Lithospheric strength and its relationship to the elastic ...ages of the oceanic lithosphere 9100 Ma. For greaterages,thereisasuggestionofa‘threshold’ beyondwhichT e exceedsT s.Thisisattributedto

Lithospheric strength and its relationship to the elastic andseismogenic layer thickness

A.B. Watts a;�, E.B. Burov b

a Department of Earth Sciences, University of Oxford, Parks Road, Oxford OX1 3PR, UKb Laboratoire de Tectonique UMR7072, Universite¤ Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France

Received 31 December 2002; received in revised form 6 May 2003; accepted 12 May 2003

Abstract

Plate flexure is a phenomenon that describes how the lithosphere responds to long-term (s 105 yr) geological loads.By comparing the flexure in the vicinity of ice, volcano, and sediment loads to predictions based on simple platemodels it has been possible to estimate the effective elastic thickness of the lithosphere, Te. In the oceans, Te is therange 2^50 km and is determined mainly by plate and load age. The continents, in contrast, are characterised by Tevalues of up to 80 km and greater. Rheological considerations based on data from experimental rock mechanicssuggest that Te reflects the integrated brittle, elastic and ductile strength of the lithosphere. Te differs, therefore, fromthe seismogenic layer thickness, Ts, which is indicative of the depth to which anelastic deformation occurs as unstablefrictional sliding. Despite differences in their time scales, Te and Ts are similar in the oceans where loading reduces theinitial mechanical thickness to values that generally coincide with the thickness of the brittle layer. They differ,however, in continents, which, unlike oceans, are characterised by a multi-layer rheology. As a result, TeETs incratons, many convergent zones, and some rifts. Most rifts, however, are characterised by a low Te that has beenvariously attributed to a young thermal age of the rifted lithosphere, thinning and heating at the time of rifting, andyielding due to post-rift sediment loading. Irrespective of their origin, the Wilson cycle makes it possible for lowvalues to be inherited by foreland basins which, in turn, helps explain why similarities between Te and Ts extendbeyond rifts into other tectonic regions such as orogenic belts and, occasionally, the cratons themselves.2 2003 Elsevier Science B.V. All rights reserved.

Keywords: lithosphere; £exure; elastic thickness; seismogenic layer; rheology; mantle

1. Introduction

Plate tectonics is based on the observation thatthe Earth’s outermost layers, or lithosphere, canbe divided into a number of plates which have

remained rigid for long periods (i.e. s 105 yr) ofgeological time. One manifestation of plate ri-gidity is the £exural response of the lithosphereto surface loads such as ice, volcanoes, and sedi-ments, sub-surface loads such as those associatedwith tectonic emplacement and magmatic intru-sions, and tectonic boundary loads such as slabpull and ridge push. By comparing the £exureobserved in the vicinity of these loads to the pre-dictions of simple elastic, plastic, and viscous

0012-821X / 03 / $ ^ see front matter 2 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0012-821X(03)00289-9

* Corresponding author. Tel. : +44-1865-272032;Fax: +44-1865-272067.E-mail address: [email protected] (A.B. Watts).

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart

Earth and Planetary Science Letters 213 (2003) 113^131

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plate models, it has been possible to determine the£exural rigidity of the lithosphere and its spatialand temporal variation.

Both continental and oceanic lithosphere aremodi¢ed by £exure. The two types of lithosphere,however, have had a distinct physical and chem-ical evolution. As a result, they respond to long-term loads in fundamentally di¡erent ways. Theoceanic lithosphere, for example, is relativelyyoung, has a single-layer rheology and, as a con-sequence, its e¡ective £exural rigidity (which isdetermined by the elastic thickness, Te) dependsmainly on thermal age [1]. The continental litho-sphere, in contrast, is relatively old, has a multi-layer rheology, and its £exural rigidity does notdepend on a single controlling parameter such asthermal age, but is an integrated e¡ect of a num-ber of other factors that include the geotherm,crustal thickness, and composition [2].

