluesdo not agreewith thosefrom
Table 7 becauseof the differentmethod of averaging.
rica and Madagascar, where the value is lower, and Australia,
where the value is higher (Table 11).
We estimate the heat loss through the continents and
shelvesto be 271 x 10iøcal/s (11.3 x 10!'•W). To thisit is necessaryto add the amount releasedby active volcanoes.Horai
and Uyeda [1969] give a value in the range 4-5 x 10iø cal/s
(1.7-2.1 x 10• W). Thuswe obtaina total valuefor the continentsof 275 x 10iøcal/s (11.5 x 10!'•W) with an errorof 50 x
10iøcal/s (2.1 x 10•'•W). The error was estimatedby multiplying half the mean absolutedeviation by the area of each
province and summing these values. Dividing the total heat
lossand the error by the area of the continentsgivesa mean
flow of 137_ 0.25/•cal/cm'•s (57 _ 11mW/m') (Table 12).
Considering that most of the continental crust is Precambrian, these figures are higher than expected. For ex-
Total Heat Loss of the Earth
We estimate the total heat loss of the earth to be 1002 x
10iøcal/s (42.0 x 1012W). More than 70%is lostthroughthe
oceans, 7% through the continental shelves,and about 20%
throughthe continents(Table 12). The error, in our estimate
of the oceanic heat loss, is between 10 and 20% of the absolute
value. If we have not grosslyunderestimatedthe effect of water circulation in young continentalcrust,the error in the continental
value is of the same order. In our treatment
we have
made no attempt to separatethe oceanicand continentalportionsof the shelves.If we assumethat one quarteris oceanic,
almost 3 times as much heat is lost through the oceansas
throughthe continents.In the caseof the oceans,nearly 90%
of this heat lossis dissipatedby plate creation,and this mechanism is responsiblefor more than 60% of the heat loss of the
ample,the mean heat flow is about 0.3/•cal/cm'•s (13 mW/
earth.
m') higher than the value estimatedby Polyak and Smirnov
Our estimate of the total heat loss of the earth is almost 40%
[1968] from a similar method. This increaseresultspartially higherthan the valueof 6.3 x 1012cal/s (26 x 1012W) given
from
a more
careful
consideration
of environmental
factors
and better conductivity measurementsin more recent publications.Also, a smallamountis a resultof concentratingon
the orogenicage rather than the age of the last thermal event.
We may have included the effectsof more recent extensional
eventsin the older province.
TABLE 12. Summary of Area and Heat Loss Information
Heat Loss,
Area, 106km: 10iøcal?s(10i: W)
Continents(includingeffect
of volcanoes)
149.3
208 (8.8)
Continental
52.2
201.5
281.7
26.9
308.6
67 (2.8)
275 (11.5)
656 (27.4)
71 (3.0)
727 (30.4)
510.1
1002(42.0)
241 (10.1)
shelves
Total (continentplus shelves)
Deep oceans
Marginal basins
Total (oceansplus marginal
basins)
Worldwide
values
Heat lossby water flow and
conductionthrough bare rock
Heat lossby plate creation
not includingradiogenic
heat loss
Mean heat flow
Continents and shelves
All oceans(observed)
All oceans(theoretical)
*Heat flow in 10-6 cal/cm: s (mW/m2).
626 (26.2)
by Lee and Uyeda [1965] and is dose to the value of 1.0 x 1013
cal/s (42 x 10!2W) of Williamsand VonHerzen[1974].Becausetheir analysiswas completedbeforethe developmentof
plate tectonics,Lee and Uyeda [1965]were unaware of the importanceof water circulationthroughthe oceaniccrust.They
underestimatedthe heat lost throughthe oceans.Williamsand
Von Herzen [1974] made a realistic estimate of the effectsof
hydrothermal circulation and therefore obtained a reasonable
value for the total heat loss.
To a first approximationwe can use our analysis(Tables
10-12 and B 1) to separatethe heat lost at the surfaceof the
earth into (1) that due to convectiveprocesses,
(2) that resulting from conductionthrough the lithosphere,and (3) that
causedby radioactivedecaywithin the continentalcrust.If we
assumethat half the heat flow throughthe youngestcontinental crust arises through magmatic activity, then convective
processes,
which we definehere to includeplate creation,account for about two thirds of the heat loss of the earth. As-
suminga backgroundmantleheat flow of 0.6/•cal/cm'•s (25
mW/m'), we calculatethe conductiveflow throughthe continentsto be 120x 10iøcal/s (5 x 1012W). Addingto this the
70 X 10iø cal/s (2.9 x 1012W) gainedby the oceanicplate
yields a conductivecontribution of about 20%. The rest, less
1.37' (57)
1.57' (66)
2.36* (99)
than 15%,is contributedby the decayof heat-producingelements in the continental
and oceanic crust. These values are
basedon a number of assumptions
and henceare only approximate.But they do emphasizethe relative importanceof
SCLATER ET AL.: OCEANIC AND CONTINENTAL
HEAT
FLOW
295
convectionover conductionasthe major mechanismby which
match the observations
heat is lost from within
cept as the framework for the rest of this section.
THERMAL
the earth.
Comparisonof the 'EquilibriumOcean'
STRUCTURE AND THICKNESS
LITHOSPHERE
and Old Continent
OF THE
Introduction
Geotherm
The oldest ocean crust is found in the western Pacific. It has
In the first part of this review we have deliberately concentrated upon the observationsand have kept speculationto a
minimum. In the secondpart we investigatethe thermal structure beneath oceansand continentsand present an integrated
review of someof the new but speculativeideas that have recently appeared on the developmentof the lithosphere.We
approach the questionof lithosphericthicknessfrom a uniformitarian viewpoint. Can we apply the conceptof a thermal
boundary layer, which has been so successful
in the oceans,to
the continents?Further, is this conceptof value in examining
the creation of continents and their development through
time?
Most of the argument concentrateson comparingthe relative thicknessof the lithosphericplate under an 'equilibrium'
ocean with that under the Proterozoic
and Archean
cratons.
Various authors have already estimated these thicknesses.
McKenzie [1967] and Sclater and Francheteau[1970], noting
that the heat flows through old oceans and continents were
roughly the same and that the surface radioactivity was
greateron the continents,suggested
that the continentallithosphere was twice as thick. Recently Jordan [1975] has suggestedthat though the rigid portion of the continent is only
approximately 100 km thick, another layer lies underneath the
old cratons.In his concept,thermal and chemical differences
in the continents could extend to 400 kin. This layer is attached to and moveswith the continental lithosphere.He uses
the term 'tectosphere'to describethe region encompassing
this layer and the lithosphere. A separate school of thought
based on examination
over old ocean floor. We use this con-
of the thermal
time constants of the
continental lithosphere favors a minimum differencebetween
the plate thicknesses.Croughand Thompson[1976] have argued that the reduced heat flow plotted against age fits the
same relation as the oceanic heat flow. Also, the exponential
subsidencenoted by Sleep [1971] for Phanerozoiccontinental
an age in excessof 180 Ma [Larson and Hilde, 1975].At this
age the oceanic lithosphere is not in thermal equilibrium,
though both the observationsand the theory suggestthat it is
close [Parsonsand $clater, 1977]. The heat flow through the
equilibriumoceanis 0.9 + 0.1 /•cal/cm2 s (38 + 4 mW/m2).
On the continents,equilibrium conditions are reached by at
least the mid-Proterozoic. The heat flux through this region,
which is older than 1700Ma, is 1.10 + 0.38/•cal/cm2 s (46 +
16 mW/m 2) (Table 7) and is 0.2/•cal/cm2 s (8 mW/m 2) higher
than that through the equilibrium ocean. However, becauseof
the large scatter around the continental mean this difference
cannot be given too much significance.
To compute the heat flux at the base of the crust and the
range in temperaturesfor the oceanic geotherm, we assumea
10-km crustal layer with a constantheat generationrate of be-
tween 1 and 2 x 10-'3 cal/cm3 s (0.4 and 0.8 x 10-6 W/m 3)
(Figure 22). These valuesbracket the publishedestimatesfor
basalt and gabbro. The correspondingcontributions to the
surfaceheat flux are therefore0.1 and 0.2/•cal/cm2 s (4 and 8
mW/m2). We obtain two extrememodelsdenotedO, and O2.
For O, the heat flow is 0.8/•cal/cm2 s (34 mW/m 2) at the surface and 0.6/•cal/cm2 s (25 mW/m 2) at the baseof the crust,
and for O2the respectivevaluesare 1.0 and 0.9/•cal/cm2 s (42
A
OEEAN
0-
02
Qo =0'8
Qo =1'0
•'
Ao = 2'0 (A(zl=Ao)Ao= 1'0
•- 10........
'• 20 0.•0.6
•z 30-
spIieres.We compareour rangeof temperatureprofileswith
Qo =1.1
Ao=5'6
A0=2'8
Qh•0'9
(A(zl--o)
=*0.s
,-, .5()-
_
(A(z}=O)
basinscan only be relatedto oceanicmodelsif the plate thicknessis roughly the same.
Our reanalysisof the heat flow data has shown that rather
than being similar the heat flow through an equilibrium ocean
is lower than the mean flux through the continents.In this section we comparethe mean heat fluxesand use estimatesof the
distributionof heat-producingelementsto computethe temperature as a function of depth underneath the two litho-
œONTINENT
O•
TEMPERATURE oœ
0
_
500
01 x•
1000
1500
02 xx
geobarometryand geothermometrydata beneath continents.
Later we consider the relation
between reduced heat flow and
_
age and the subsidenceof continentalbasins.
When describingthe lithospherewe use the model of a flat
•100 -Z
plate with a constant temperature at its base. Any process
ßIwhich creates a significant component of additional heat at
Q.
_
depth will produce the oceanic observations[Forsyth, 1977].
t-•
_
This could be shear stressheating [Schubertet al., 1976], ra150 -dioactivity in the upper 300 km [Forsyth, 1977], or some
anomalousheat source[Croughand Thompson,1976].We preFig. 22. (a) Models usedto computethe rangeof geothermsbefer the conceptof two scalesof flow and the idea of a mechanneath an 'equilibrium' ocean O i and 02 and an old stablecontinent
ical and thermal boundary layer [Parsons and McKenzie, (Central AustralianShield(seetext for justification))C, and C2. (b)
1978]. The small-scale convection beneath the mechanical Predictedrangein old continental(C. and C2) and 'equilibrium' oceboundary layer provides the heat flux which is required to
anic (O i and 02) geotherms.
-
296
SCLATER ET AL.: OCEANIC AND CONTINENTAL
and 38 mW/m2). We have pickedthermal conductivitiesof 6
and 8 x 10-3 cal/cm øC s (2.5 and 3.4 W/m ø C) for the crust
and mantle. The value for the mantle is the mean thermal
conductivitydeterminedfrom the equationsrelatingheat flow
and depth to age for young crust [Lister, 1977]. We assume
throughout these calculationsthat the radioactive contribution from the mantle is negligible.
It is difficult
to make a realistic estimate of the heat flux
HEAT
FLOW
ducingelementswere concentratedin a crustof depth h. Under theseconditions,Ao dependsupon the assumedvalue for
the reducedheat flow Qr and the model chosenfor the distributionof the radiogenicelementsin the crust.We chosean
exponential
decrease
withdepth.In thismodeltheheatflow
fromthemantle
is approximated
by thereduced
heatfløw
[Lachenbruch,1970]. It is important to realize that.once the
heatflowatthesurface
andthatattheMohoarespecified,
the
through the continental lithosphereand consequentlythe
temperatureat the depth of the Moho is not significantlyaf-
temperature as a function of depth. The distribution of heatproducing elements with depth is not known with any certainty. As was mentionedbefore, the scatterin the linear relation of heat flow and radioactivityis large, and it is surprising
that Qr varies so little for provincesolder than 250 Ma. The
fected by the form of the radioelement distribution. Under
theseconditions,Ao is given by
valuesrangefrom 0.5 •tcal/cm2 s (21 mW/m :) for the Superior Provinceto 0.64 •tcal/cm:s (27 mW/m :) for the Central
AustralianShield.Taking an absoluteerrorof 0.10/tcal/cm: s
(4 mW/m2), we arriveat a rangeof valuesfor Qrbetween0.40
and 0.75 •tcal/cm:s (18 and 32 mW/m:). This rangerepresentsthe best estimate allowed by present data for the heat
flux at the base of the crust. All reported values of reduced
heat flow are compatible with the upper and lower bounds.
This includesthe reducedheat flow through the northern latitude provinces (i.e., the Canadian, Baltic, and Ukranian
shields and the United Kingdom), which may have to be
raisedby as much as 0.2 •tcal/cm:s (8 mW/m :) to allow for
the effects of Pleistoceneglaciation. This correction brings
their values for Qr closeto the upper bound. Our estimate of
the range of heat flow at the base of the continental crust
overlapsthe estimatedrangein heat flux of 0.6-0.9 •tcal/cm2 s
(24-36 mW/m :) at the baseof the oceaniccrust.
For comparisonwith the oceanicgeothermwe computeda
range of realistic temperatureversusdepth profiles for the
lithosphere beneath the Central Australian Shield. We chose
this shield in order to use real data in an area unaffectedby
Pleistoceneglaciation where D is closeto the world average.
