* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download The Heat Flow Through Oceanic and Continental Crust and the Heat
Survey
Document related concepts
Space Shuttle thermal protection system wikipedia , lookup
Solar water heating wikipedia , lookup
Thermal conductivity wikipedia , lookup
Solar air conditioning wikipedia , lookup
Intercooler wikipedia , lookup
Building insulation materials wikipedia , lookup
Reynolds number wikipedia , lookup
Heat exchanger wikipedia , lookup
Cogeneration wikipedia , lookup
Dynamic insulation wikipedia , lookup
Heat equation wikipedia , lookup
R-value (insulation) wikipedia , lookup
Copper in heat exchangers wikipedia , lookup
Thermal conduction wikipedia , lookup
Transcript
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.)