Thermal structure of continental upper mantle inferred fromS-wave velocity and surface heat £ow

Axel H.E. Ro«hm, Roel Snieder *, Saskia Goes, Jeannot TrampertFaculty of Earth Sciences, Utrecht University, Utrecht, The Netherlands

Received 20 April 2000; accepted 13 June 2000

Abstract

Results from seismic tomography provide information on the thermal structure of the continental upper mantle. Thisis borne out by the good agreement between tectonic age, surface heat flow and a tomographic S-wave velocity modelfor depths less than 180 km. The velocity anomalies of tomographic layers deeper than 230 km have relatively smallamplitudes and show little correlation with surface heat flow or shallow velocities. We associate the drop in correlationand amplitude of the velocity perturbations between 180 and 230 km depth with the maximum thickness of the thermalboundary layer (TBL), in which larger variations in temperature and possibly composition than in the underlyingconvecting mantle can be sustained. Velocity profiles for different tectonic provinces are converted to temperature usingmineralogical data. Both anharmonic and anelastic effects on the wave speeds are taken into account. The resultinggeotherms differ most at depths of 60^120 km with variations of up to 900³C. Below 230 km, differences do not exceed300³C. These geotherms agree well with one-dimensional conductive geotherms for the observed range of continentalheat flow values using the empirical relationship that 40% of the surface heat flux stems from upper crustal radiogenicheat production. The S-wave velocity in the continental upper mantle appears to be adequately explained (within theuncertainties of the tomography and the conversion to temperature) by a thermal signature. A compositionalcomponent can, however, not be ruled out as it may have only a minor effect on the velocity and the heat flow. Thesurface heat flow is controlled by the shallow heat production and the thickness of the TBL. Seismology helps todetermine the relative importance of the two factors and our results confirm the similar importance of both factors.Variations of TBL thickness could be controlled by compositional differences and/or by the effect of temperature on therheology. ß 2000 Elsevier Science B.V. All rights reserved.

Keywords: lithosphere; surface waves; tomography; heat £ow; upper mantle; geothermal gradient

1. Introduction

Oceanic lithosphere is continuously recycled bymantle convection. It is formed at mid oceanic

ridges, thickens when it cools and ¢nally subductsat plate boundaries. In contrast, continental crustdoes not participate in recycling. Old continentalregions are many times older than the oldest ex-isting ocean £oor. They contain Archean nucleiaround which younger material is accreted. Sev-eral basic questions about the continents are notyet fully answered, e.g. what is the growth rate asa function of geological time [1]? The mantle part

0012-821X / 00 / $ ^ see front matter ß 2000 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 0 0 ) 0 0 2 0 9 - 0

* Corresponding author. Present address: Department ofGeophysics, Colorado School of Mines, Golden, CO 80401,USA.; E-mail: rsnieder@mines.edu

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of the continental lithosphere raises some addi-tional questions. Is it always of the same age asthe continental crust and, if so, what causes thislong-term stability? What is its present-day thick-ness? Answers to these questions depend on theadopted de¢nition of lithosphere, which can bebased on very di¡erent quantities [2^4]. De¢ni-tions which can be found in the literature referto the mechanical lithosphere, the seismic litho-sphere, the chemical lithosphere, the electricallithosphere and the thermal lithosphere.

This study is concerned with the seismic uppermantle structure (down to the transition zone be-ginning at about 400 km depth) and the corre-sponding thermal structure. Since the low-velocityzone is often absent in stable continental regions[5,6] and since we consider smooth perturbationsfrom a seismic reference model, we de¢ne theseismic lithosphere in this article as the regionwhere the seismic velocity perturbations correlatewith tectonic provinces and the surface heat£ow. This de¢nition includes a larger part ofthe mantle than, for example, the mechanicallithosphere as will become clear later when theseismic lithosphere is related to the thermalboundary layer (TBL). The TBL is viewed asthe region with a predominantly conductive heattransfer.

Many di¡erent values for the thickness of theseismic continental keels are reported in the liter-ature, ranging from several tens of kilometers be-neath tectonically active regions to a few hundredkilometers below ancient cratons. There is no con-sensus on the maximum depth extent of continen-tal high-velocity roots and estimates range fromless than 200 km to more than 400 [2,7,8].