Two extreme values of Qr were estimated by plotting the
range of straightlineswith a constantslopeD which can be fit
realisticallyto the heat flow versussurfaceheat production
data (Figure 23). They rangebetween0.5 and 0.8 ttcal/cm• s
(21 and 34 mW/m2). We assumedthat the heat flux was 1.1
/•cal/cm• s (46 mW/m 2) at the surfaceand that the heat-pro-
Ao = (Qo- Qr)/D
(3)
and the temperatureat depthz within the radioactivelayer is
QrZ
T=-•
+ D2Ao
K, [1- e_z/D]z<h
(4)
where K• is the thermal conductivityof the crustallayer. Below the crustal layer we follow the usual assumptionsthat
steadystateconditionsprevail and that there is no convection.
The temperature at depth z is
(z-
h)
T--T(h)
+ g2"Qr z> h
(5)
where K: is the conductivityof the upper and lower layers.To
computethe probablerangein the temperaturedepthprofiles,
we usedthe two extremesfor Qr and assumedvaluesof 0.006
and 0.008 cal/cm øC s (2.5 and 3.4 W/m øC) for K• and
respectively.
The range in temperatures allowed by the models that we
have chosenis large (Figure 22). Though the continentaltemperaturesare generallyhigher in the upper portion of the lithosphere, there is a significant overlap below 100 km. The
thicker low-conductivity continental crust completely compensatesfor the slightly higher oceanic mantle heat flow.
Given this overlap,the heat flow data are clearly compatible
with a model which has a similar temperaturestructureat
depth under both continentsand oceans.
ComparisonWith Geothermometry
and GeobarometryData
The pressure-temperature (PT) conditions in the litho-
spherecanbe inferredfromthe studyof mineralassemblages
-6
HEAT
GENERATION
IN10 W/M
3
2
•
•3.0
•E
•2.0
- •e
:•
• •
•
1-0
6
in xenoliths.Beforecontinuingwe comparetheseconditions
8
with our temperature profiles.
The thermodynamicalinterpretation of analysesof coexist-
100
•.
ing phasesin xenolithsis plagued by two basic problems.
First, the assumptionswhich are involved in the derivation of
geothermometers
andgeobarometers
of practical
usea•enot
o
-50
5
HEAT
6ENERATI•
Fig. 23. Heat flow and heat productionfor the Central Australian
Shield Province. The heavy cu•e representsa least squaresfit to the
obse•ed data excludingthe open circles.Upper and lower cu•es representan estimatedrange of correlationswith the sameslopecompatible with the obse•ed data. Plusesrepresentgneisses;
solid and open
circles,granites [after •a•
alwaysjustified[Wiltshireand Jackson,1975].They are that
theobserved
mineralsarein equilibriumwitheachother,that
thesolutions
areidealandthatrealsystems
canbeapprOxi
matedby simpleones.Second,
theprocesses
Ofmagmageneration and xenolith formation are still not understood and
probably
involveperturbations
of the verY*
temperatures
which are to be estimated[Irving, 1976;Hoffman and Hart,
19781.
Recentimprovements
havebeenmadeto the existingmethods,in particularby Woodand Banno[1973] for temperature
determinations
based
on theenstatite-dioPsid½
equilibrium,
by Ak½l!a[1976]for pressure
estimations
in the system
CaSiO3-MgSiO3-AI203
appliedto the assemblage
garnet+
SCLATER ET AL.' OCEANIC
AND
CONTINENTAL
HEAT
TEMPERATURE
INøC
enstatite+ diopside,and by DixonandPresnall[1979]for the
systemCaO-MgO-A1203-SiO2applied to the assemblageforsterite + spinel + enstatite + diopside.These new geothermometers and geobarometers are not used consistently
throughoutthe literatureand this posesan obviousproblem
whencomparisons
areneeded.We plotin Figure24 a number
297
FLOW
500
-i
1000
1500
!
'
5O
of PT determinations from recent publications or older
sourceswhich we corrected ourselves following Wood and
Banno[1973],Akella [1976],and Dixon and Presnall[1979].
lOO
We stressedin our searchthe data points for the lowest tem-
peratures.Suchstudiesof xenoliths,while they are not a reliable tool for calculating geotherms,do provide maximum
temperatureestimatesat any depth. They are therefore perfectly acceptablefor our purposes.
Not surprisingly,the lowest temperature estimatesat any
ß
lSO
givendepthare foundbeneathold continents(cf. in Figure24
the data of Griffin et al. [1979], Eggler et al. [1979], and F. R.
Boyd and P. H. Nixon (unpublisheddata, 1978)). The errors
in each PT determinationare very large, around +_100øCand
+_5kbar (or +_15 km) [Mori and Green,1975;Dixon and Pres"•
hall, 1979]. The data provided (Figure 24) are consistentwith
any of our continentalgeothermsdown to a depth of 100 km.
Below this depth the upper conductiveprofile is ruled out.
However, it is not certain that the assumptionof conductionis
warranted in the mantle. The mechanisms of heat transfer de-
200
estimate of errors
Fig. 24. Comparisonof the range of old continentalgeotherms
with geothermometryand geobarometrydata. Small and large solid
circlesrepresentdata of Griffin et al. [1979]; open stars,Smith and
Levy [1976]; open circles,Bishopet al. [1979]; solid stars,Francis
[1976];mediumsolidcircles,Aoki and Shiba[1974];invertedtriangles,
Ernst [1979];crossedcircles,Carswellet al. [1979];solid squares,Carter Hearn and Boyd [1975]; crosses,Reid et al. [1975]; open squares,
Eggleret al. [1979];triangles,Gurneyet al. [1975].The shadedarea is
taken from F. R. Boyd and P. H. Nixon (unpublisheddata, 1978).
pend criticallyon the thermal historyof the earth and remain
largely unknown. If small-scaleconvectionexistsin the oceanic lithosphere,it perturbssignificantlythe conductivetemperatureprofile below a certaindepth. This critical depth is lation of the reducedheat flow the simplicity of the variation
definedby a changein the rheologyof mantle material from a of Qr with age is surprising.The characteristic
time span for
rigid to a viscousbehavior.
the decrease is between 200 and 300 Ma and is close to the
Given the errorsinherentin geothermometryand geobaro- thermal time constantfor the oceaniclithosphere.
metry and the lack of certainty about the dominant heat
transport mechanismin the mantle, the present knowledge Subsidenceof ContinentalBasins
about the PT conditionsin the continental lithospherepreThe most important.observationjustifying a simple model
cludes any separationbetween the two temperature profiles of the oceanic lithosphereis the relation between depth and
that we have computed on the basisof the surfaceheat flow age. Sleep[1971]showedthat severalcontinentalbasinshave
observations.More data points at shallow depths (above 120 the sameexponentialsubsidence
as the oceans.Recently,a sekm) are necessaryto verify our conclusions.
ries of studies have been made of various Cenozoic and Mesozoic continentalshelvesand inland basins(Table 13). Their
Relation BetweenReducedHeat Flow and Age
subsidencecan be divided into two phases.First, there is a
One of the major factorsaffectingcontinentalheat flow val- chaoticperiodduringwhichthe basinis formed.In this phase
ues in the Proterozoic and the Archean is the distribution of
the subsidencehistory is complex. It can vary from rapid, if a
heat-producingelements.If it is assumedthat theseelements deepgrabenis created,throughslowand linear,if the basinis
are concentrated in the crust, then the reduced heat flow is an
initiated by a long and continuousevent, to no subsidenceat
estimate of the heat contribution from below this radioactive
all, if the basin startsby uplift. In contrastto the complexinilayer. Thus using Qr, we examinedthe variationwith time of tial conditionsthe subsidenceof the secondphase is widethe nonradiogeniccomponentof heat flow. The scatterin the spreadandgeneral.In certainplacesit is rapid,andthe depth
young valuesis high, and the relation cannot be considered increasesas the squareroot of the age. Examplesare the Gulf
valid for the Cenozoic or late Mesozoic. The reduced heat
of Lyon ['Wattsand Ryan, 1976]and the Labrador Sea [Keen,
1979]. In other placesthe relation betweendepth and age is
flow decayswithin 200-300 Ma to a constantvalue lying between0.50 and 0.64/xcal/cm2 s (21 and 27 mW/m2). In this linear, e.g., the PannonianBasin [Sclateret al., 1979]and the
andChristie,
1979].
Afterabout50million
decay,which is more rapid than that shownby the heat flow NorthSea[Sclater
measurementsalone [cf. Chapmanand Pollack, 1975a,Figure yearsthedepthshows
an expønential
decrease
to a constant
1], the key values are those from New England [Roy et al., value. Examplesof this• exponentialsubsidenceare the U.S.
1968] and England and Wales [Richardsonand Oxburgh, east coast wells examined by Sleep [1971], the Cost B-2 well
1978].It is of interestto note that Foland and Faul [1977] have [Stecklerand Watts, 1978], and the wells off Nova Scotia
shown that the eastern United States has been subjectedto
[Keen, 1979].
Cenozoic
plutonism
with the youngest
episode
terminating Most Phanerozoic continental basins have been subjected
pulsesof sedixaentation.
Each major pulse is
around100Ma. Thespread
in tectonic
agein theNewEng- tø successive
land provinceis larger than was previouslythought to be'the
case.
characterized
by complexinitialconditions
followedby an exponentialincreasein depth.EXamplesof suchregionsare the
Giventhelargenumberof variables
whichaffectthecalcu- North Sea and the Sverdrup Basin [Sweeney,1977]. In con-
298
SCLATER ET AL.: OCEANIC AND CONTINENTAL
HEAT
FLOW
TABLE 13. A Summary of the Subsidenceof Various PhanerozoicContinental Basinsand Shelves
Measured
Subsidence
Age Range,
Ma
Age, Ma
Depth, km
Pannonian
16-0
16-0
1-4
Gulf of Lyon
25-0
Basinor Shelf
Labrador
25--0
4
75-0
65-0
2-4
Basement
Depth, km
1-4
4
Mode of
Subsidence
linear
Reference
•clateretal.[1979]
t •/2
WattsandRyan[1976]
2-4
t •/2
Keen[ 1979]
linear
Sclater and Christie[ 1979]
t •/: -->exp
Keen[1979]
North Sea
100-0
100-0
3-5
3-5
Nova Scotia
175-0
140-0
3-5
6-11
Cost B-2
U.S. eastcoast
U.S. Gulf Coast
Kansas
Elk Point
175-0
175-0
175-0
330-230
370-230
125-0
110-0
110-0
330-230
370-230
5
1-3
2-4
1-2
3-4
15
?
?
1-2
3-4
exp (-60)
exp (-50)
exp (-50)
exp (- 50)
exp (-50)
Stecklerand Watts[ 1978]
Sleep[1971]
Sleep[1971]
Sleep[ 1971]
Sleep[1971]
Appalachian
Michigan
450-360
450-330
450-360
450-330
1-3
1-3
1-3
1-3
exp(-50)
exp(- 50)
Sleep[1971]
Sleep[1971]
The agerangefor the subsidence
data is not alwaysthe agerangeof the basin,asthe wellsdo not alwaysreachthe baseof the sedimentary
layer. We consideronly the post-Mid-Cretaceoussubsidence
of the North Sea.
trast the four Phanerozoicbasins,Kansas, Elk Point, Appalachian, and Michigan, have a simpler history [Sleep, 1971]
(Table 13).
probable that some other mechanism such as localized dyke
intrusion or subcrustalextensionalso occurs.In the following
discussionwe do not separate between the models and for
The Phanerozoic, Mesozoic, and Cenozoic basins have two
simplification analyze the data within the framework of the
general features. First, the maximum sedimentationis be- stretchingmodel [McKenzie, 1978].
tween 10 and 15 km for the continental shelves and between 3
During the extensionalphase the upper crust cracks by
and 8 km for the inland basins. Second, the observable subbrittle failure and extends along low-angle listric faults, the
sidenceoccursover a time span of about 200 million years lower crust flows ductilely, and the lithosphere attenuates.
There is much faulting, and horst and grabens are formed.
and follows an exponentiallaw with a time constantof 50-60
million years [Sleep, 1971; $teckler and Watts, 1978]. This Though mostof the area subsides,someis elevated.Following
time constantis closeto the figure of 62.8, which best fits the this phase,general subsidencecommences.After 50 million
subsidencehistory of old ocean floor [Parsonsand $clater, years, processesat the bottom of the lithosphere become
dominant, and the basin subsidesexponentially to a constant
1977].
depth.
Three modelshave been proposedwhich underlinethe imThe similarity betweenMesozoicand Cenozoicbasinsand
portanceof the lithospherein the formation of thesebasins.
The first involves thermal doming, followed by erosion and shelvesand the ocean floor can be extended back to the early
then thermal relaxation with sedimentbeing depositedin the Proterozoic(Table 14). For example,the Proterozoicbasinsof
hole left by the eroded material [Sleep, 1971].If the continen- southern Africa can be separatedinto a suite of clearly detal plate thicknessis of the order of 100-150 kin, the sub- fined basinswith well-dated basementand overlying volcanics
1973;Hoffman, 1973].The floorsof thesebasins
sidencewill be exponentialwith a time constantof roughly 60 [Anhaeusser,
million years. This model has two problems. First, only as are continental and the sedimentshave been depositedunimuch sediment can be deposited as is eroded; and second, formly in shallow water. Two other Proterozoic basins, the
erosion increases toward the center of the basin. Neither feaHamersleyfrom Western Australia [Button, 1976]and the Coture is observed.Two other models, the first involving exten- ronation geosyncline[Hoffman, 1973] in northwesternCansionby dyke intrusion[Roydenet al., 1980]and the secondex- ada, show similar features. Various authors [e.g., Hoffman,
tension by stretching of the lithosphere [McKenzie, 1978], 1973; Windley, 1978]have pointed out the structuralsimilarity
have been proposed.Both models involve extensionand the between these basins and Phanerozoic basins and continental
replacement of light crust by dense asthenosphere.They do shelves.They show almost exactly the same range of maximum subsidenceand cover approximatelythe sametime span
not require extensiveerosionto produce the basin.