Rock mechanics data suggest that the £exuralrigidity of the lithosphere is determined by thebrittle and ductile properties of the constitutiverocks that comprise it. Since brittle behaviour,as described by Byerlee’s law, is only possible atrelatively low con¢ning pressures and depths, it islikely that this deformation type will determinethe strength of only the uppermost part of thelithosphere [3^5]. Ductile strength, in contrast,only slowly increases with con¢ning pressure,but strongly decreases with temperature [6]. Thetransition to brittle, elastic or ductile behaviour ismainly determined by the weakest rheology at therespective depth [4,5]. However, brittle frictionalsliding is improbable at great depths (i.e. s 50^70km), irrespective of the ductile strength.

As ¢rst shown by Goetze and Evans [7], loadson the lithosphere are supported by a quasi-elasticlayer that separates the brittle and ductile defor-mation ¢elds. This competent layer is the strongportion of the lithosphere that is capable of sup-porting loads for long periods (i.e. s 105 yr) ofgeological time. Watts et al. [8] and Burov andDiament [9] dubbed this layer the elastic ‘core’and it has become popular to associate Te withits thickness. It is important to point out, how-ever, that the Te revealed by £exure studies is thedepth integral of the bending stress, which is notnecessarily associated with a particular competent

layer. Indeed, the brittle and ductile ¢elds alsocontribute to the apparent strength of the litho-sphere. In the oceans, the depth of the brittle^ductile transition (BDT) falls approximatelymid-way in the elastic portion of the lithosphere.As a result, the brittle and ductile deformation¢elds are roughly equally involved in the supportof loads. In the continents, there may be morethan one BDT and so the relationship of the brit-tle and ductile ¢elds to the elastic portion of thelithosphere is more complex.

Plate £exure studies [2,10,11] have shown thatTe corresponds to, or indeed exceeds, the strongportion of the lithosphere, the thickness of whichranges from 2 to 50 km for oceanic lithosphereand as high as 100+ km for the continental lith-osphere.

Probably the best known manifestation of brit-tle deformation is seismicity data. It has beenknown for some time [12], for example, that con-tinental earthquakes are con¢ned to a seismogeniclayer, Ts, in the uppermost brittle part of thecrust. More recent studies, using improved hypo-centre location techniques [13], have shown thatin regions such as California, the Aegean, Tibetand the Zagros mountains, Ts is remarkably uni-form in thickness and rarely exceeds 20 km. Seis-micity extends to depths as great as 40 km in oldshield areas such as the Tien Shan, the Indianshield, and in the vicinity of the East Africa andLake Baikal rift systems, but is usually less intensethan it is in the upper crust.

Rock mechanics data help constrain the mech-anisms that control the distribution of earth-quakes. These data suggest, for example, that de-spite its usual representation as pressure-dependent Byerlee behaviour, frictional sliding incontinental rocks is controlled by other factorssuch as geotherm, strain rate, mineralogical inclu-sions, and £uid content. In general, frictional slid-ing is limited to a depth of V15 km (and 6 6^8km depth on large faults). Beginning at thisdepth, a semi-brittle/semi-ductile strain rate-de-pendent plastic £ow occurs, with a frictional com-ponent that is no longer signi¢cant at depthss 40^50 km [14^16]. This helps explain why seis-micity in the oceanic lithosphere is actually lim-ited to this depth range. It also accounts for why


A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131114

earthquakes are so rare in the continental sub-crustal mantle. This is because these depths typi-cally correspond to the lowermost part of the con-tinental crust where ductile creep is dominant.

There are, of course, regions where earthquakesextend to depths s 40 km, for example, in sub-duction zones. However, it is generally agreed[4,5] that deep seismicity is not related to friction-al sliding, at least not in the form expressed byByerlee’s law, but to various other metastablemechanisms. These mechanisms are only weaklyrelated to absolute rock strength. For example, ithas been known for some time that unlike shallow(i.e. depths 6 50^70 km) earthquakes, deep earth-quakes produce very few aftershocks. Shallowearthquakes, on the other hand, are characterisedby numerous aftershocks that decay exponentiallywith time. This aftershock behaviour is a strongargument that the earthquake-generating mecha-nism di¡ers between shallow and deep earth-quakes.