Variations in continental lithospheric thickness(all de¢nitions) can be caused by several mecha-nisms which have distinct spatio^temporal signa-tures that can be used to distinguish betweenthem.

1. Plate tectonic events, such as continental colli-sion or rifting, thicken or thin the lithosphereaccompanied by thermal disturbances and pos-sibly also by accretion or delamination of achemically distinct layer. The thermal relaxa-tion time of these events is (depending on their

depth) estimated to be between 15 Ma and 235Ma [3,9]. Hence, tectonic events have a signi¢-cant in£uence for several hundred millionyears, but old stable regions should be closeto thermal equilibrium.

2. Mantle convection can cause undulations ofthe lithosphere[3].

3. Erosion has a 2-fold e¡ect on the heat £ow.First, it is accompanied by uplift which bringsdeeper isotherms closer to the surface. Forhigh erosion rates of tectonically active regionswith pronounced topography, this might be re-sponsible for up to 50% of the surface heat£ow [9]. Second, it removes part of the radio-genic crust, thus permanently decreasing thesurface heat £ux and the shallow temperaturegradient. This change in the crustal blanketinge¡ect may also in£uence the thickness of theTBL. This issue is addressed below in moredetail.

4. A compositional root of depleted mantle ma-terial can originate through extraction of par-tial melt [10,11]. The reduced weight of de-pleted material presents an explanation forthe proposed stability of the continental litho-sphere.

The temporal behavior is one di¡erence be-tween these mechanisms. A second one is the orig-inal depth of the disturbances which is within themechanical lithosphere for (1), below the TBL for(2), close to the surface for (3), or mainly in thelower part of the TBL for (4). Of course, theseexplanations do not exclude each other and acombination of the di¡erent sources is possible.From this, it should be clear that young continen-tal regions can have a wide diversity of thermalstructures, while old continental regions are ex-pected to show less thermal variation.

Several studies have used seismic models to in-fer the thermal structure [12^16]. In this article,we ¢rst show the good accordance between thetomographic model of Woodhouse and Trampert[17], the compilation of surface heat £ow mea-surements of Pollack et al. [18] and the continen-tal regionalization of Nataf and Ricard [13], anduse this to investigate the thermal structure of thecontinental lithosphere.

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2. Seismic tomography and tectonic regionalization

Surface wave dispersion measurements and seis-mic tomography have revealed the correlation be-tween tectonic setting and lithospheric seismic ve-locities, with old cratons showing the highest, andtectonically active regions having relatively lowvelocities [5,19,20]. In this study, the tomographicmodel of Woodhouse and Trampert [17] is usedto analyze the continental upper mantle structureabove 400 km depth.

Their model presents an improved depth reso-lution over previous models. This is achieved byincorporating fundamental mode Love and Ray-leigh wave dispersion measurements in the periodrange 40^150 s together with a large waveformdata set similar to that employed in the construc-tion of earlier mantle models [20]. The surfacewave data set corresponds to that of Trampertand Woodhouse [17] and consists of 62 141 Loveand Rayleigh wave measurements. They showedthat this data set could resolve unbiased structureat least up to degree 16. Compressional velocity(Nvp/vp) is scaled to shear velocity (Nvs/vs) which isparameterized in spherical harmonics up to degree16 and cubic splines as a function of depth. Theknots are placed at increasing depth intervals (24,74, 128, 188, 253, 323, 400, 484T km) resulting ina vertical resolution length of about 50^70 km in

the ¢rst 400 km of the model, the area of ourprimary interest. This improved vertical resolu-tion in the upper part of the mantle is primarilyachieved by the incorporation of short period sur-face waves. Surface topography and bathymetryhave been speci¢ed while crustal thickness hasbeen inverted for. Within the uncertainties ofthe tomographic model, the inverted crust andthe crustal model of Mooney et al. [21] give thesame results.

To investigate the correlation between tectonicregion and deeper mantle structure, the tomo-graphic model is compared with the regionaliza-tion of model 3SMAC [13], which divides conti-nental areas into three di¡erent tectonic types:Archean cratons, stable platforms and tectoniccontinents (Fig. 1). The resolution of the tomo-graphic model does not justify a division intomore types which would yield smaller provinces.The 2³U2³ lateral discretization of the model is¢ne enough for the comparison with the tomo-graphic model.