In passiveregionswhere the dominant regimeis extensional as the Phanerozoic basins. These observations indicate that
the stretchingmodel with lithosphericattenuation is favored. the basinswere created by similar processesand that the conIn complex compressionalregions,such as the Alps and the tinental lithosphere has had a thickness of 100-150 km
Carpathians, the initial subsidenceis lessuniform, and it is throughoutgeologichistory. Inaccuraciesin dating and probTABLE 14. A Summary of the Subsidenceof Various Archean and ProterozoicSedimentaryBasins
Time
Maximum
Mean Rate,
Basin
Age, Ma
Span, m.y.
Subsidence,km
km/m.y.
Reference
Pongola
Witwatersrand
Transvaal
Hamersley
Coronation geosyncline
Waterburg
3060(2940)-2810
2720-2340*
2350-2125
2350-2000
2100-1800
1950-1790
190-70
280*
225
350
300
160
10.7
11.9
9
10
10.7
6.5
0.10
0.05
0.04
0.03
0.03
0.04
Anhaeusser
[1973],Hunter [1974]
Anhaeusser[1973], Hunter [1974]
Button[1976]
Button[1976]
Hoffman [1973]
Anhaeusser[1973], Hunter [1974]
*The ageis now thoughtto be older, and the range>200 m.y. (H. L. Allsopp,personalcommunicationto vanNiekerk and Burger[1978]).
SCLATER ET AL.: OCEANIC AND CONTINENTAL
TEMPERATUREIN
500
1000
0
N4.'
'
'
• ....
I '
sO-
N•
,?; -. Therrn•
bounary
i•'
•!
•
/
•
I ItHcKness
N •
I | I
$c•e ronwrfion
•
.....
\ \!
\
--
thickness.
We compared our range of continental geothermswith this
model (Figure 25). The oceanic geotherm lies between our
two continental geothermsand, as was explained before, is
compatiblewith the resultsderived from geothermometryand
geobarometry.There is no evidencefor a major difference between the temperature structureunder an equilibrium ocean
_l_
\',
Fig. 25. Comparison of two continental geotherms(C• and C2
from Figure 22) with the equilibrium geotherm in the oceanic plate
(heavy curve) showing the role played
the boundary layer. A' is the thicknessof the mechanical boundary
layer, and 8 is the thermal length scalegoverningthe actual temperature structurein the boundary layer. Also shown is the plate thicknessobtainedby the fit to the depth and heat flow observations[after
Parsonsand McKenzie, 1978].
lemswith mappingmay have led to overestimates
of both the
time spanand the depth of subsidence
of the Proterozoicbasins. If indeed the time span and depth have been overestimated, the lithosphere was thinner at that time but certainly not thicker.
In summary,we have shownthat an equilibrium ocean and
an Archean continent probably have similar temperature
structuresat depth.This suggests
that the continentaland oceanic lithosphereshave the samethickness.The behaviorof the
reduced heat flow and the subsidencehistory of continental
basinssupportthis conclusion.
CONVECTION
IN THE
STRUCTURE
MANTLE
OF THE
AND THE THERMAL
LITHOSPHERE
The heat flow through old oceansis closeto that through
old continents.In the past it was proposedthat the radioactive
elements were more abundant
in the thicker
continental
crust.
Thus the heat flow at the base of the crust was lower under
continents than under oceans. However, in our analysis we
have found that the heat flow through the old continentsis in
general higher than that through an equilibrium ocean and
that the contribution from radioactivity is lower than was previously assumed.Thus we have proposeda model in which
the temperaturesat depthsgreater than 100 km are the same
under
both an old stable continent
299
m øC), following Parsonsand McKenzie [1978], we computed
the geothermbeneathan oceanwere it at equilibrium (Figure
25). Fundamentally, the model of a fiat plate is a way of reconciling the mechanical and thermal behavior of the lithosphere.The two behaviorsare not alwaysconsistent,and they
are also not directly related to the seismicstructurein the upper mantle. Note that the total thickness of the thermal
boundary layer is greater than the plate thickness as previously determined.The rigid portion in which the dominant
heat transfer mechanism is conduction is less than the plate
1500
'
HEAT FLOW
and an ocean were it at
equilibrium.
Conduction is not the only mechanismof heat transfer in
the upper mantle. Parsonsand McKenzie [1978] proposed a
model in which the lithosphere is consideredas a thermal
boundary layer whosethicknessincreaseswith age until it becomesunstable. Below a given temperature it is assumedthat
the lithosphericmaterial behavesas a solid and formsan upper mechanical boundary layer. At greater temperaturesthe
equivalentviscosityis low, and the material behavesas a fluid
over geologictimes. The temperature structure is conductive
in the solid portion and governed by small-scaleconvection
below. Assuminga mantle heat flow of 0.75 /•cal/cm2 s (31
mW/m :) and a conductivity
of 8 x 10-3 cal/cm øC s (3.4 W/
and an old continent.
The original argumentswhich are presentedto justify the
difference in lithosphere thicknesscame from the conductive
interpretation of heat flow measurementsand surface wave
dispersionstudies[Bruneand Dorman, 1963].We now reevaluate the constraintsplacedupon thermal modelsof the upper
mantle by seismologicalobservations. Such seismic studies
fall into two categories:(1) surfacewave dispersionand (2) S/
$cS time delays. In 1963, Brune and Dorman [1963] showed
that there were significantdifferencesin the shear wave velocity structurebeneaththe Canadian Shield and the oceanfloor.
Dziewonski [ 1971], using 'pure-path' dispersiondata, found
that these differenceswere confined to the upper 200 km of
the mantle. More recently, Jordan [1975] and Sipkin and Jordan [1975] on the basis of $c$ travel times and the discrepanciesbetween models inverted from body and surface
wave data have suggestedthat lateral heterogeneitiesbetween
oceans and continents extended to depths of 400 km. The
analysisof S/ScS/ScS2 travel time delays is difficult, and
Okal and Anderson[1975] have questionedboth their results
and their conclusions.In the light of the strongdependenceof
thesedelayson the age of the oceanfloor [Sipkin and Jordan,
1975], the position of the earthquakeschosenfor the surface
reflection points, and the errors in the delays the difference
betweenthe old oceansand the shieldsis not large. Furthermore, from long-period Rayleigh wave velocitiesand taking
account of lateral heterogeneitieswithin oceanic plates Okal
[1977] showed that all observationalseismicdata related to
shields were not significantly different from oceanic models
below 250 km. He points out that the velocitiesderived from
the models of Jordan [1975] are inconsistentwith the set of
data that he used. Cara [1979], using higher Rayleigh wave
modes which are more sensitiveto the structure at depth,
showed that the differences
between
oceans and continents
are confined to depths of less than 250 km. At shallower
depths he finds as much variation between the western and
easternUnited Statesas betweena path acrossthe Pacific and
the easternUnited States.He also showsthat the slight low-
velocity
zonewhichisnotrequired
w•hen
inverting
thefundamental mode data for the easternUnited Statesis requiredby
the inversion of the higher modes.
Surface wave data are stronglydependentupon the age of
the ocean floor [Forsyth,1977] and show large variationsfor
periodslessthan 140 s, indicating variation in the shear wave
structure above 200 kin. Below this depth all the data are
compatible with the same model [Okal, 1977]. If small-scale
300
SCLATER ET AL.: OCEANIC AND CONTINENTAL HEAT FLOW
•l.•
•,o
HEAT
1-•
o,
11'•
•
1.•
•oo
i
1.18
•,o
•o,oCONTINENT
OLD
0.99
1-1
FLOW
measurements at sea should be contemplated without due
care being given to selectinga suitable environment. On the
continents,slow circulation of water has long been known to
perturb the surfacegradients.Fortunately, suchwater circulation can usually be detected,and it is possibleto avoid such
areas.Becauseof the greater depth of measurement,environmental problemsare consideredto be lessimportant on continents than on the ocean floor.
We calculate the total heat loss of the oceans to be of the or-
der of 7 x 10•: cal/s (29 x 10•: W), of which 90% is due to
plate creation.We estimatethat about 30% is not observedbecause of the unmeasuredheat loss by advection near active
spreadingcenters.Our estimateof the heat lossthrough the
Fig. 26.
Schematicdiagram modified from Parsonsand McKenzie
[1978]showingthe divisionof the lithosphereinto two regionsof different theologiesbeneathboth oceansand continents.All the depth
estimatesare speculative.The dashedline indicatesthe plate of constant thicknessapproximation.The temperaturestructuresbeneath
the equilibriumoceanand the old continentcan be found in Figure
22. The heatflowis in unitsof 1/•cal/cm2 s (41.8mW/m2).
continentsis 3 x 10•: cal/s (13 x 10•: W). The total heat loss
of the earth is of the order of 1 x 10•3cal/s (42 x 10•2 W).
Over two thirds of the surfaceheat is lost by plate creation
and continental orogeny, 20% by conduction,and the rest by
the radioactivedecay of heat-producingelementsin the crust.
Convection is the dominant mechanismby which the internal
heat of the earth is released.
We conclude from a careful analysisof the thermal strucconvectiondoesexist in the upper mantle under both oceans ture of the lithosphere that there is no observabledifference
and continents, significant temperature differences are ex- betweenthe geothermfor old continentsand that for an ocean
pectedas deepas the bottomof the thermalboundarylayer at equilibrium.However,thereis someevidencefrom seismol(Figure25). This depthis not knownat present,but it is prob- ogy that there may be significantshearwave velocity differably deeperthan 150kin. The oldestoceanconsideredby For- ences at depth even if the temperature differencesare not
syth [1977] is 100-130 Ma and is significantlyabove thermal large.
equilibrium.It is plausiblethat temperaturevariationsassociAs well as answeringsomequestionsthis studyhas revealed
atedwith convection
are responsible
for lateraldifferences
i•
a few problemsin the interpretationof oceanicheat flow data.
seismic
strucfure
downto depthsof 250kin.Further,theequi- One of them is the relation betweenage and heat flow in marlibrium oceanicgeothermat depthsbelow 70 km is closeto ginal basins.Is the simplisticapproachtaken in this review
the solidus.Forsyth[1977]hassuggested
that beyond200 Ma justified,and why do the depthsin this regionnot showthe
the geotherms
may not interceptthe wet solidusat any point same relation with age as normal ocean floor?Another prob[Forsyth, 1977, Figure 12]. Such a differencewould have a lem arises in the well-sedimented areas where the heat flow is
largeeffecton seismicwavesbut little effecton the temper- lower than expected.Is the differencefrom the expectedheat
ature•tructure.
Thisis an alternative
andequally
plausibleflow environmentallycontrolled (i.e., circulationin the baseexplanationasto why a smalldifferencein temperaturecould ment or sediment),or doesit require somemodificationof our
correspondto a relatively strikingdifferencein seismicstruc- ideas about the tectonic processesactive in the crust?
ture beneath oceans and continents.
A variety of questionshave been raised by our analysisof
With presently available information we see no reason to the continental data. What is the actual distribution of the rabelieve that there is difference between the thermal structure
diogenicelementsin the lower crust?What is the meaning of
Qr and D in the light of the discoverythat the linear relation
tinent.We suggest
that the continents
aremerelythe equilib- between heat flow and surface heat production holds for
rium portionof the lithosphere
whichhasnot beendestroyed metasedimentsand other metamorphic rocks as well as for
in the subductionprocess(Figure26). We favorthisuniformi. granitic plutons?
tarJanmodelbecauseit is simpleand compatiblewith all obIn our analysiswe have concentratedon the radioactive
servationspertaining to the thermal structureof oceansand rather than the orogenicage. To examine the actual decay of
continents.
heat flow with age, the Phanerozoicvaluesneed a more careful analysisin which the effectsof continentalextension,basin
CONCLUSIONS
formation, mountain building, and erosion are all examined
The observed subsidence of the ocean floor and the meain an integratedapproach.Suchan analysisis particularlyimunder an equilibriumocean and that under an old stablecon-
sureddecrease
of heatflowwith ageare accounted
for by the
portant in view of the rapid decayof the reducedheat flow
creation
oflithospheric
plate.Further,
wehaveshown
thatthe with age and the 50-m.y. time constantindicatedby the sub-
marginal basinsexhibit the same relation between heat flow
and age as the deep ocean floor. On the continentsthe heat
sidence of continental basins through the Proterozoic and
Phanerozoic.The studyof continentalbasinsthroughgeologic
flow is generallyhigh in the youngerregions,decreasing
to a time promisesto be a subjectworthy of more attention.If our
constantvalue after 800 Ma. However,the nonradiogenic speculations
are correct,the lithospherewas su•ciently rigid
componentreachesan equilibriumvalue after only 200-300 to supporta significantsedimentaryload in the Archean.PreMa.
liminary data suggestthat the plate thicknessat that time was
We havestressed
the importance
of localgeologic
variables. the sameasit is today.The development
of •ucha thick
For example, hydrothermal circulation and unmeasuredloss
of heat by advectionare responsiblefor the scatterand low
mean valueson youngeroceancrust.Obviously,no further
boundary
layerearlyinthehistory
oftheearti
• musthavehad
a major effecton the lossof heat and thermal convectionin
the mantle beneath the lithosphere.
SCLATER ET AL.: OCEANIC
AND
We have deliberately taken a uniformitarian approach.