Because both Te and Ts re£ect the strength ofthe lithosphere, Jackson and White [17] assumedthat the two parameters are the same. While thereis some similarity between Te and Ts in the oceans[18], their relationship in the continents is unclear.Recently, Maggi et al. [19] suggested that thestrength of the lithosphere is determined by theextent of the brittle deformation and thereforethat Ts is the same as Te. Hence, Te, like Ts,should be low (6 20 km), except perhaps in oldshield regions where it might extend to depths asgreat as 40 km. Such an assertion, which impliesthat the crust, rather than the mantle, is mainlyinvolved in the support of long-term loads, raisesserious questions concerning the observations of£exure, the extrapolations of data based on exper-imental rock mechanics, and the results of analyt-ical and numerical modelling of £exure.

The purpose of this paper is to consider therelationship between the elastic thickness, Te,and the seismogenic layer, Ts. We begin by re-viewing the results of £exure studies. The physicalmeaning of Te and Ts is then discussed in the lightof analytical and numerical models for plate £ex-ure with both a single- and multi-layer rheology.We conclude that Te and Ts re£ect the fundamen-tally di¡erent ways that the Earth’s lithosphere

responds to loads of variable spatial and temporalscales and, therefore, while both parameters areindicative of strength, they are not the same.

2. Observations of £exure

There have been a number of studies that havefocussed on the estimation of Te and Ts. Fig. 1shows a histogram plot of Te derived from £exurestudies and Ts as revealed by the depths of intra-plate earthquakes. Although there are currentlydebates about the reliability of both Te [20] andTs [13] estimates, we believe that the distributionsshown in Fig. 1 are representative and will notchange signi¢cantly as more direct measures ofthe surfaces of £exure are used to constrain Teand improved earthquake hypocentral locationtechniques are used to de¢ne Ts.

Fig. 1 shows that Te and Ts are similar in theoceans with the large majority of values 6 50 km.Moreover, both Te and Ts clearly exceed the aver-age thickness of oceanic crust. Therefore, not onlydo earthquakes occur in the sub-oceanic mantle,but it is also involved in the support of long-termloads. The continents, by way of contrast, show aTs that is con¢ned to the crust and, interestingly,a Te that sometimes exceeds Ts.

While Te and Ts are similar in the oceans andin some continents, we believe that they have fun-damentally di¡erent meanings. Ts re£ects the

Fig. 1. Histograms of global compilations of elastic thick-ness, Te, and seismogenic layer thickness, Ts. (a) Oceans.(b) Continents. The compilation is based on data in tables6.1 and 6.2 of Watts [80], tables 1^6 of Chen and Molnar[12], and table 1 of Wiens and Stein [18].


A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 115

strength of, or more precisely the stress level in,the uppermost brittle layer of the lithospherewhile Te is indicative of the strength of the elasticportion of the lithosphere that supports a partic-ular load and, importantly, the brittle and ductilestrength of the entire elastic layer. The di¡erenceis most obvious in un£exed lithosphere when Ts iszero and Te takes on its highest possible value [2].Di¡erences persist into £exed lithosphere whereTe slowly decreases with increasing curvatureand, hence, bending stress [11,21] while Ts simplyre£ects the local stress level. Yield strength enve-lope (YSE) considerations (e.g. Fig. 2) suggestthat in the case of the oceans, with their single-layer rheology, the BDT just happens to fall ap-proximately mid-way in the strong elastic portionof the lithosphere. Therefore, Te and Ts may wellbe similar.

These conclusions are in accord with observa-

tions at deep-sea trenchôuter rise systems. Be-cause of the high curvatures that are experiencedby the oceanic lithosphere as it approaches atrench, Te is less than it would otherwise be onthe basis of plate age because of yielding. Judgeand McNutt [22], for example, have shown that inthe high-curvature region of the seaward wall ofthe northern Chile trench (curvatureK=1.3U1036 m31) Te is 22R 2 km, which isless than the Te of 34 km that these workers ex-pected on the basis of the thermal age of the sub-ducting oceanic lithosphere.