We calculated an average velocity pro¢le foreach region from the tomographic model ofWoodhouse and Trampert [17]. Since the tomo-graphic model has a ¢nite lateral resolution, onlythe area of each province, which is located at adistance of at least 5³ from the boundary to an-other province, is used. These areas are shown in

Fig. 1. Continental tectonic provinces after the 3SMAC regionalization [13] marked by the gray shades. Shown is only the innerpart of each province that is at least 5³ away from any other province.

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Fig. 1 in gray shades. Fig. 2 shows the corre-sponding velocity pro¢les. The strongest featureis the decrease in variation of the seismic velocityfrom more than 10% at shallow depths to lessthan 4% below a depth of 230 km. All seven Ar-chean pro¢les (no. 1^7 in Fig. 1) from ¢ve di¡er-ent continents show a striking similarity. In theupper 200 km, they are clearly separated from thetectonic regions which show a much larger diver-

sity. The pro¢les for stable platforms span almostthe complete range from the fast pro¢les of Ar-chean cratons to the slow pro¢les of tectonic con-tinents. Closer inspection of the stable platformprovinces reveals possible causes for this broadrange. The three fastest pro¢les, which show thesame velocities as the Archean provinces, are no.9 (Eastern USA), which also shows a lower me-dian surface heat £ow of 47 mW/m2 compared toother provinces of the same type (Table 1), no. 14(Central Australia), which forms in the tomo-graphic model one fast anomaly together withthe Archean region no. 7, and no. 17 (EasternAntarctica), which is a Precambrian shield. Onthe other side are the three slowest pro¢les ofstable platforms: no. 10 (Arabian peninsula),which is surrounded at all sides by active plateboundaries, no. 11 (Northern Africa), which con-tains the Hoggar and Tibesti hotspots [22,23], andno. 12 (China), which is in active extension [24].We ¢nd from the tomographic model (Fig. 2) thatthe thickness of the seismic lithosphere, de¢ned asthe upper mantle region which shows strong var-iations of seismic velocity related to surface tec-tonics, is slightly more than 200 km.

The average pro¢le of all continental regionswith a distance of at least 5³ from oceanic litho-sphere, shown as the thick gray line in Fig. 2, ispositive at all depths down to 400 km. Since theglobal average is subtracted, this implies that theS-wave velocity below oceans is on average slowerthan the subcontinental velocity. Relative to theglobal average, i.e. zero in Fig. 2 for all depths,some provinces have fast velocity perturbations ofup to about 2% throughout the upper mantle.This can partly explain why other studies [7,8]found much deeper roots than the 200 km foundin this study. However, this type of anomaly isnot correlated with age (Fig. 2).

The di¡erences between pro¢les above and be-low a depth of about 200 km are even more strik-ing in the correlation of the velocity perturbationsat two di¡erent depths. Fig. 3 shows the correla-tion of the velocity ¢eld of continental area (witha distance of at least 5³ from the oceans) betweena depth of 100 km and a second depth indicatedby the vertical axis. The correlation pro¢le can bedivided into two regions. Between 60 and 180 km

Fig. 2. Velocity pro¢les are obtained by averaging the veloc-ity perturbations of the global tomographic model of Wood-house and Trampert [17] over the interior regions of theprovinces from the 3SMAC continental regionalizationshown in Fig. 1. The dots denote the maximum crustal thick-nesses for each province which are used for the crustal cor-rection of the tomography. The global average velocity per-turbation (degree 0 term of the spherical harmonicexpansion) for each depth is subtracted. Di¡erent line tex-tures denote the three types of continental provinces. Thevery thick gray line displays the mean pro¢le of all continen-tal regions with a distance of at least 5³ from oceanic litho-sphere.

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depth, the correlation coe¤cient is higher than0.8. Below 230 km depth, the correlation dropsto values between 0.1 and 0.3. The transitionfrom high to low correlations marks the depthof the seismic lithosphere, which we have de¢nedas the region where the velocity correlates withsurface tectonics. The low values of the correla-tion coe¤cient at depths less than 60 km is caused

by crustal e¡ects since the crustal correction is notapplied in the calculation for Fig. 3. The verysmall correlation between the seismic lithosphereand the underlying structure suggests that thestrong shallow anomalies are not controlledfrom below by the convection but have a shalloworigin, i.e. within the upper 200 km. However, thein£uence of plume activity cannot completely beruled out because mantle plumes could be toosmall in size or temperature contrast to be re-solved in the tomographic model.