This is permittedby our presentknowledge.Someproblems
remain, and the most important is the interpretationof the
seismicinformatien. However, it is possibleto interpret this
information in a variety of different ways, someof which are
compatiblewith our approachto the thermal data. In light of
the lack of constraintsplaced by the seismicinformation we
prefer a simpleinterpretationof the heat flow data. Hence we
favor a model which has a similarthermal structureat depth
beneath an equilibrium ocean and an old stable continent.
CONTINENTAL
HEAT
FLOW
301
Forthecentral
Indian
Ocean
andWharton
Basin
themagneticanomalylineationsweretakenfromPitmanet al. [1974].
Thesehave been supplemented
by data from Simpsonet al.
[1979]in the North MozambiqueBasinand BerghandNorton
[1976]in the SouthMozambiqueBasin.The lineationsshown
off northwestern
Australiain the Gascoyneabyssalplain are
from Larson [ 1975].
Deep-Sea Drilling Sitesand
Bathymetric Contours
As a few of the lineationsare difficult to identify and much
of the sea floor is not coveredby lineations,we supplemented
FOR OCEANIC CRUST
our anomaly identificationswith deep-seadrilling holeswhich
We calculatedthe positionof isochronson the deep-sea reached basement (Plate A1). The data for these sitescan be
floor usingthree techniques:(1) magneticanomaly identifica- found in the Initial Reportsof the Deep Sea Drilling Project,
tions,(2) deep-seadrilling samples,and (3) rotatingthe pres- volumes1-44, issuedby the U.S. GovernmentPrinting Office.
ent ridge axis through appropriate rotation parameters.For Also presentedare the 2000- and 4000-m contoursfrom the
the marginal basinswe determinedthe age of the seafloor us- world bathymetric chart of Chase[1975]. The 2000-m contour
ing the first two techniquesand a relation between age and outlines most of the continents and continental shelves surmean heat flow establishedearlier in this paper.
roundingthe continents.The 4000-m contourgivesa good indication of the positionof the midoceanridgeswithin the maMagnetic Anomaly Identifications
jor oceanic basins.
We superimposedidentified magnetic lineations upon an
Time Scale
interruptedequal area chart of the world [Goode,1923].We
startedwith the compilationof Pitman et al. [1974] and upIt is necessaryto have a consistenttime scalewhich relates
dated or changed the lineations in areas where more data anomaly number and biostratigraphicepoch to time in order
have been collected(Plate A1). For the sake of brevity we to determineabsoluteage from magneticanomalyidentificahave cited compilationsof data rather than the original pub- tionsand sedimentsrecoveredat the baseof deep-seadrilling
lications.The original data can be found by referenceto these holes.For magneticanomaly numbers0-34 (0-80 Ma), prescompilations.
ent through the Late Cretaceous,we used LaBrecque et al.
For the Arctic Ocean, Norwegian Sea, and Atlantic Ocean [1977]. We followed van Hinte [1976a, b] for the Mesozoiclinnorth of 53øN we usedthe compilationof J. D. Phillipset al. eations and the rest of the Cretaceous and the Jurassic.
(unpublisheddata, 1979). For the Labrador Sea the lineations
were taken from Kristoffersen
and Talwani [1977] and for the Why SpecificlsochronsWere Chosen
APPENDIX
A: RELATION
BETWEEN
AREA AND AGE
central North Atlantic from Pitman and Talwani [1972]. Off
the east coast of North
America
and the west coast of Africa
we employedthe compilationsof Schoutenand Klitgord[1977]
and H. Schoutenand K. Klitgord (unpublisheddata, 1979).
For the centralSouthAtlantic we followedthe compilationof
Ladd [1974] and for the west coast of Africa the lineations of
Rabinowitz and LaBrecque [1979]. The Scotia Sea lineations,
the ridge axis around the Bouvet triple junction, and the
SouthwestIndian Ridge from Bouvet Island to 40øE are from
Barker and Burrell [1977], $clater et al. [1976c],and $clater et
al. [1978], respectively.
For the North Pacificwe usedthe compilationof Pitman et
al. [1974], updated in the western Pacific with the data of
Hilde et al. [1976]. For the marginal basinsof the sameocean
we followed Louden [1976] for the Philippine Sea, Watts and
Weissel[1975] for the Shikoku Basin,and Bracey[1975] for
the North
Carolina
Basin. For the Panama Basin the linea-
tions are from Lonsdaleand Klitgord [1978].
In the central South Pacific we have followed the lineations
of Handschumacher[1976] near the ridge axis and for anomalies older than anomaly 13, Pitman et al. [1974]. For the Chile
Rise and the BellingshausenBasin we used data of Weisselet
al. [1977] and for the rest of the South Pacific, Molnar et al.
[1975]. In the marginal basinsof the South Pacificthe Tasman
Sea lineationsare from Weisseland Hayes [1977],thosein the
South Fiji Basinfrom Wattset al. [1977],and thosein the Lau
Basinfrom Lawyeret al. [1975]and Weissel[1977].The lineations presentedfor the west Coral Sea are from J. K. Weissel
(personalcommunication,1978).
Exceptfor the first 20 million yearswe separatedthe oceans
into nine almost equal intervalsof time. We chosefour intervals between 0 and 20 Ma and nine between 20 and 160 Ma
and added everything on crust older than 160 Ma into one
time span.The individual isochronswere selectedfor different
reasons. The 9-, 20-, and 35-Ma isochrons were chosen be-
cause these are the ages of the easily identifiable magnetic
anomalies5, 6, and 13. The oceancrustcoolsrapidly immediately after formation. To better estimatethe heat lossin the
first 9 Ma, we separatedthis interval into three subdivisions,
0-1, 1-4, and4-9 Ma. We chosethe 52-Ma isochron(anomaly
22) becausethis is the time at which significantmotion started
between Australia
and Antarctica.
The 65-Ma
isochron over-
lies anomaly29 and marksthe Cretaceous-Tertiaryboundary.
The 80-Ma isochronoverliesanomaly 34, which is the last
clearly identified magnetic anomaly of the Tertiary-Cretaceoussequence.The 125-Ma isochron(anomaly M7) was
selected because this is the time of creation of the South At-
lantic and Indian
oceans. We chose the 95- and 115-Ma
iso-
chronsbecausethey are equallyspacedin time betweenthe 80and 125-Ma isochrons. The 140-Ma isochron overlies anom-
aly M22. We selected160 Ma as the final isochronbecauseit
is the time of jump in early spreadingin the North Atlantic
and to permit a separationof the very old crustin the western
Pacific. There is no known ocean crust older than 180 Ma.
We have assumed that the 2000-m contour on the continental shelf marks the break between continent and ocean. This is
an oversimplification,but on the scaleof our analysisany errors introduced can be neglected.
302
SCLATER ET AL.: OCEANIC AND CONTINENTAL
Positionof the Isochrons
We used the magneticanomaly compilation,the basement
ages inferred from sedimentrecoveredin deep-seadrilling
holes, the above time scales,and published plate reconstructions to draw the isochronson the equal area chart of the
oceans.We determined the position of the isochronsin the
Atlantic by rotating the ridge axis about the polesand by the
anglesgivenby $clateret al. [1977].For the SouthwestIndian
and America/Antarctic ridges we calculated the position of
the isochronsby rotating the ridge axis by the rotational parametersgiven by Norton and $clater [1979].Care was taken
not to violate the basicconceptsof plate tectonicsin the development of the Azores, central Atlantic, and Bouvet triple
junctions.
In the North and South Pacific, except for the Macquarie
Ridge, the East PacificRise, and the Chile Rise before9 Ma,
we used the magneticlineationsto determinethe positionof
the isochrons.For the two youngestisochronswe rotated the
ridge axis through the appropriate rotation parameters of
Minster et al. [1974]. In the Indian Oceanthe isochronson the
SouthwestIndian Ridge from presentto 80 Ma, on the Central
Indian Ridge from presentto 35 Ma, and on the SoutheastIndian Ridge from 0 to 53 Ma were determinedby rotating the
ridge axis throughthe rotation parametersfrom Norton and
$clater [1979]. For the Red Sea we assumed that it had
openedat 20 Ma and sincethen had spreadat a constantrate.
The
rest of the isochrons
in the Indian
Ocean were inter-
polated from the publishedlineationsexceptfor the Somali
Basin close to the coasts of India
and Antarctica.
For this
crust we determined the position of the isochronsfrom the
early opening history of Norton and $clater [1979] and then
transferredthem by hand to the large chart. These isochrons
are hypothetical.
In the caseof the marginal basinswe usedpublishedmagnetic lineationsand sedimentrecoveredfrom deep-seadrilling
holes. However these data are not sufficientto permit agesto
be assignedto more than half thesebasins.In the text we justify a relation between heat flow and age for these basins.
Where other data are not available, we applied this relation.
For the western Mediterranean
we used the heat flow data
of Erickson et al. [1977]. We assumedthat the northern portion of the Messina Basin was young and, on the basisof the
low heat flow values, that the rest of the eastern Mediterra-
nean was old. In the Caribbean we assumedthat the Cayman
Trough was initiated at 50 Ma and has been spreadingat a
uniform rate since then. For the rest of this area we based our
estimateon the age of the surroundingcontinentsand the surface heat flow. Some support for the age that we have assigned to the Venezuela Basin comesfrom the recognition of
east-west
lineated
anomalies
in the Columbia
Basin which
have been tentatively identified as 29-33 [Christofferson,
1973]. For the Scotia Sea we have used the lineations presented by Barker and Burrell [ 1977].
In the Arctic Ocean we estimated the age from the heat
flow. For the Bering Sea we followed Cooperet al. [1976]. We
assumedthat the Kamchatka Basin was young and used the
heat flow to estimate the age of the Sea of Okhotsk and the
Sea of Japan. In the North Pacific marginal basins we estimated the age of the Ryukyu Trough, Celebes Sea, Scotia
Sea, Andaman Sea, and South China Sea from the heat flow.
We took the age for the Mariana Trough from Karig [1971],
and for the rest of the basinswe used either magnetic lineations (West Philippine Basin and Shikoku Basin) or the sedi-
HEAT
FLOW
SCLATER
ET AL.: OCEANIC
AND
CONTINENTAL
FLOW
303
B
A
t4.0
HEAT
t4.0
-
-
12.0
t2.0
10.0
'
--
NORTHPACIFIC
,
---
SOUTH PACIFIC
8.0
t0.0
' F--',
--
NORTH
ATLANTIC
....
SOUTH
ATLANTIC
8.0
6.0
/
,
4.0
t
2.0
'
r - -,
2.0
__J
0
• i
• i
• I
• I
20
40
60
80
0
•
•
•
I
t00
•
I
• I--,- -I
t20
140
o
t60
0
t80
c
t4.o -
14.0
I•-t2.o
-
INDIAN
20
40
GO
$0
100
t40
t60
t80
-
t2.0
OCEAN
t20
D
MARGINAL
BASINS
_
to.o
to.o
8.0
8.o
6.0
6.o
4.0
4.0
2.0
20
o
0
, I •I , I •I , I , i , I , i , i
20
40
60
80
t00
120
t40
160
o
t80
0
4GE
•i8. AI.
IN
20
40
60
80
100
120
t40
160
180
M4
Stepfunctionrepresentation
of t•½ area as a functionof a•½for t•½ oceans:(•) No•t• and Sout• •acific, (b)
No•t• and Sout• Atlantic, (½) Indian Ocean, and (8) mar•ina! basins.
We have included them for the sake of completeness.As they
representlessthan 10%of the area of the oceanfloor, the er-
ment recovered at the base of deep-seadrilling holes (Parece
Vela Basin). The age of the Carolina Basin was taken directly
from the magnetic lineations [Bracey, 1975].
In the southwestPacific marginal basinswe took the age for
the Solomon Sea and Woodlark Basin from Luyendyk et al.
[1973]. We assumedthat the east Coral Sea had the same age
rors introduced
in the calculated total heat loss are small.
Area VersusAgefor the Oceans
as the South Fiji Basin,i.e., between20 and 35 Ma [Watts et
al., 1977],and for the west Coral Sea we useddata of Burnset
al. [1973].For the Fiji Plateau our age estimateis from Chase
[1971], and we assumedthat the Lau and Kermadec basins
were between 0 and 4 Ma [Lawyer et al., 1975a; Weissel,1977].
The lineations in the Tasman Sea were employed to determine the positionof the isochrons,and for the Banda Sea in
the absenceof any concreteinformation we guessedthe age
from the depth to be 52-65 Ma.
The age estimatesfor the marginal basinsare not reliable.
Apart from the South Pacific the oceansexhibit the same
linear decreaseof area with age (Tables 10 and A I and Figures Ala-A2d). This similarity is the result of a combination
of spreadingand crustal consumption.The Atlantic and Indian oceanshave roughly the same spreading rate, and the
North Pacific, which has twice the spreadingrate, has only a
westernlimb. The South Pacifichas both limbs to anomaly 22
(53 Ma) and is spreadingat 4 times the rate for the Atlantic
and Indian oceans. Thus this ridge axis creates most of the
youthful sea floor. However, it doesnot alter the linear decreaseof area with age (Figure A2a). For our computationsof
40
ALL
OCEANS
3O
20
t0
--
I
I
20
I
I
40
,
I
60
,
I
80
45œ/N
,
I
100
I
I
t20
I
I
140
i
I
t60
i
180
M4
Fig. A2a. Stepfunctionrepresentation
of theareaasa functionof agefor all theoceans,
includingthemarginalbasins.