Fig. 3 compares Te and Ts at northern Chile aswell as other di¡erent deep-sea trenchôuter risesystems in the Paci¢c and Indian oceans. The ¢g-ure shows that Te and Ts are similar, at least forages of the oceanic lithosphere 9 100 Ma. Forgreater ages, there is a suggestion of a ‘threshold’beyond which Te exceeds Ts. This is attributed tothe fact that as the lithosphere ages, its strengthincreases, and so the curvature and, hence, thebending stress associated with the same load de-creases. Therefore, Te, which mainly re£ects theintegrated strength of the lithosphere, increaseswhile Ts, which depends more directly on thestress level, decreases.

We have based the discussion thus far on aYSE that only considers the stresses generatedin a £exed plate by bending. We have not, there-fore, taken into account the e¡ect of any in-planestresses that act on the plate due, for example, totectonic boundary loads. It is di⁄cult to concep-tualise Te and Ts from a YSE in the presence ofsuch stresses. However, we can say that Ts will beconditioned by the brittle failure due to thesestresses and, as a consequence, will be even lessrelated to the bending stress and, hence, the localTe.

The oceanic Te estimates plotted in Fig. 1 arebased on more than 48 individual studies and socan be considered a reliable measure of the long-term (s 105 yr) £exural properties of oceanic lith-osphere. The continental Te estimates, in contrast,are based on fewer studies (16) and some authors[20] have recently questioned their validity, espe-cially estimates that are in excess of 25 km.

The evidence for high continental Te is basedon forward models in which observations of £ex-

Fig. 2. Te and Ts for an idealised case of £exure of the oce-anic lithosphere. Thin solid line shows the YSE for 80 Maoceanic lithosphere. The brittle behaviour is described byByerlee’s law, the ductile behaviour by an olivine power law(stress constant, A, of 7U10314 Pa33 s31 ; creep activationenergy, Q, of 512 kJ/mol [81]), and the thermal structure bythe cooling plate model [82]. Thick solid line shows the stressdi¡erence for a load which generates a moment, M, of2.2U1017 N/m and curvature, K, of 5U1036 m31. The ¢gureshows that the load is supported partly by a strong elasticlayer or ‘core’ and partly by the brittle and ductile strengthof the lithosphere. The dashed lines show the cases of K of1U1037 m31 and 1U1036 m31 which bracket the range ofobserved values at deep-sea trenchôuter rise systems[7,11,22]. The ¢gure shows that Ts corresponds to the depthof the intersection of the moment^curvature curve with thebrittle deformation ¢eld, but could extend from the surface,Ts (min), to the BDT, Ts (max). Te, in contrast, could ex-tend from the thickness of the elastic ‘core’, Te (min), to thethickness of the entire elastic plate, Te (max). Both Ts andTe depend on the moment generated by the load and, hence,the plate curvature.



ure are compared directly to predictions, andspectral, or inverse, methods in which the rela-tionship between gravity anomalies and topogra-phy is analysed as a function of wavelength. For-ward modelling of late-glacial rebound in NorthAmerica, for example, reveals Te values as high as80^90 km [23]. These estimates are in accord withforward modelling of some of the foreland basinsthat form by £exure in front of migrating thrustand fold loads. The Ganges basin, for example, isassociated with values that are in the range 80^90km [24^27]. Similar high values have been re-ported from spectral studies of parts of Australia[28], Siberia [29], Brazil [30], North America [31],and Africa [32].

McKenzie and Fairhead [20], however, havecriticised the results of spectral studies, especiallythose that are based on the Bouguer coherencetechnique which they consider upper boundsrather than true estimates. These workers suggest

the use of the free-air admittance instead sincethis technique takes into account what are consid-ered the only known loads: surface loads. There ispersuasive geological evidence, however, that sub-surface or buried loads are also present in thecontinents [33] and, possibly, the oceans [34].Such loads, which include intra-crustal thrusts[35], dynamically induced viscous stresses [36],and buoyant magmatic underplate [37], contributeto both the gravity anomaly and the topography.