3. Surface heat £ow

Surface heat £ow measurements form another,completely independent, data source giving valua-ble constraints on the thermal structure of thecrust and shallow mantle. Several studies [18,25^27] have found a systematic decrease of surfaceheat £ow with the age of tectonic provinces. Forthis study, the global heat £ow compilation ofPollack et al. [18] is used.

Three points concerning the heat £ow datahave to be considered in the comparison: (1) thereis a considerable amount of scatter in the mea-surements due to environmental problems, e.g.water circulation and past climatic changes, anddi¤culties with early conductivity determinations[26], (2) the surface heat £ow can have largechanges over short distances due to the local geol-ogy and topography, and (3) the measurementsare highly unevenly distributed over the Earth'ssurface. A simple pointwise comparison for allmeasurement sites of surface heat £ow and vol-ume-averaged quantities, such as seismic velocitiesrevealed by waveform tomography, is complicatedby each of the three points listed above. Appro-

Table 1Median values for surface heat £ow of di¡erent provinces, 99% con¢dence intervals around the median and the mean absolutedeviations about the median

Median 99% con¢dence interval Mean absolute deviation(mW/m2) (mW/m2) (mW/m2)

Continental area 55 54^56 26.1Archean craton 42 40^44 10.8Stable platform 54 51^56 11.3Tectonic continents 76 70^81 24.3

Fig. 3. Correlation coe¤cient between S-wave velocity at thedepth given on the ordinate and the S-wave velocity at 100km depth (solid line) and averaged surface heat £ow (dashedline). Only continental areas with a distance of at least 5³from oceanic crust are included in the calculation. The aver-aging of heat £ow values is explained in the text.

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priate averaging methods have to be used to con-struct average heat £ow values for larger areasthat can be used for the comparison. In order tosuppress any overweighting from clustered mea-surement points, we ¢rst averaged all heat £owmeasurements within 20 kmU20 km cells.

Fig. 4 shows histograms of heat £ow values forthe three di¡erent types of continental provincesand for all continental values. Just as for the ve-locity pro¢les of Fig. 1, only measurements with adistance of at least 5³ from the tectonic bound-aries are used. Median values and absolute devia-tion about the median are listed in Table 1.

For comparison with the tomographic model,the heat £ow values were averaged a secondtime with the aim to estimate the average heat£ow of an area similar in size to the resolutionof the velocity model. For this, a heat £ow valuewas assigned to each node of a 2³U2³ coordinategrid if at least one 20 kmU20 km average valuewas within 110 km and three values were within550 km distance of the node. All nodes on con-

tinents that were more than 5³ away from theoceans and that received an averaged heat £owestimate were used in the subsequent calculationof the correlation coe¤cient between surface heat£ow and S-wave velocity perturbation as a func-tion of depth. The result is shown in Fig. 3 as thedashed line.

This correlation function has almost the sameshape as the correlation function of two di¡erentdepth layers of the tomographic model but hasthe opposite sign and a lower amplitude. The neg-ative sign is due to the anticorrelation betweentemperature and seismic velocities. Consideringthe scatter in the heat £ow measurements and anon-linear relation between temperature andS-wave velocity, the anticorrelation is remarkablylarge. The strong anticorrelation between heat£ow and velocity between 60 km and 180 kmdepth suggests that the velocity perturbationsare predominantly caused by temperature e¡ects.The small correlation coe¤cients above 60 kmdepth are again caused by crustal e¡ects. Yan etal. [15] have used S-wave velocities at 150 kmdepth to predict global heat £ow and found aqualitative agreement to the observed globalheat £ow pattern for the lowest 6³ of a sphericalharmonic expansion. The strong anticorrelation inFig. 3 shows that this is also valid for continentalregions only and at smaller scales.

4. Constraints on temperatures from S-wavevelocity

The strong anticorrelation between heat £owand seismic velocity favors a thermal interpreta-tion of the tomographic model. Other studies[16,28,29] also con¢rm that the expected e¡ectof reasonable variations in upper mantle compo-sition as found in xenoliths is of minor impor-tance compared to the expected temperature e¡ectand is probably of similar magnitude as the un-certainties in the tomography. In our subsequentanalysis, we concentrate on the mantle below 60km depth to avoid complications due to the pres-ence of crustal material and give an interpretationin terms of temperatures alone.