SCLATER ET AL.: OCEANIC
304
AND
4.0
CONTINENTAL
HEAT
FLOW
Cretaceous [Hays and Pitman, 1974]. However, we have not
considered the area of material consumed in the trenches, and
it is not possibleto determinewhetheror not suchan increase
occurred.A definitive test awaits global reconstructionsof the
3.0
oceans and continents.
APPENDIX
B: RELATION
AND
AGE
BETWEEN
AREA
FOR CONTINENTS
In this studywe have chosenfour intervalsof time. The first
interval includes all continent older than 1700 Ma. It spans
0
50
100
AGE
t50
the Archeartand the early Proterozoicand terminateswith the
orogenicpulsebetween1900and 1700Ma. The secondinterval extendsthrough the middle Proterozoicfrom 1700 to 800
Ma and includes the major continent-formingphase between
200
11• MA
Fig. A2b. Rate of increasein areaof the oceansasa functionof age.
1100 and 900 Ma. The third interval
runs from 800 Ma to the
start of the Mesozoic at 250 Ma. The fourth and final interval
is the Mesozoic and Cenozoic, which covers the crust formed
heat loss the age/area distribution has three important features. (1) Almost half the seafloor, not including the marginal
basins,is located in the Pacific.(2) The marginal basins,as we
define them, represent 8% of the ocean floor. (3) The continental shelvescover about 10% of the surfaceof the globe. If
we assume that the shelves are continental, the ratio of ocean
to continent is 3:2. This is different from the 2:1 figure determined from previous studies [Kossinna, 1921; Menard and
Smith, 1966] (Table A 1). We compared our values for the
oceans with those of Menard and Smith [1966]. Once allowance is made for the different definitions of shelf and ocean,
the agreementis excellent.From this comparisonwe estimate
that our errors in comparison of areas of continents and
oceans are of the order of 2%. The errors in the area of the in-
dividual age provinces are difficult to calculate. More than
60% of the ocean is coveredby well-identified magnetic lineations, and for a further 20% the positionof the isochroncan be
predictedwith someconfidence.Thus we estimateour errors
in the areas to be less than 20%.
From the histogramsof area versusage (Figure A2a) we
calculated the rate of increaseof oceaniccrust including marginal basinswith age (Figure A2b). The amount of crustpresent decreaseslinearly with age (Table A I and Figure A2b).
Both the values for total area in a given time interval and the
rate of decreaseof crust are closeto those determined by Berger and Winterer [1974] in a similar but cruder study. The similarity of the two valuesis evidencethat more careful analysis
will not change the conclusionthat the oceanshave a roughly
linear decreaseof area with age.
It is tempting to use our analysisto investigatewhether or
not there was a rapid increase in area of young crust in the
or altered during the latestepisodeof plate motion and creation of sea floor.
For our separationof the continentsinto the appropriate intervalswe have followed Hurley and Rand [1969] and Hurley
[1971]. This material has been supplementedwherever possibleby information gatheredfrom geologicalmapsof various
continentsand by more recentcompilationof radiometricage
data. We have separatedthe crustinto tectonicprovincesand
have assumedthat all rocks within a province have the age of
the last orogeny.
For North America we used the data compilation of Hurley
and Rand [1969] in conjunction with the tectonic chart of
North America by King [1969]. For South America we followed Hurley and Rand's[1969]data, extensivelymodifiedby
new data from de Alrneida et al. [1974, Figure 1] and Urien
and Zarnbrano [1973, Figure 5]. For Africa, to which we
added both Arabia and Madagascar,we startedwith the compilation of Hurley and Rand [1969], to which we added data
for central Africa from ½houbertand Foure-Muret [1968]. Our
separationof Arabia into differentageintervalsis speculative
(P.M. Hurley, personalcommunication,1978). For Eurasia
we followed the chartspresentedby Hurley [1971] and supplemented these with data from the Russian TectonicAtlas [Ministry of Geology,1969] and the ChineseTectonicChart of Asia
[ChineseGeologicalSociety,1975].We assignedthe Russian
platform betweenthe Urals and the Siberianplatform the
younger age of the tectonic chart rather than that given by
Hurley [1971]. In essence,we have given this area the age of
the oldest sedimentsdepositedrather than the crustal age of
basement. In this particular case we believe such an assig-
nation is justified by the great thicknessof sedimentswhich
TABLE B 1. Areas of Continental Age Provinces
Age, Ma
Africa
0-250
250-800
800-1700
> 1700
Continental
Shelf
Total
Area
and
Madagascar
0.5
16.2
5.4
11.5
4.2
37.8
South America
2.6
5.1
4.9
5.2
4.5
22.3
North America
Australasia
Antarctica
5.8
0.9
1.2
3.7
2.9
4.6
3.6
3.3
10.5
1.8
6.6
10.3
9.9
5.2
33.9
18.8
17.6
EuropeandAsia
17.6
18.9
All continents
28.5
51.3
21.2
3.9
9.3
2.4
12.7
18.0
48.3
52.2
71.1
201.5
Area/age
(km/yr) x 10-2
11.4
2.1
5.0
Valuesfor areasare givenin 106 km2. Resultsfrom totalingcolumnsmay differslightlyfrom those
given owing to rounding.
SCLATER ET AL.: OCEANIC
AND
CONTINENTAL
HEAT
FLOW
305
30-
30-
AFRICA
AND
SOUTH
AMERICA
MADAGASCAR
20
2O
I0
I-
,,
I
I000
i
2000
I
I
3000
,I
,
4000
30 -
0
I
,
I
3000
I
I000
2000
I
I
4000
30 -
NORTH
AUSTRALASIA
AMERICA
20
2O
!
, ,,I
I000
0
,
I
2000
I
I
3000
,
I
4000
30 -
0
•
I
I
,
I000
!
i
2000
I
3000
I
I
4000
30
EURASIA
ANTARCTICA
20
20
i
0
, I 2000
I
AGE
IN
,
I
3000
,
I
4000
0
!
I
I000
MA
2000
AGE
3000
IN
I
I
4000
MA
Fig. B1. Stepfunctionrepresentation
of the area as a functionof age for the individualcontinents.
could only have been createdby an orogenyof this age. For
India, which we included in Eurasia, we used the chart presented by Hurley and Rand [1969] and a more recent com-
pilation of radioactivedatesmade by Naqui et al. [1974,Figure 2]. We took the age rangesfor Australiafrom Hurley and
Rand [1969,Figure 6], and for Antarctica,for which there are
very few data, we employedthe same source[Hurley and
Rand, 1969, Figure 7].
We superimposedthe provinceboundarieswhich we determined from the papersmentionedaboveonto Goode's[1923]
interruptedequal area map of the world. We alsoplotted the
2000-m contour, which for the purposeof this paper defines
150,
CUMULATIVEAREA
VERSUS AGE
100
_
I
1
,
more
continent
I
i,
2
AGE
IN HAx103
Fig. B2. Cumulativeplot of the area of the continentsas a function
of age.
in the Mesozoic
and Cenozoic
and a much
larger area in the interval prior to 1700 Ma. The increasein
the latter interval is expected. As more radiometric age dates
on continental basementare published,it is becomingapparent that the area of the oldest portions of the Precambrian has
been underestimatedin the past. On the other hand the problems of relating radioactive age to orogenic age still exist.
Thus we have inadvertently included a few youthful orogenic
regionsin the older provinces.This is particularly true on the
Russian and West Siberian platforms. Until this problem in
continental tectonicsis resolved,age/area estimatesbased on
basementradioactive agesmust be consideredat best good estimates rather than quantitative values.
APPENDIX
-....
,
o
the continental shelf line. Using a planimeter, we computed
the area in each of the age intervals and the total amount of
shelf around each continent (Table B 1, Figure B 1).
Almost l•alf the continental area is formed in the two intervals older than 800 Ma (Figure B2). Our distribution of area
with age for the continents is similar to that of Hurley and
Rand [1969] and Veizer [1976]. However, we have slightly
C: THE
MODIFIED
PLATE
MODEL
We follow here the derivation of McKenzie [1967], using the
boundary conditions of Davis and Lister [1974]. In nondimensional variables the differential equation and boundary
conditions for the modified plate model are
O2T
aT
O2T
Oz
2 2R-•-.+
Oz O-•--0
306
SCLATER ET AL.' OCEANIC AND CONTINENTAL
TABLE
Cl.
Surface Heat
Flow From
Plate Model SpreadingRate, cm/yr
Age, Ma
1
3
5
1
l 1.60
11.30
11.26
4
5.69
5.62
5.62
9
20
35
52
65
80
95
110
3.77
2.51
1.90
1.56
3.75
2.5 l
1.90
1.56
1.39
1.26
1.16
1.08
125
140
160
180
3.74
2.51
1.89
1.55
1.02
0.97
0.92
0.89
HEAT
Different
FLOW
Models
Cooling
Exponential
Half-Space
Approximation,
Model, 3 cm/yr
3 cm/yr
McKenzie
[ 1967],
3 cm/yr
11.30
5.65
3.77
2.53
2.37
2.30
2.19
1.96
11.46
5.64
3.75
2.51
1.91
1.57
1.40
1.26
1.16
1.08
1.01
0.96
1.72
1.50
1.37
1.25
1.15
1.08
1.02
0.97
1.90
1.56
1.39
1.26
1.16
1.08
1.02
0.97
0.89
0.84
0.93
0.89
0.92
0.89
Heat flow valuesare in unitsof/•cal/cm2 s.
T(z= 1)--0
(Cl)
I thicknessof the plate, equal to 125 km;
T• temperature at the base of the plate, equal to 1333øC.
T(z -- O) = 1
10T
----+T=
1
R Ox
at
x=0
whereR is the Pecletnumber,equal to ul/2k; u is the plate velocity, I the plate thickness,and k the thermaldiffusivity;x denotesthe horizontal coordinate,and z the vertical (z = I at the
uppersurface).The third boundaryconditionequatesthe heat
broughtin at the originwith that losthorizontallyto the plate
[Davis and Lister, 1974]. The nondimensional horizontal
coordinatex is given by
x -' ut/l
wheret is the ageof the crustat distancex = ut from the ridge
axis.
The solutionto (C1) is
T= 1- z+ • A,v
exp
(-a,x)sin
(mrz) (C2)
N=!
where
an= -R + (R2 + n2•)
and
Thesevaluesyield an asymptoticheat flux of 0.8 x l0 -6 cal/
cm2 s as time goesto infinity.
The McKenzie [1967]model has the disadvantageof yielding an infinite heat flux at the ridge axis, as the seriessolution
divergesfor x - 0. The modified plate model is therefore more
appropriate for our heat losscalculations.The two plate models only differ significantly in their predictions for times less
than 1 Ma, as can be seen in Table C 1.
We give in Table C 1 the theoretical heat flow at the discrete
agesthat we used to define the isochronson the oceanic crust,
together with the cooling half-space solution of Davis and
Lister [1974] and the exponential approximation of Parsons
and Sclater [ 1977] which is asymptoticto the plate solution as
time goes to infinity. We list in Table C2 the three corresponding expressions.We make the computationsfor plate
velocitiesof 1, 3, and 5 cm?yr and find little differencein the
results, even for the earliest ages. The theoretical values derived from (C2) are in good agreementwith the other values.
In Table C3 we give the mean heat flow through the upper
and lower surfacesof the plate for the time intervals defined
by two consecutiveisochrons.The same plate velocitiesare
used, and the resultsdiffer slightly before 9 Ma.
All these calculations
A•v--
2(-1) "+•
2R
n•r
2R + an
do not include
the contribution
of the
radioactive decay of U, Th, and K. For equivalencewith val-
Used to Predict the Surface Heat
The originalplate model of McKenzie[1967]usedthe same TABLE C2. Three Expressions
Flow
equationsbut a different initial condition at x = 0. This condi-
Numerical
tion was
Expression
T= 1
at x=0
(C3)
Plate model
The solutionto theseequationsis still of the form (C2) with
a,, = -R + (R2 + n2•) •/2
and
As = 2(-1)N+•/mr
For our calculationswe use the following parameterswhich
can be found in the work of Parsonsand Sclater[1977]:
K
k
thermalconductivity,equalto 7.5 x 10-3 cal/øC cm s;
thermal diffusivity,equal to 8.0 x l0 -3 cm2/s;
Approximation
__
1+ __•
2R+
Cooling
half- (_•)(•rk)•/2
I r•/2
1
space
model
11.3/t
•/2
Exponential
(_•)+(2/•T,
+1.6
approximation
)exp
[_(•_•_
k)t] 0.8
exp
(-t/62.8)
McKenzie
[ 1967] model
I 1+2 • e-a,•
N-----!
K is thermalconductivity,
andk is thermaldiffusivity
K/pCp.
SCLATER ET AL.: OCEANIC AND CONTINENTAL
HEAT
FLOW
307
TABLE C3. Mean Heat Flow Through the Upper and Lower Surfacesof the Lithosphere
Upper SurfaceSpreadingRate, cm/yr
Age, Ma
0-1
1-4
4-9
9-20
20-35
35-52
52-65
65-80
80-95
95-110
110-125
125-140
140-160
160-180
1
3
5
21.31
22.30
7.65
4.53
3.02
2.17
1.71
7.51
4.50
3.01
2.16
1.71
1.47
1.32
1.20
1.11
1.05
0.99
0.95
0.91
Lower SurfaceSpreadingRate, cm/yr
I
3
5
22.40
0.00
0.00
0.00
7.50
4.49
3.01
2.16
1.71
0.00
0.00
0.00
0.02
0.10
0.00
0.00
0.00
0.02
0.10
0.21
0.31
0.41
0.49
0.56
0.61
0.66
0.69
0.00
0.00
0.00
0.02
0.10
Heat flowvaluesare in/•cal/cm2 s.
ues of Parsonsand $clater [1977] a value of 0.1 /•cal/cm2 s
should be added throughout.