As Forsyth [33] has shown, however, increasingthe ratio of buried to surface loading shifts theisostatic ‘roll-over’ in the free-air admittance toshort wavelengths while increasing Te shifts it tolong wavelengths. It is always possible, therefore,to interpret a free-air admittance that has beenattributed to surface loading of a lithospherewith low Te by a model of combined surfaceand buried loading of a high-Te lithosphere.McKenzie and Fairhead [20] are correct whenthey state that there is no advantage in usingthe Bouguer coherence over the free-air admit-tance if surface loads are the only ones that areoperative. However, if buried loads are alsopresent, then the coherence is better because it isless sensitive to the amount of buried loading andmore sensitive to Te than is the admittance [33].

McKenzie [38], in a recent paper, has taken intoaccount buried loading. His focus, however, is onthe buried loads that because of the modifyinge¡ects of erosion and sedimentation generategravity anomalies, but no topography. The e¡ectof such loads is to reduce the Bouguer coherence^ in much the same way as would a surface loadwhich is emplaced on a su⁄ciently rigid plate thatthere is no £exure and, hence, Bouguer anomaly.McKenzie [38] showed that in the region of theUS Mid-Continent gravity ‘high’ the free-air co-herence is nearly zero for wavelength, V, 6 200km suggesting there is no topography that mightbe caused by buried loading. The topography ofthe region is indeed subdued. However, it is by nomeans clear that erosion and sedimentation willalways reduce a landscape to a £at plane. To thecontrary, erosion and sedimentation are part ofan isostatic cycle that involves uplift and subsi-dence, both of which would be expected to con-tribute to the gravity anomaly and the topogra-

Fig. 3. Summary of Te and Ts estimates for deep-sea trench^outer rise systems. (a) Plot of Te and depth of earthquakesas a function of the age of the oceanic lithosphere approach-ing the trench. Data based on table 6.1 of Watts [80] and ta-ble 1 of Seno and Yamanaka [83]. The Te estimates havebeen corrected for curvature. Solid lines show the YSE basedon the same rheological structure as assumed Fig. 1, a stressdi¡erence of 10 MPa, and thermal ages of oceanic litho-sphere of 0^200 Ma. (b) Summary of Te and depth of earth-quakes for age of oceanic lithosphere of 85^115 Ma. Notethe similarity between Te and the depth to which earth-quakes extend.



phy. The contributions may, because of thestrength of the lithosphere, be small and so weagree with McKenzie [38] that it is always impor-tant to determine whether the coherence (free-airor Bouguer) is high enough to yield a reliable Teestimate. This is now possible using techniquessuch as the maximum entropy method (MEM)[39,40] where spectral estimates are calculated inboxes that are moved step-wise across a studyarea.

Signi¢cantly for this discussion, spectral tech-niques are not the only means of estimating con-tinental Te. The large majority of these estimatesare based on forward modelling methods in whichobservations are compared directly to the predic-tions of elastic plate models. Forward modellinghas the advantage that it is not sensitive as towhether the free-air or Bouguer gravity anomalyis used. Indeed, many forward modelling studiesare not based on the gravity anomaly at all, buton direct observations of the surfaces of £exuresuch as those derived from seismic re£ection andrefraction pro¢le, stratigraphic, and deep welldata. Where ¢eld geological data exist for buriedloads (e.g. in the region of the US Appalachiangravity ‘high’), they can be explicitly taken intoaccount in forward modelling [41].

One way to verify the Te derived from spectralanalysis is to compare it to the results of forwardmodelling. Although only a few such comparisonshave been carried out, they show [42^44] goodagreement between the Te estimated using thetwo di¡erent approaches. Armstrong and Watts[44], for example, used the MEM method of ana-lysing Bouguer anomaly and topography data andshowed that Te in the southern Appalachians is inrange 50^60 km. This is in agreement with themean estimate of 57.5 km based on the forwardmodelling of pro¢les [41].

However, McKenzie and Fairhead [20] havealso queried the high Te values determined fromforward modelling. They obtained, for example, abest ¢t Te for the Ganges foreland basin of 42km, which is about a factor of 2 smaller thanthe previous estimates by Lyon-Caen and Molnar[25] and Karner and Watts [24]. Their forwardmodelling followed a ‘no-load’ approach (D.P.McKenzie, written communication) in which

only the £exure and gravity anomaly to one sideof a load is used to derive Te. This is di¡erentfrom the approach of Lyon-Caen and Molnar[25] and Karner and Watts [24] who used the to-pography to de¢ne the load. In this approach, the£exure and gravity anomaly to one side of and,importantly, beneath a load is used to estimateTe.