Following the procedure developed by Goes et

Fig. 4. Histograms for continental heat £ow measurementsand HF measurements for the interiors of the three di¡erenttypes of tectonic provinces. Histograms are normalized; thenumber of measurements is given on the right side of eachhistogram.

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al. [16], the conversion of S-wave velocity to tem-perature is carried out by using laboratory mea-surements of density and the elastic moduli forvarious mantle minerals. These values are ex-trapolated to mantle temperature and pressuresunder the in¢nitesimal strain approximation. (Fi-nite strain theory would be more correct, but acomparison has shown that the error introducedis relatively small for our depth range of interest(Vacher, personal communication)). The elasticmoduli for an average mantle composition aredetermined by using the Voigt^Reuss^Hill averag-ing method. Anelasticity, which is an importante¡ect for ¢nite frequencies [30] but unfortunatelyless well constrained by experimental data, is alsotaken into account. The importance of anelasticityincreases with temperature and does not allow theapplication of a linear relation between velocityand temperature anomalies. For further details,including the mineralogical data used, we referto Goes et al. [16].

Due to the non-linear relation between velocityand temperature, the conversion has to be doneusing absolute velocities rather than velocity per-turbations. This causes an extra di¤culty, sincethe reference model used for the tomography[31] incorporates an anisotropic layer down tothe Lehmann discontinuity at 220 km depth.The equivalent isotropic PREM model also con-tains this discontinuity in form of a 5% step ofS-wave velocity. Many di¡erent explanations havebeen proposed for the Lehmann discontinuity,such as a chemical boundary or the base of apartially molten layer [32], or an anisotropic layerabove the discontinuity [5,32,33]. The global oc-currence of the discontinuity is questioned andlittle seismological evidence exists that the corre-sponding isotropic velocities are discontinuous atthis depth, e.g. the global waveform stacks ofShearer [34] show the 410, 520 and 660 km dis-continuities but not the Lehmann discontinuity.

It would be best to include this discontinuity inour modeling, e.g. through a discontinuous com-position or rheology. However, the lack of a clearthermodynamic understanding of it makes thisapproach impossible. We have decided, as a sec-ond-best approach, to slightly modify the seismicreference model. If the changes of the reference

model are small, the phase velocities and the sen-sitivity kernels of the surface waves remain similarand a tomographic inversion yields only slightlydi¡erent velocity perturbations. We veri¢ed thatthese changes are much smaller than the velocityperturbations displayed in Fig. 2. Using PREM asreference model, the absolute S-wave velocity Vfor a pro¢le i is given by:

V i � VPREM � NVglobal � NV i

where VPREM is the PREM S-wave velocity,NVglobal is the global mean velocity perturbationfrom PREM found in the inversion (i.e. the de-gree 0 term of the spherical harmonic expansion)and NVi is the velocity perturbation as displayedin Fig. 2. Using the absolute velocities Vi wouldyield discontinuous temperatures due to the dis-continuity in VPREM. Therefore, we have chosento introduce a new, thermally based, referencemodel. Since all Archean pro¢les are very similar(Fig. 2) and also Archean heat £ow values showthe least scatter (Table 1), an obvious choice is tospecify a geotherm representative for Archeancratons. This geotherm is calculated using themethod of Chapman [35] for the median Archeanheat £ow of 42 mW/m2. Below the intersection ofthe conductive geotherm with the adiabat (poten-tial temperature of 1200³C) at about 200 kmdepth, temperatures along the adiabat are takenfor the geotherm. This gives new absolute velocitypro¢les ViP :

V i0 � V�TArchean�3NVArchean � NV i

V(TArchean) is the velocity pro¢le calculated fromthe Archean reference geotherm and NVArchean themean Archean velocity perturbation (weighted bythe area of each province). The relatively coldadiabat was chosen for two reasons. First, ascan be seen from Fig. 2, continental regions atdepths below 200 km are approximately 1% fasterthan the global average and Archean cratons areon average slightly faster than average continentalregions (small positive correlation coe¤cient inFig. 3). Therefore, if no lateral variation in com-position is assumed, temperatures below Archeanprovinces are somewhat lower than the global

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average. The second reason is that for a colderadiabat, the new reference model (V(TArchean)^NVArchean^NVglobal) is closer to the reference modelof the tomography (VPREM). For each pro¢le NVi

in Fig. 2 the absolute velocity pro¢le ViP was cal-culated and converted to temperature. The resultis shown in Fig. 5.