Acknowledgments.This paper has a long history.Important initial
input came from S. Uyeda, P. D. McKenzie and N.H. Sleep.M. S.
Steckler,L. Bales,and L. Dobinov helpedwith the analysisand plotting of the continemalheat flow data. L. Royden wrote the computer
programsfor Goode'sprojection,and P. Pollen digitized someof the
oceaniccontours.P.M. Hurley and C. Burchfielaided us in the separation of the continentsinto age provinces.The original manuscript
was reviewed by B. F. Windley, P. C. England, and J. H. Sass.We
benefitedgreatly from their comments.E. Nisbet provided information on the early Proterozoicbasins,and B. Kennett discussedthe implicationsof the seismologicalinformation with us. This study was
supportedby National ScienceFoundationgrants76-82076 OCE and
DPP76-19053A01. The work was completedwhen J. G. Sclater was
on sabbaticalat the Departmentof Geodesyand Geophysics,University of Cambridge,Cambridge,United Kingdom, and C. Jaupart was
enjoying active military duty at the Place Balard air force base in
Paris.
REFERENCES
Akella, J., Garnet pyroxeneequilibria in the systemCaSiO3-MgSiO3A1203 and in a natural mineral mixture, Amer. Mineral., 61, 589598, 1976.
Anderson, R. N., Oceanic heat flow, in The Sea, vol. 7, Wiley-Interscience,New York, in press, 1979.
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., G. Moore, S. Schilt, R. Cardwell, A. Trehu, and V.
Vacquier,Heat flow near a fossilridgeon the north flank of the Galapagosspreadingcenter,J. Geophys.Res.,81, 1828-1838, 1976a.
Anderson,R. N., M. G. Langseth,V. Vacquier, and J. Francheteau,
New heat flow measurementson the Nazca plate, Earth Planet. Sci.
42, part 1, edited by K. J. Hsu et al., pp. 509-514, U.S. Government
Printing Office, Washington,D.C., 1978.
Barker, P. F., and J. Burrell, The opening of the Drake Passage,Mar.
Geol., 25, 15-34, 1977.
Bayer,R., J. L. LeMouel, and X. LePichon,Magneticanomalypattern in the western Mediterranean, Earth Planet. Sci. Lett., 19, 168176, 1973.
Beck, A. E., Climaticallyperturbedtemperaturegradientsand their
effecton regional and continentalheat flow means, Tectonophysics,
41, 17-39, 1977.
Berger,W. H., and E. L. Winterer, Plate stratigraphyand the fluctuating carbonateline, Int. Ass.Sedimentol.
Spec.Publ.,1, 11-48, 1974.
Bergh,H. W., and I. O. Norton, PrinceEdwardfracturezoneand the
evolution of the Mozambique Basin, J. Geophys.Res., 81, 52215239, 1976.
Berry, M. J., Structureof the crustand upper mantle in Canada, Tectonophysics,
20, 183-201, 1973.
Bickle, M. J., Heat loss from the earth: A constraint on Archean tec-
tonicsfrom the relation betweengeothermalgradientsand the rate
of heat production,Earth Planet. Sci. Lett., 40, 301-315, 1978.
Birch, F., R. F. Roy, and E. R. Decker, Heat flow and thermal history
in New Englandand New York, in Studiesof AppalachianGeology,
edited by E. An-Zen, pp. 437-451, Interscience,New York, 1968.
Bishop,F. C., J. V. Smith, and J. B. Dawson,Na, K, P, and Ti in garnet pyroxene and olivine from peridotite and eclogite xenoliths
from African kimberlites, Lithos, 11, 155-173, 1979.
Blackwell, D. D., The thermal structure of the continental crust, in
The Structureand PhysicalPropertiesof the Earth's Crust,Geophys.
Monogr., vol. 14, edited by J. G. Heacock,AGU, Washington,
D.C.,
1971.
Bottinga,Y., Thermal aspectsof sea-floorspreadingand the nature of
the suboceaniclithosphere,Tectonophysics,
21, 15-38, 1974.
Bracey,D. R., Reconnaissance
geophysicalsurveyof the Caroline Ba-
sin, Geol. Soc. Amer. Bull., 86, 775-784, 1975.
Brune, J., and J. Dorman, Seismic waves and earth structure in the
Canadian Shield, Bull. Seismol. Soc. Amer., 53, 167-210, 1963.
Lett., 29, 243-254, 1976b.
Burke, K., J. F. Dewey, and W. S. F. Kidd, Dominance of horizontal
Anderson, R. N., M. G. Langseth,and J. G. Sclater, Mechanismsof
movements,arc, and microcontinentalcollisionsin the later perheat transfer through the floor of the Indian Ocean, J. Geophys.
mobile region, in The Early History of the Earth, edited by B. F.
Res., 82, 3391-3409, 1977.
Windley, pp. 113-129, John Wiley, New York, 1976.
Anderson,R. N., M. G. Langseth,D. E. Hayes,T. Watanabe, and M.
Burns, R. E., et al., Initial Reportsof the Deep Sea Drilling Project,
Yasui, Heat flow, thermal conductivity, thermal gradiem, in Geovol. 21, 931 pp., U.S. Government Printing Office, Washington,
D.C., 1973.
physicalAtlas of the East and SouthEast Asian Seas,Map Chart
Ser., vol. MC-25, edited by D. E. Hayes, Geological Society of
Button, A., Transvaal and Hamersley basins--Review of basin develAmerica, Boulder, Colo., 1978.
opment and mineral deposits,Minerals Sci. Eng. Repub.S. Afr., 8,
262-293, 1976.
Anhaeusser,C. R., The evolution of the early Precambrian crust of
southern Africa, Phil. Trans. Roy. Soc. London, Ser. A, 273, 359Cara, M., Lateral variations of S velocity in the upper mantle from
388, 1973.
higher Rayleigh modes,Geophys.J. Roy. Astron.Soc.,57, 649-670,
1979.
Aoki, K., and I. Shiba, Petrologyof websteriteinclusionsof ItinoneGata, Japan, Sci. Rep. Tohoku Univ., Ser. 3, 12, 395-411, 1974.
Carswell, D. A., D. B. Clarke, and R. H. Mitchell, The petrologyand
Artemjev, M. E., and E. V. Artyushkov,Structureand isostasyof the
Baikal Rift and the mechanism of rifting, J. Geophys.Res., 76,
1197-1211, 1971.
Barberi, F., et al., Age and nature of basalts from the Tyrrhenian
abyssalplain, in Initial Reportsof the Deep Sea Drilling Project,vol.
geochemistryof ultramaficnodulesfrom pipe 200, in Proceedings,
SecondInternational Kimberlite Conference,Santa Fe, 1977, AGU,
Washington, D.C., 1979.
Carter Hearn, B., Jr., and F. R. Boyd, Garnet peridotitexenolithsin a
Montana, USA, kimberlite, Phys. Chem. Earth, 9, 247-255, 1975.
308
SCLATER ET AL.: OCEANIC
AND
Chapman,D. S., and H. N. Pollack,Global heat flow:A new look,
Earth Planet. ScœLett., 28, 23-32, 1975a.
Chapman,D. S., and H. N. Pollack,Heat flow and incipientrifting in
the Central African Plateau, Nature, 256, 28-30, 1975b.
Chase, C. G., Tectonic history of the Fiji Plateau, Geol. Soc. Amer.
BulL, 82, 3687-3710, 1971.
Chase,T. E., Topographyof the oceans,IMR Tech.Rep. Ser. TR57,
ScrippsInst. of Oceanogr.,La Jolla, Calif., 1975.
ChineseGeological Society,ChineseTectonicChart of Asia, Peking,
China, 1975.
Choubcrt, G., and A. Fourc-Murct, International tectonicmap of Affica, Unesco, Paris, 1968.
Christoffcrson,E., Linear magneticanomaliesin the Columbia Basin,
central Caribbean Sea, Geol. Soc.Amer. BulL, 64, 3217-3230, 1973.
Cooper,A. K., D. W. Scholl,and M. S. Marlow, A plate tectonic
model for the evolution of the easternBering Sea Basin, Geol. Soc.
Amer. BulL, 87, 1119-1126, 1976.
Corliss,J. B., The origin of metal-bearingsubmarinehydrothermal
solutions,J. Geophys.Res., 76, 8128-8138, 1971.
Corliss,J. B., et al., Explorationof submarinethermalspringson the
GalapagosRift, submittedto Science,1979.
Crough, S. T., Thermal model of oceaniclithosphere,Nature, 256,
388-390, 1975.
Crough, S. T., and G. A. Thompson,Thermal model of continental
lithosphere,J. Geophys.Res.,81, 4857-4862, 1976.
Davis, E. E., and C. R. B. Lister, Fundamentalsof ridge cresttopography, Earth Planet. ScœLett., 21, 405-413, 1974.
Davis, E. E., and C. R. B. Lister, Heat flow measuredover the Juan de
Fuca Ridge on a quasi-regulargrid, •. Geophys.Res., 82, 48454853, 1977.
de Almeida, F. F. M., G. Amaral, U. G. Gordani, and K. Kawashita,
The Precambrian evolution of the South American eratonic margin
south of the Amazon fiver in the ocean basinsand margins, in The
SouthAtlantic, vol. 1, edited by A. Naim and F. Stchli, pp. 411-466,
John Wiley, New York, 1974.
Dixon, J. R., and D.C. Presnall, Gcothcrmomctry and gcobaromctry
CONTINENTAL
HEAT
FLOW
Goodwin, A.M., Giant impacting and the developmentof the continental crust, in The Early History of the Earth, edited by B. F.
Windley, 619 pp., John Wiley, New York, 1976.
Griffin, W. L., D. A. Carswell, and P. H. Nixon, Lower-crustal granulites and eclogitesfrom Lesotho,southernAfrica, in Proceedings,
SecondInternational Kimberlite Conference,Santa Fe, 1977, AGU,
Washington, D.C., 1979.
Gurney, J. J., B. Harte, and K. G. Cox, Mantle xenolithsin the Matsku kimberlite pipe, Phys. Chem.Earth, 9, 507-523, 1975.
Handschumachcr,D. W., Post-Eoceneplate tectonicsof the eastern
Pacific,in The Geophysics
of the PacificOceanBasinand Its Margin,
edited by G. H. Sutton et al., pp. 177-202, AGU, Washington,
D.C.,
1976.
Hawkesworth, C. J., Vertical distribution of heat production in the
basementof the easternAlps, Nature, 249, 435-436, 1974.
Hays, J. D., and W. C. Pitman III, Lithosphericplate motion, sea
level changes and climatic and ecological consequences,Nature,
246, 12-18, 1974.
Heier, K. S., and J. A. S. Adams, Concentration of radioactive ele-
mentsin deep crustalmaterial, Geochim.Cosmochim.Acta, 29, 5361, 1965.
Heier, K. S., and J. M. Rhodes, Thorium, uranium and potassium
concentrationsin granites and gneissesof the Rum Jungle Com-
plex,NorthernTerritory,Australia,Econ.Geol.,61, 563-571, 1966.
Herman, B. M., M. G. Langseth,and M. A. Hobart, Heat flow in the
oceanic crust bounding western Africa, Tectonophysics,
41, 61-77,
1977.
Hilde, T. W. C., N. Isezaki, and J. M. Wageman, Mesozoic sea floor
spreadingin the North Pacific, in The Geophysics
of the Pacific
Ocean Basin and Its Margin, Geophys.Monogr., vol. 19, edited by
G. H. Sutton et al., pp. 205-226, AGU, Washington,D.C., 1976.
Hoffman, P., Evolution of an early Proterozoiccontinental margin:
The Coronation geosyncline and associated aulacogens of the
northwest Canadian Shield, Phil. Trans. Roy. Soc. London, Ser. A.,
273, 547-581, 1973.
Hoffman, A. W., and S. R. Hart, An assessment
of local and regional
isotopic equilibrium in the mantle, Earth Planet. Sci. Lett., 38, 44of syntheticspinellhcrzolitcin the system,CaO-MgO-A1203-SiO2,
62, 1978.
in Proceedings,SecondInternational Kimberlite Conference,Santa
Holmes, A., Principlesof PhysicalGeology,2nd ed., 1288pp., Ronald,
Fe, 1977, AGU, Washington, D.C., 1979.
New York, 1965.
Dzicwonski, A.M., Upper mantle modelsfrom 'pure-path' dispersion
Horai, K., Effectsof past climaticchangeson the thermal field of the
data, J. Geophys.Res., 76, 2587-2601, 1971.
earth, Earth Planet. Sci. Lett., 6, 29-42, 1969.
Eggler,D. H., M. E. McCallum, and C. B. Smith,Discretenoduleassemblagesin kimberlites from northern Colorado and southern Horai, K., and S. Uyeda, Terrestrial heat flow in volcanic areas, in
The Earth's Crustand UpperMantle, Geophys.Monogr., vol. 13, pp.
Wyoming: Evidence for a diapiric origin of kimberlite, in Pro95-109, edited by P. J. Hart, AGU, Washington,D.C., 1969.
ceedings,SecondInternational Kimberlite Conference,Santa Fe,
Hsu, K. J., et al., Initial Reportsof the Deep Sea Drilling Project, vol.
1977, AGU, Washington, D.C., 1979.
42, part 1, 1249pp., U.S. Government Printing Office, Washington,
England, P. C., Some thermal considerations
of the Alpine metaD.C., 1978.
morphism--Past, present and future, Tectonophysics,
46, 21-40,
1978.