Fig. 4 compares the Te derived using the twoapproaches along a composite of ¢ve closelyspaced pro¢les of the Ganges foreland basin.The ¢gure shows that they yield similar results.Te is high and V60 km. However, the minimumin the root mean square (RMS) error betweenobserved and calculated Bouguer gravity anomalyis broad. This makes it di⁄cult to resolve theactual value of Te. We can say though that Te ishigh since application of the same approaches toa pro¢le of the Hawaiian ridge shows that if Tewas lower, as it is in this tectonic setting, then theminimum would be sharper.

These considerations of spectral and forwardmodelling results suggest there is no reason toquery high continental Te, especially those esti-mates that are based on the MEM techniquewhere a coherence criterion is applied and for-ward modelling which takes into account the pos-sibility of both surface and sub-surface loading.While a majority of the Te estimates are, indeed,low, there are values of up to 80+ km. Hence, Tein the continents can be signi¢cantly larger thanthe crustal thickness and, importantly, Ts.

Unfortunately, there are still only a few conti-nental regions where Te and Ts have been com-pared directly. The main reason is that seismicityin the continental plate interiors is limited in itsspatial extent. Seismicity, ¢rst of all, implies somelevel of tectonic stress. These stresses would beexpected to be higher in the oceans, where thedisplacement rates, and probably strain rates,are typically an order of magnitude higher thanthey are in the continents [45]. Moreover, stressesdecrease away from plate boundary zones [46]and the tectonic strains may be insu⁄ciently largein the slowly deforming interior regions of thecratons to cause seismicity. Indeed, Byerlee’s law(e.g. Fig. 2) implies that in order to produce seis-micity below depths of 25 km, a di¡erential stress



on the order of 0.4 GPa (tension) to 1.4 GPa(compression) is required.

We concur with Maggi and co-workers [19] thatcontinents, like oceans, show cases where TeWTsand, indeed, where Te 6Ts. However, there are

many cases of TeETs. Two examples are Fenno-scandia and the Baikal Rift. In Fennoscandia, thethickness of the seismogenic layer based on anearthquake data set that spans 1965^1995 and amagnitude threshold of 3.0 is 25^30 km whereasYSE considerations [47] and Bouguer coherencestudies using both periodogram [48] and MEM[49] methods suggest a Te that is locally in excessof 60 km. In the Baikal Rift, historical seismicitypeaks at depths of 15^20 km [50]. This is signi¢-cantly less than the 45^55 km, 30^50 km and 40^60 km reported [51^53] for Te based on forwardmodelling of free-air and Bouguer gravity anom-aly data along west^east topographic pro¢les ofthe rift.

3. Analytical and numerical models

Mechanical models that take into account bothbrittle and ductile deformation provide additionalinsight into the manner that the lithosphere re-sponds to long-term loads. Moreover, they arecapable of predicting the relationship that wouldbe expected between parameters such as Te andTs.

Consider ¢rst the £exure of a thin elastic platethat overlies an inviscid £uid, a well-known prob-lem in mechanical engineering. As has beenshown by Turcotte and Schubert [54], amongothers, the thickness of such a plate, Te(elastic)is given by:

T eðelasticÞ ¼Melastic12ð13e 2Þ

EK

� �1=3ð1Þ

where Melastic = the bending moment, K= curva-ture, and E and e are the Young’s modulus andPoisson’s ratio respectively. Melastic and K are in-dicative of the total amount of £exure and, hence,are directly related to the stress and strain thataccumulates in a deformed plate.