To demonstrate the in£uence of di¡erent com-positions and the anelastic e¡ect, we selected threevelocity pro¢les for provinces 1, 8 and 19 (see Fig.1), one of each tectonic type. The correspondingtemperatures were calculated with respect to twodi¡erent compositions and two Q models. Onecomposition represents an average continentallherzolite based on xenolith data which is depletedrelative to a primitive mantle, the other a primi-tive garnet lherzolite [28]. The compositions aredescribed in Table 2. The Q models represent anaverage model (Q1 of Goes et al. [16] ; after model2 of Sobolev et al. [12]) calibrated to seismic dataand a fully experimental Q model which is a rel-atively strong estimate of temperature dependence(Q2 of Goes et al. [16] ; after Berckhemer et al.[36]). Fig. 6 shows the resulting geotherms. Thesolid lines show the three pro¢les for the preferredcomposition (average continental garnet lherzo-lite, Q1), also used for Fig. 5. A change of com-position to a primitive mantle (dotted line, sameQ model) shows only negligible e¡ects. A changeto the anelastic model Q2 (long dashed line) hasalso only small e¡ects, except for the very hightemperatures of the tectonic pro¢le around 100km depth. The very slow velocities of tectonicprovinces in this depth region give temperatureswhich are about 100³C lower for the strongeranelastic e¡ect of model Q2 than the temperaturescomputed for model Q1. It should be noted thatthe Archean pro¢les show almost no di¡erencebecause the pro¢les are so close to the ¢xed new

reference model. The short dashed line illustratesa shift of the reference model; the temperatures ofthe reference Archean geotherm, which has beenconverted to the reference velocity pro¢le, wereincreased by 100³C everywhere. This results in ashift of the Archean pro¢le by the same amount.The other pro¢les, especially of tectonic provincesat shallow depths, show a somewhat lower in-

Fig. 5. Temperature pro¢les calculated for the velocity pro-¢les from Fig. 2. In the upper, 55 km geotherms after Chap-man [35] for surface heat £ows of 40^90 mW/m2 are shown.The thick gray lines show a wet and dry peridotite solidustaken from Thompson [50].

Table 2Volume fraction of minerals in the two mantle rocks tested in Fig. 6

Garnet lherzolite Olivine Orthopyroxene Clinopyroxene GarnetMg2SiO4 MgSiO3 CaMgSi2O6 Mg3Al2Si3O12

average 0.65 0.28 0.03 0.04volume fraction of Fe for all minerals: 0.09

primitive 0.58 0.18 0.10 0.14volume fraction of Fe for all minerals: 0.11

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crease due to the anelastic e¡ect. This shows thatan erroneous estimate of the average continentalcomposition has only little e¡ect on the relativeposition of the computed geotherms, whereas awrong thermal reference model can shift all geo-therms systematically to higher or lower temper-atures. Of course, we have not yet discussed thee¡ect of a laterally varying composition. Thiscould shift some of the geotherms by amountscomparable to the variation of the reference mod-el (by 100³C), which is much less than the totalobserved variation.

5. Comparison with heat £ow-derived geotherms

The geotherms in Fig. 5 for most tectonic con-tinents and some stable platforms show a maxi-

mum at depths of about 130 km. This might besurprising because for an upward heat, £ow tem-peratures increase monotonically with depth. Thiscould be due to plume activity in these relativelyhot regions. Geotherms calculated from convec-tion models often overshoot the adiabat due tothe spreading plume heads at the base of theboundary layer [37]. However, it could also becaused by the presence of partial melt. If the man-tle in these regions was partially molten, the cal-culated temperatures are overestimated. Since themaxima are close to the dry solidus, this is a likelyexplanation as well. About 4% of melt would beneeded to obtain geotherms which are about200³C colder around the maxima. A di¡erent ane-lasticity model would have a similar in£uence.Fig. 6 demonstrates that invoking a stronger ane-lastic e¡ect, such as in model Q2, also decreasesthe estimated temperatures in this temperature^depth region.