Hunter, D. R., Crustal developmentin the Kaapvaal Craton, 2, The
Proterozoic, Precambrian Res., 1, 295-326, 1974.
England, P. C., and S. W. Richardson,The influenceof erosionupon
Hurley, P.M., Distribution of age provinces in Laurasia, Earth
the mineral facies of rocks from different metamorphic environPlanet. Sci. Lett., 8, 189-196, 1971.
ments, J. Geol. Soc. London, 134, 201-213, 1977.
Hurley, P.M., and J. R. Rand, Pre-drift continental nuclei, Science,
Erickson,A. J., G. Simmons,and W. B. F. Ryan, Review of heat flow
164, 1229-1242, 1969.
data from the Mediterranean and Aegean seas, in International
Symposium
on the StructuralHistoryon the Mediterranean
Basins, Irving, A. J., On the validity of paleogeothermsdetermined from
edited by B. Bign-Duval and L. Montadert,pp. 2263-2280, Editions Tecknip, Paris, 1977.
xenolith suites in basalts and kimberlites, Amer. Mineral., 61, 638642, 1976.
Ernst,W. G.,Comparative
chemical-mineralogis(investigation
offive Jessop,A.M., The distributionof glacial perturbationof heat flow in
westernAlpine lherzolitecomplexes,in Proceedings
SecondInternationalKimberliteConference,
SantaFe, 1977,AGU, Washington,
D.C.,
1979.
Fischer A. G., et al., Initial Reportsof the Deep-SeaDrilling Project,
Canada, Can. J. Earth Sci., 8, 162-166, 1971.
Jessop,A.M., and T. Lewis, Heat flow and heat generationin the Superior Province of the Canadian Shield, Tectonophysics,
50, 55-77,
1978.
vol. 6, 1329 pp., U.S. GovernmentPrinting Office, Washington, Jessop,A.M., M. Hobart, and J. G. Sclater, World Wide Compilation
D.C.,
1971.
Foland, K. A., and H. Faul, Ages of the White Mountain intrusives,
New Hampshire,Vermontand Maine, U.S.A., Amer.J. Sci., 277,
888-904, 1977.
Forsyth,D. W., The evolutionof the uppermantlebeneathmid ocean
ridges,Tectonophysics,
38, 89-118, 1977.
Francis, D. M., Amphibole pyroxenite xenoliths:Cumulate or re-
placementphenomena
from the uppermantle,Nunivak Island,
Alaska, Contrib. Mineral. Petrol., 58, 51-61, 1976.
Francis, T. J. G., I. T. Porter, and R. C. Lilwall, Microearthquakes
near the easternend of St. Paul's fracture zone, Geophys.J. Roy. Astron. Soc., 53, 201-217, 1978.
Goode, J.P., The homolosineprojection,in An Introductionto the
Studyof Map Projections,
editedby J. A. Stears,chap.10, University of LondonPress,London, 1923.
of Heat Flow Data, Geothermal$er., no. 5, Department of Energy,
Mines and Resources, Ont., 1976.
Jordan, T. H., The continental tectosphere,Rev. Geophys.Space
Phys., 13, 1-12, 1975.
Karig, D. E., Ridges and basins of the Tonga-Kermadec island arc
system,J. Geophys.Res., 75, 239-254, 1970.
Karig, D. E., Structural history of the Mariana island arc system,
Geol. Soc. Amer. Bull., 82, 323-344, 1971.
Karig, D. E., et al. Initial Reportsof the Deep Sea Drilling Project, vol.
31,927 pp., U.S. Government Printing Office, Washington, D.C.,
1974.
Katz, M. B., Earth Precambrian granulites--Greenstones,transform
mobile belts and ridge-rifts in early crust, in The Early History of
the Earth, edited by B. F. Windley, pp. 147-158, John Wiley, New
York, 1976.
SCLATER ET AL..' OCEANIC AND CONTINENTAL HEAT FLOW
Keen, C. E., Thermal history and subsidenceof rifled continental
margins•Evidence from wells on the North Scotianand Labrador
shelves,Can. J. Earth $ci., 16, 505-522, 1979.
Killeen, P. G., and K. S. Heier, A uranium and thorium enriched
province of the FennoscandianShield in southernNorway, Geochim. Cosmochim. Acta, 39, 1515-1524, 1975.
King, P. B., Tectonic map of North America, 1:5,000,000, U.S. Geol.
Surv., Washington, D.C., 1969.
Kossinna, E., Die Liefen des Weltmeeres, Inst. Meereskunde Veroeff.
Geogr.Naturwiss.,9, 70 pp., 1921.
Kristoffersen,C., and M. Talwani, The extincttriple-junction southof
Greenland and the Tertiary motion of Greenland relative to North
America, Geol. Soc. Amer. Bull., 88, 1037-1049, 1977.
Kutas, R. I., Investigationof heat flow in the territory of the Ukraine,
Tectonophysics,
41, 139-145, 1977.
LaBrecque, J. L., D. V. Kent, and S.C. Cande, Revised magnetic
polaritytime scalefor Late Cretaceousand Cenozoictime, Geology,
5, 330-355, 1977.
Lachenbruch,A. H., Crustal temperatureand heat production:Implications of the linear heat flow relation, J. Geophys.Res., 75, 32913300, 1970.
Lachenbruch, A. H., Heat flow in the Basin and Range Province and
thermal effectsof tectonic extension, Tectonophysics,
in press, 1979.
Lachenbruch, A. H., and C. M. Bunker, Vertical gradients of heat
309
in Catalogue of Data, 1964-1972, Soviet Geophysical Committee,
Academy of Sciencesof the USSR, Moscow, 1973.
Luyendyk, B. P., K. C. MacDonald, and W. B. Bryan, Rifting history
of the Woodlark Basin, southwest Pacific, Geol. Soc. Amer. Bull.,
84, 1125-1134, 1973.
McKenzie, D. P., Some remarks on heat flow and gravity anomalies,
J. Geophys.Res., 72, 6261-6273, 1967.
McKenzie, D. P., Some remarks on the developmentof sedimentary
basins, Earth Planet. Sci. Lett., 40, 25-32, 1978.
McKenzie, D. P., and N. Weiss, Speculationson the thermal and tectonic history of the earth, Geophys.J. Roy. Astron. Soc., 42, 131174, 1975.
Menard, H. W., and S. M. Smith, Hyposometryof ocean basin provinces, J. Geophys.Res., 71, 4305-4326, 1966.
Ministry of Geology, Russiantectonicatlas, 16 sheets,Moscow, 1969.
Minster, J. B., T. H. Jordan, P. Molnar, and E. Harris, Numerical
modeling of instantaneousplate tectonics,Geophys.J. Roy. Astron.
Soc., 36, 541-576, 1974.
Molnar, P., and P. Tapponier, Cenozoic tectonicsof Asia; effectsof a
continental collision, Science, 189, 419-426, 1976.
Molnar, P., T. Atwater, J. Mammerickx, and S. M. Smith, Magnetic
anomalies, bathymetry and the tectonic evolution of the South Pacific since the Late Cretaceous, Geophys.J. Roy. Astron. Soc., 40,
383-420, 1975.
productionin the continentalcrust,2, Someestimatesfrom borehole data, J. Geophys.Res., 76, 3852-3860, 1971.
Moorbath, S., The oldest rocks and the growth of continents, Sci.
Lachenbruch, A. H., and J. H. Sass,Heat flow in the United States
and the thermal regime of the crust, in The Earth's Crust, Geophys.
Monogr., vol. 20, edited by J. G. Heacock, pp. 626-675, AGU,
Washington, D.C., 1977.
Ladd, J. W., South Atlantic sea floor spreadingand Caribbean tectonics, Ph.D. thesis,251 pp. Columbia Univ., New York, 1974.
Lambert, I. B., and K. S. Heier, The vertical distribution of uranium,
thorium, and potassiumin the continentalcrust, Geochim.Cosmochim. Acta, 31, 377-390, 1967.
Lambert, R. S. J., Archcan thermal regimes,crustal and upper mantle
temperaturesand a progressiveevolutionarymodel for the earth, in
The Early History of the Earth, edited by B. F. Windley, 363-387,
John Wiley, New York, 1976.
Langseth,M. G., and M. A. Hobart, Interpretationof heat flow measurementsin the Vema fracture zone, internal report, 12 pp., Lamont-Doherty Geol. Observ., Palisades,N.Y., 1976.
Langseth, M. G., and G. W. Zielinski, Marine heat flow measurements in the Norwegian-Greenland Sea and in the vicinity of Iceland, in Geodynamicsof Iceland and the North Atlantic Area, edited
by L. Kristansson,pp. 277-295, D. Reidel, Hingham, Mass., 1974.
Larson, R. L., Late Jurassicsea-floor spreadingin the eastern Indian
Ocean, Geology,3, 69-71, 1975.
Larson, R. L., and T. W. C. Hilde, A revised time scale of magnetic
reversalsfor the Early Cretaceousand Late Jurassic,J. Geoœhys.
Mori, T., and D. H. Green, Pyroxenes in the system Mg2Si206CaMgSi206 at high pressure,Earth Planet. Sci. Lett., 26, 277-286,
Res., 80, 2586-2594, 1975.
Lawver, L. A., J. W. Hawkins, and J. G. Sclater, Magnetic anomalies
and crustal dilation in the Lau Basin, Earth Planet. $ci. Lett., 33,
27-35, 1975a.
Lawver, L. A., J. R. Curray, and D. G. Moore, Magnetics in the Andaman Seaand the effectof high sedimentationrates(abstract),Cos
Trans. AGU, 56, 1064, 1975b.
Lee, W. H. K., and S. Uyeda, Review of heat flow data, in Terrestrial
Heat Flow, Geoœhys.
Monogr., vol. 8, edited by W. H. K. Lee, pp.
87-190, AGU, Washington, D.C., 1965.
Lewis, T. J., and A. E. Beck, Analysis of heat flow data--Detailed observationsin many holes in a small area, Tectonoœhysics,
41, 41-59,
1977.
Lister, C. R. B., On the thermal balance of a mid-ocean ridge,
Geoœhys.
J. Roy. Astron. $oc., 26, 515-535, 1972.
Lister, C. R. B., On the penetration of water into hot rock, Geoœhys.
J.
Roy. Astron. $oc., 39, 465-509, 1974.
Lister, C. R. B., Estimators for heat flow and deep rock properties
basedon boundary layer theory, Tectonoœhysics,
41, 157-171, 1977.
Lonsdale, P., and K. Klitgord, Structure and tectonic history of the
eastern Panama Basin, Geol. $oc. •4mer. Bull., 59, 981-999, 1978.
Louden, K., Magnetic anomaliesin the West Philippine Basin, in The
Geophysicsof the Pacific Ocean Basin and Its Margin, Geophys.
Monogr., vol. 19, edited by G. H. Suttonet al., pp. 253-268, AGU,
Washington,D.C., 1976.
Lubimova, E. A., B. G. Polyak, Ya. B. Smirnov, R. I. Kutas, F. V.
Firsov, S. I. Sergienko,and L. N. Liusova,Heat flow in the USSR.
Amer., 236, 92-105, 1977.
1975.
Mueller, S., A new model of the continental crust, in The Earth's
Crust, Geophys.Monogr. vol. 20, edited by J. G. Heacock, pp. 289318, AGU, Washington, D.C., 1978.
Naqui, S. M., V. Divakara Rao, and H. Narain, The protocontinental
growth of the Indian Shield and the antiquity of its rift valleys,Precambrian Res., 1, 345-398, 1974.
Norton, I., and J. G. Sclater, A model for the evolution of the Indian
Ocean and the breakup of Gondwanaland,J. Geophys.Res., 84,
6803-6830, 1979.
Okal, E. A., The effectof intrinsicoceanicuppermantleheterogeneity
on regionalization of long-period Rayleigh-wave phase velocities,
Geophys.J. Roy. Astron. Soc., 49, 357-370, 1977.
Okal, E. A., and D. L. Anderson, A study of lateral inhomogeneities
in the uppermantleby multiple ScStravel-timeresiduals,Geophys.
Res. Lett., 2, 313-316, 1975.
Oldenburgh, D. W., A physical model for the creation of the lithosphere, Geophys.J. Roy. Astron. Soc., 43, 425-451, 1975.
Padovani, E. R., and J. L. Carter, Aspectsof the deep crustal evolution beneath south central New Mexico, in The Earth's Crust,
Geophys.Monogr., vol. 20, edited by J. G. Heacock, pp. 19-56,
AGU, Washington, D.C., 1977.
Palmasson, G., On heat flow in Iceland in relation to the mid-Atlantic
ridge, Soc. Sci. Islandica, 38, 111-117, 1967.
Parker,R. L., and D. W. Oldenburg,Thermal model of oceanridges,
Nature, 242, 137-139, 1973.
Parsons, B., and D. P. McKenzie, Mantle convection and the thermal
structureof the plates,J. Geophys.Res., 83, 4485-4496, 1978.
Parsons,B., and J. G. Sclater, An analysis of the variation of ocean
floor bathymetry and heat flow with age, J. Geophys.Res., 82, 803827, 1977.
Phair, G., and D. Gottfried, The Colorado Front Range, Colorado,
USA, as a uranium and thorium province, in The Natural Radiation
Environment,edited by J. A. S. Adams and W. M. Lowder, pp. 738, University of Chicago Press,Chicago, II1., 1964.
Pitman, W. C., III, and M. Talwani, Sea floor spreadingin the North
Atlantic, Geol. Soc. Amer. Bull., 83, 619-646, 1972.
Pitman, W. C., III, R. L. Larson, and E. M. Herron, Magnetic Lineationsof the Oceans,Map Chart Ser.,vol. MC-6, GeologicalSociety
of America, Boulder, Colo., 1974.
Polyak, B. G., and Y. A. Stairnov, Relationshipbetweenterrestrial
heat flow and the tectonics of continents, Geotectonics,Engl.
Transl., 4, 205-213, 1968.
Rabinowitz, P. D., and J. L. LaBrecque, The mesozoicsouth Atlantic
and evolution of its continentalmargins,J. Geophys.Res.,84, 59736002, 1979.
Rao, R. U. M., and A.M. Jessop,A comparisonof the thermal characters of shields, Can. J. Earth Sci., 12, 347-360, 1975.
Rao, R. U. M., G. V. Rao, and H. Narain, Radioactive heat genera-
310
SCLATERET AL.: OCEANIC AND CONTINENTAL HEAT FLOW
tion and heat flow in the Indian Shield,Earth Planet.Sci.Lett., 30,
57-64, 1976.
Reid, A.M., C. H. Donaldson,R. W. Brown,I. Ridley,and J. B.
Dawson,Mineral chemistryof peridotitexenolithsfrom the Lashine volcano,Tanzania, Phys.Chern.Earth, 9, 525-544, 1975.
Richardson,
S. W., and E. R. Oxburgh,Heat flow,radiogenic
heat
productionand crustal temperaturesin England and Wales, J.
Geol. Soc. London, 135, 323-337, 1978.
Richter, F. M., Convectionand the large-scalecirculationof the
mantle, J. Geophys.Res., 78, 8735-8745, 1973.
Richter, F. M., and B. Parsons,On the interaction of two scalesof
convectionin the mantle,J. Geoœhys.
Res.,80, 2529-2541, 1975.
Roy, R. F., D. D. Blackwell,and F. Birch,Heat generation
of plutonic rocksand continentalheat flow provinces,Earth Planet. Sci.
Lett., 5, 1-12, 1968.
Roy, R. F., D. D. Blackwell,andE. R. Decker,Continentalheatflow,
in The Natureof the SolidEarth, editedby E. C. Robertsonet al.,
pp. 506-543, McGraw-Hill, New York, 1972.
mantledeterminedfrom the traveltimesof ScS,J. Geophys.
Res.,
80, 1474-1484, 1975.
Sleep,N. H., Thermal effectsof the formation of Atlantic continental
marginsby continentalbreakup,Geoœhys.
J. Roy.Astron.Soc.,24,
325-350, 1971.
Smith, D., and S. Levy, Petrologyof the Green Knobs diatreme and
implicationsfor the upper mantle below the Colorado Plateau,
Earth Planet. Sci. Lett., 29, 107-125, 1976.
Smithson,S. B., Modeling continentalcrust:Structuraland chemical
constraints,Geoœhys.
Res. Lett., 5, 749-752, 1978.
Sollogub, V. B., et al., New D.S.S. data on the crustal structureof the
Baltic and Ukranian shields,Tectonoœhysics,
20, 67-84, 1973.
Steckler,M. S., and A. B. Watts,Subsidence
of the Atlantic-typecontinental margin off New York, Earth Planet. Sci. Lett., 41, 1-13,
1978.
Swanberg,C. A., Vertical distributionof heatproductionin the Idaho
batholith, J. Geoœhys.
Res., 77, 2508-2513, 1972.
Swanberg,C. A., M.D. Chessman,
G. Simmons,S. B. Smithson,G.
Gr•tnlie,and K. S. Heier, Heat flow-heatgenerationstudiesin Nor-
Royden,L., J. G. Sclater,andR. P. Von Herzen,Continental
margin
subsidence
andheatflow:Importantparameters
in formationof peway, Tectonoœhysics,
23, 31-48, 1974.
troleumhydrocarbons,
Bull.Arner.Ass.Petrol.Geol.,in press,1980. Sweeney,J. F., Subsidence
of the SverdrupBasin,Canadianarcticis-
Rybach,L., Radioactiveheat productionin rocksand its relationto
otherpetrophysical
parameters,
PureAœœ1.
Geoœhys.,
114,309-317,
1976.
lands, Geol. Soc. Arner. Bull., 88, 41-48, 1977.
Sykes,L. R., and M. Sbar, Intraplate earthquakes,lithospheric
stresses
and the driving mechanismof plate tectonics,Nature, 245,
Sass,J. H., and A. Lachenbruch,
Thermalregimeof the Australian
298-302, 1973.
continentalcrust,in The Earth, Its OriginStructureand Evolution, Talwani,M., C. C. Windisch,andM. G. Langseth,
ReykjanesRidge
editedby M. W. McElhinny,pp. 301-351,Academic,New York,
crest:A detailedgeophysicalstudy,J. Geoœhys.
Res., 76, 473-517,
1978.
1971.
Sass,J. H., A. H. Lachenbruch,
and A.M. Jessop,
Uniformheatflow
Tarney,J., and B. F. Windley, Chemistry,thermalgradientsand evoin a deepholein theCanadian
Shieldanditspaleoclimatic
implicalution of the lower continentalcrust, J. Geol. Soc. London, 134,
tions, J. Geophys.Res., 76, 8586-8596, 1971.
Schouten,
H., andK. Klitgord,Mesozoic
magnetic
anomalies
in western North Atlantic, Map MF 915, U.S. Geol. Surv., Reston,Va.,
153-172, 1977.
Tarney,J., I. W. D. Dalziel, and M. J. de Wit, Marginal basin'Rocas
Verdes'complexfrom S. Chile; a model for Archeangreenstone
1977.
belt formation,in TheEarly Historyof theEarth,editedby B. F.
Schubert,
G., C. Froideveaux,
andD. A. Yuen,Oceaniclithosphere Windley, pp. 131-146, John Wiley, New York, 1976.
andasthenosphere:
Thermalandmechanical
structure,
J. Geoœhys. Tilling,R. I., D. Gottfried,andF. C. W. Dodge,Radiogenic
heatpro-
Res., 81, 3525-3540, 1976.
Sclater,J. G., and P. A. F. Christie,Continentalstretching:
An explanation of the post-Mid-Cretaceoussubsidenceof the Central
North SeaBasin,submittedto J. Geoœhys.
Res.,1979.
Sclater,J. G., andJ. Crowe,A heatflowsurveyat anomaly13on the
Reykjanes Ridge: A critical test of the relation betweenheat flow
and age, J. Geoœhys.
Res., 84, 1593-1602, 1979.
Sclater,J. G., and J. Francheteau,The implicationsof terrestrialheat
flow observations
on currenttectonicand geochemicalmodelsof
the crustand uppermantleof the earth, Geophys.
J. Roy. Astron.
Soc., 20, 509-542, 1970.
ductionof contrastingmagmaseries:Bearingon interpretationof
heat flow, Geol. Soc. Arner. Bull., 81, 1447-1462, 1970.
Urien, C. M., and J. J. Zambrano,The geologyof the basinsof the
Argentine continental margin and Malomas Plateau, in The Ocean
Basinsand Margins,vol. 1, The SouthAtlantic,editedby A. Nairn
and F. Stehli,pp. 135-170,JohnWiley, New York, 1973.
Uyeda,S.,Heat flow,in Crustand UpperMantleof theJapanese
Area,
editedby S. Miyamuraand S. Uyeda,pp. 97-105,EarthquakeResearchInstitute,University of Tokyo, Tokyo, 1972.
van Hinte, J. E., A Jurassictime scale,Arner.Ass.Petrol. Geol. Bull.,
60(4), 489-497, 1976a.
Sclater,
J. G., R. N. Anderson,
andM. L. Bell,Theelevation
of ridges van Hinte, J. E., A Cretaceoustime scale, Arner. Ass. Petrol. Geol.
and evolutionof the centraleasternPacific,J. Geoœhys.
Res.,76,
7888-7915, 1971.
Sclater,J. G., R. P. Von Herzen,D. L. Williams,R. N. Anderson,and
K. Klitgord,The Galapagosspreadingcentre:Heat flow low on the
north flank, Geoœhys.
J. Roy. Astron.Soc., 38, 609-626, 1974.
Sclater,J. G., J. Crowe,andR. N. Anderson,
On thereliabilityof oceanic heat flow averages,J. Geoœhys.
Res.,81, 2997-3006,1976a.
Sclater,J. G., D. E. Karig,L. A. Lawver,andK. Louden,Heat flow,
depth,and crustalthicknessof the marginalbasinsof the South
PhilippineSea,J. Geoœhys.
Res.,81, 309-318, 1976b.
Sclater,
J. G., C. Bowin,R. Hey,H. Hoskins,
J. Peirce,J. Phillips,and
C. Tapscott,The Bouvettriplejunction,J. Geoœhys.
Res.,81, 18571869, 1976c.
Bull., 60(4), 498-516, 1976b.
vanNiekerk,C. B., andA. J. Burger,A newagefor the Ventersdorp
acidic lavas, Trans.Geol. Soc. S. Afr., 81, 155-163, 1978.
Veizer,J.,87Sr/86Sr
evolution
of seawater
duringgeologic
historyand
its significance
as an index of crustalevolution,in The Early Historyof theEarth,editedby B. F. Windley,pp. 569-578,JohnWiley,
New York, 1976.
Von Herzen,R. P., and W. H. K. Lee, Heat flowin oceanregions,in
TheEarth'sCrustand UpperMantle, Geophys.
Monogr.,vol. 13,edited by P. J. Hart, AGU, pp. 88-94, Washington,D.C., 1969.
Watanabe, T., M. G. Langseth,and R. N. Anderson,Heat flow in
back-arcbasins,of the westernPacific,in IslandArcs,DeepSea
Trenches,and Back-Arc Basins,edited by M. Talwani and W. Pitman III, pp. 137-162, AGU, Washington,D.C., 1977.
Atlantic Ocean,J. Geol.,85, 509-552, 1977.
Watts,A. B., andW. B. F. Ryan,Flexureof thelithosphere
andcontiSclater,
J. G., H. Dick,I. O. Norton,andD. Woodruffe,
A geophysi- nental margin basins,Tectonoœhysics,
36, 25-44, 1976.
cal andpetrological
studyof theantarcticplateboundary
eastand Watts,A. B., and J. K. Weissel,Tectonichistoryof the Shikokumarwestof BouvetIsland,Earth Planet.Sci. Lett., 37, 393-400, 1978.
ginal basin, Earth Planet. Sci. Lett., 25, 239-250, 1975.
Sclater,J. G., L. Royden,S. Semken,
C. Burchfiel,
L. Stegena,
andF. Watts,A. B., J. K. Weissel,and F. J. Davey, Tectonicevolutionof the
Horvath,The Miocenethroughpresentdevelopment
of the intraSouthFiji marginalbasin,in IslandArcs,DeepSea trenches,
and
Carpathianbasins,Earth PlanetSci. Lett., in press,1980.
Back-ArcBasins,editedby M. TalwaniandW. PitmanIII, pp. 419Simmons,G., and K. Horai, Heat flowdata,2, J. Geophys.
Res.,73,
428, AGU, Washington,D.C., 1977.
Sclater,J. G., S. Hellinger,and C. Tapscott,
Paleobathymetry
of the
6608-6629, 1968.
Simmons,G., and A. Nur, Granites:Relationof properties
insituto
laboratorymeasurements,
Science,162, 789-791, 1968.
Simpson,E., J. G. Sclater,B. Parsons,
I. Norton,andL. Meinke,Mesozoicmagneticlineationsin the MozambiqueBasin,Earth. Planet
Sci. Lett., 43, 260-264, 1979.
Weissel,J. K., Evolutionof the Lau Basinby the growthof small
plates,in Island Arcs, Deep Sea Trenches,and Back-ArcBasins,edited by M. Talwani and W. Pitman III, pp. 429-436, AGU, Washington, D.C., 1977.
Weissel,J. K., and D. E. Hayes,Evolutionof the TasmanSea,Earth
Planet. Sci. Lett., 36, 77-84, 1970.
Sipkin,S. A., andT. H. Jordan,Lateralheterogeneity
of the upper Weissel,J. K., D. E. Hayes,and E. M. Herron,Platetectonicsyn-
SCLATER ET AL.: OCEANIC AND CONTINENTAL
thesis: The relative motions of the Australian, New Zealand and
antarctic continental fragments since the Early Cretaceous,Mar.
Geol., 25, 231-277, 1977.
Williams, D. L., and R. P. Von Herzen, Heat loss from the earth: New
estimate,Geology,2, 327-328, 1974.
Williams, D. L., R. P. Von Herzen, J. G. Sclater, and R. N. Anderson,
The Galapagosspreadingcenter:Lithosphericcoolingand hydrothermal circulation, Geoœhys.J. Roy. Astron. Soc., 38, 587-608,
HEAT
FLOW
Windley, B. F., The EvolvingContinents,385 pp., John Wiley, New
York, 1978.
Windley, B. F., and J. V. Smith, Archeanhigh-gradecomplexesand
modern continental margins, Nature, 260, 671-675, 1976.
Wood, B. J., and S. Banno, Garnet-orthopyroxene and orthopyroxene-clinopyroxene
relationshipsin simple and complex systems, Contrib. Mineral. Petrol., 42, 109-124, 1973.
1974.
Wiltshire, H. G., and E. D. Jackson,Problemsin determiningmantle
geotherms from pyroxene compositionsof ultramafic rocks, J.
Geol., 83, 313-329, 1975.
311
(Received September 28, 1978;
acceptedAugust 30, 1979.)