Kinks can be seen in the temperature pro¢les ofFigs. 5 and 6 at 200 km depth which are artifactsthat originate from the abrupt transition from aconductive geotherm to an adiabat in the refer-ence pro¢le. In reality, the geotherms are expectedto be smooth across this transition. We concen-trate on the gross pattern in Fig. 5 and point outtwo robust features. First, there is a large range oftemperatures at a depth of 60 km of about 900³.Second, tectonic regions reach the adiabat atdepths shallower than 80 km as opposed to Ar-chean regions which reach the adiabat at depthsof around 200 km.

First, the temperature variation at 60 km depthmatches the range given by the Chapman [35]geotherms for surface heat £ow.

Fig. 7 shows the geotherms for surface heat£ow values every 10 mW/m2 between 40 and 90mW/m2 for three di¡erent one-dimensional ther-mal models which di¡er only in the distribution ofradiogenic elements. The frame in the centershows geotherms as proposed by Chapman [35]and one of these was used as a reference for thecalculations of the pro¢les shown in Fig. 5. Thesegeotherms for steady-state conductive heat trans-fer use the surface heat £ow as the only parameterto which the heat production is linked by therelationship that 40% is attributed to upper crus-

Fig. 6. The three pro¢les for regions no. 1, 8 and 19 of Fig.1 converted to temperatures for di¡erent compositions, ane-lastic e¡ects and a change of reference geotherm. Geothermsin upper 55 km and solidi are the same as in Fig. 5.

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tal radiogenic heat sources and 60% to deepersources (the total crustal contribution is 57%and 44% for a surface heat £ow of 40 mW/m2

and 90 mW/m2, respectively) [38,39]. The Chap-man geotherms [35] diverge in the crust and shal-low mantle and predict temperature di¡erences ofmore than 500³C below the crust. This large var-iation is also found in geothermobarometric dataobtained of xenoliths from di¡erent regions [40^42]. At high temperatures in greater depths, heattransfer is dominated by advection which is incor-porated by truncating the conductive geothermswith an adiabat with a potential temperature of1300³C although potential temperatures of1400³C and 1280³C have been reported as well[43,44]. These uncertainties in the thermal proper-ties could cause a systematic shift of all geothermsof Fig. 5 by at most 100^200³C.

Next to the middle panel of Fig. 7, two extremeend-members of possible geotherm families areshown. They are calculated for the same parame-ters with the only di¡erence in the amount ofcrustal heat production. The left plot shows geo-therms for the case without any crustal heat pro-duction. These geotherms are almost straight lines(some deviation from straight lines is caused bychanges in the thermal conductivity) until theycross the adiabat and their slope is proportionalto the surface heat £ow. In other words, if the

temperature of the convecting mantle follows anadiabat, the surface heat £ow is solely determinedby the thickness of the conductive boundarylayer. If it is assumed that the seismic anomaliesshown in Fig. 2 are mainly caused by temperaturee¡ects (since compositional variations are veryunlikely to explain such large variations), thesegeotherms can be ruled out as an explanation be-cause they do not explain the di¡erences in seis-mic velocity below 100 km depth.

Another extreme family is the case in which themantle heat £ow for all geotherms is the same.Estimates for the non-radiogenic component ofthe surface heat £ow range from 6 mW/m2[45]to 25 mW/m2 [26]. In this example, a value of15 mW/m2 was used. The di¡erent surface heat£ow is in this example only caused by di¡erencesin the crustal heat production. Comparison ofthese geotherms with the ones from Fig. 5 showsthat the di¡erences in temperature are far toosmall. Additionally, these geotherms would notallow partial melting for depths less than 100km which is expected for many tectonically activeregions.

Therefore, continental geotherms are deter-mined by a combination of (1) the crustal heatproduction and (2) the thickness of the conductiveboundary layer. A variable thickness of the TBLcan be seen in Fig. 5 but this thickness alone is

Fig. 7. Three di¡erent geotherm families for surface heat £ows of 90, 80, 70, 60, 50 and 40 mW/m2 (top down). All geothermsare truncated by the 1300³C adiabat. The left panel displays geotherms for a crust without any heat production. The middle pan-el shows geotherms proposed by Chapman [35]. Geotherms in the right panel have all the same reduced mantle heat £ow of 15mW/m2.

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not su¤cient to explain the large variation of ob-served heat £ow values. The Chapman geothermfamily, which includes a correlated variation inboth, gives temperatures very similar from whatis found in Fig. 5 and is thus consistent with thetomographic S-velocity. The temperature varia-tions are largest at shallow depths around 60km where they reach a maximum of about900³C. Below the seismic lithosphere, temperaturevariations do not exceed 300³C.

6. Discussion

Di¡erent heat £uxes lead to diverging geo-therms but at depths where heat transfer is dom-inated by material transport and not by conduc-tion, the temperatures come closer to a meanmantle adiabat. The Chapman geotherm family[35] for surface heat £ow values between 42 and90 mW/m2 covers a broad temperature^depthspace (down to 225 km depth and up to 900³Ctemperature variation). This depth range is ingood accordance with the seismic lithosphere,which was de¢ned as the region of strong velocityvariation related to tectonic provinces, obtainedfrom Figs. 2 and 3. Additionally, the temperaturerange explains the S-velocity di¡erence of up to12% found in the lithosphere.

Variations of the surface heat £ow are some-times mainly ascribed to the thickness of the con-tinental roots or to di¡erences in the crustal heatproduction [46^48]. Seismic studies yield impor-tant extra information to resolve this. The goodcorrespondence of our results with the Chapmangeotherms suggests that both causes are of similarimportance and correlated. The extreme geothermfamilies depicted in the left and right panels ofFig. 7, which involve only one cause, cannot ex-plain the seismic velocity variations. Therefore,both mechanisms must be operative. The crust isenriched in radiogenic elements, mainly Cs, Rb,Th and U, relative to the depleted mantle becausemost of these elements are incompatible, whichmeans that they do not ¢t readily into crystallattices, and thus are easily removed from themantle by the extraction of partial melt, in whichthey are concentrated. Erosion, in turn, removes

the enriched crustal rocks exposed to the surfacefrom a particular region. Thus, di¡erentiation ofmantle material and erosion are the factors deter-mining the crustal heat production.

The thickness of the TBL in£uences the temper-ature gradient and thus the conductive heat £ow.One question that remains is what causes thisvariation in thickness. Since the seismic velocitiesin the lithosphere have only a small correlationwith the velocities below the TBL (Fig. 3), adeep cause, e.g. mantle convection, is unlikely.Two other possibilities exist. First, the TBL couldbe determined by a compositionally di¡erentlayer. To explain the stability and geoid signatureof continental lithosphere, di¡erentiation process-es are needed that generate a mantle residue,which has a lower density, a higher solidus tem-perature and a higher viscosity [10,11,49], andthus forms a layer that does not participate inconvection. This chemical layer could imposethe TBL. Second, the thickness could be deter-mined thermally by the amount of crustal thermalblanketing. Little shallow heat production resultsin a smaller temperature increase through thecrust and thus more e¤cient cooling of the lowerlithosphere resulting in a thick TBL caused by atemperature-dependent rheology. The oppositewould be true for high concentrations of heatproducing elements in the crust. If this explana-tion is correct, then the concentration of radio-genic elements would be the dominant controllingfactor for the TBL in thermal equilibrium by in-£uencing the temperature directly through heatproduction and indirectly by determining thethickness of the TBL.

Our results do not support the hypothesis thatthe convection pattern dictates the thermal struc-ture of the TBL. On the contrary, they point to atop-down cause^e¡ect relation in which variationsin the shallow radiogenic heat production producethe large-scale velocity anomalies in the shallowmantle. Beneath old cratons, where erosion hasremoved most of the upper crustal radiogenic el-ements, a thick TBL, associated with fast velocityanomalies, has formed. In addition, variations inthe thickness of the TBL play a role as well. Thesevariations could be caused by the e¡ect of temper-ature on the TBL through a temperature-depen-

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dent rheology, but other causes such as composi-tional variations cannot be ruled out on the basisof the data used in this study.

Acknowledgements

We thank Hana Cizkova, Frederic Deschamps,Dirk Kraaijpoel, Everhard Muyzert, Jeroen deSmet, Christophe Sotin and Volker Steinbachfor many bene¢cial discussions and J.-P. Mon-tagner and H.-C. Nataf for helpful reviews. Thisresearch was supported by the Netherlands Orga-nization for Scienti¢c Research (NWO) throughthe Pionier project PGS 76-144.[AC]

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