Theoretical considerations suggest that, withsome modi¢cation, Eq. 1 is valid for any rheology(e.g. elastic, ductile, or viscous) that is capable ofmaintaining stresses over a su⁄cient (for a quasi-static approximation) amount of time. YSE con-siderations suggest, however, that only in the caseof a single-layer, elastic rheology, high Te, and

Fig. 4. Comparison of observed and calculated Bouguergravity anomalies along a pro¢le of the Ganges foreland ba-sin, north-central India. (a) Topography and £exure. Thickline= topography. Thin lines show the calculated £exure dueto surface (topographic) loading of a semi-in¢nite (i.e. bro-ken) plate with a plate break at x=0 and Te of 30, 60 and90 km. Thick grey horizontal bar shows the estimate of Bur-bank [84] for the depth to the base of the foreland basin se-quence. Curved half-arrow indicates the approximate locationof the main boundary thrust. (b) Bouguer anomaly. Soliddots =observed based on a 5U5 min grid of GETECH’sSouth-East Asia Gravity Project (SEAGP) data (J.D. Fair-head, personal communication). Thin lines show the cal-culated anomaly based on the £exure pro¢les in panel a.(c) RMS di¡erence between observed and calculated Bougueranomalies. Upper plot=Ganges basin. Lower plot =Ha-waiian Ridge. The two curves for each plot compare theRMS based on McKenzie’s ‘no load’ (lowermost plot) caseto the ‘load’ (uppermost plot) case for the Ganges basin[24,25] and the Hawaiian Ridge [1]. Note: the RMS in the‘no load’ case is based only on the Bouguer anomaly to oneside of the load whereas in the ‘load’ case the RMS is basedon the Bouguer anomaly both beneath and to one side ofthe load.



small curvatures, will Te(elastic) approach the ac-tual mechanical thickness of the lithosphere. Fora multi-layered structure, Te is determined by thebending moment, MYSE, which is the sum of allthe moments associated with the brittle, elastic,and ductile parts of the YSE. The correspondenceprinciple allows the behaviour of any competentplate (elastic, plastic, or viscous) to be related tothat of an ‘equivalent’ elastic plate.

In oceanic lithosphere, the equivalent elasticthickness, Te(YSE), that generates the bendingmoment MYSE and has the same curvature of anelastic plate, K, is :

T eðYSEÞ ¼MYSE12ð13e 2

EK

� �1=3¼ MYSE

D0K

� �1=3ð2Þ

where D0 =E/12(13e2). Since D0 is determined bythe elastic properties of the plate and MYSE isdetermined by depth integration of the YSE,Eq. 2 can be used to calculate Te(YSE) for di¡er-ent values of plate curvature, K. Again, Te(YSE)is not the actual thickness of the plate. Rather, itis a ‘condensed’ thickness that re£ects the ‘inte-grated’ strength of the £exed, competent, plate.

McAdoo et al. [55] used Eqs. 1 and 2 to calcu-late the ratio of Te(YSE) to Te(elastic) for a plateof thermal age 80 Ma, an olivine rheology, and auniform strain rate of 10314 s31. They showedthat for low curvatures (i.e. K6 1038 m31) theratio is 1, indicating little di¡erence between theelastic thickness values. However, as curvature in-creases, the ratio decreases as Te(YSE) decreasesand the £exed plate yields. For K=1036 m31 theratio is V0.5, indicating 50% yielding and a cor-responding reduction in the elastic thickness.

The fact that the oceanic lithosphere yields canbe understood in terms of simple mechanics. Idealelastic materials support any stress level. In thecase of real materials, however, stress levels arelimited to the rock strength at the correspondingdepth. Strains in a bending plate increase withdistance from the neutral surface. Consequently,the upper and lowermost parts of a £exed plateare subject to higher strains and may experiencebrittle or ductile deformation as soon as the straincan no longer be supported elastically. These de-formed regions constitute zones of mechanicalweakness since the stress level there is lower

than it would be if the material maintained itselastic behaviour and, importantly, is lower thanit would be in the elastic portion of the plate thatseparates these two regions. The level of stress inthe brittle and ductile region, however, is notzero. A load emplaced on the oceanic lithospherewill therefore be supported partly by the strengthof the elastic ‘core’ and partly by the brittle andductile strength of the plate. The signi¢cance ofTe that has been estimated in regions such astrenches where yielding occurs is that it re£ectsthis combined, integrated, strength of the plate.

Ts has its own signi¢cance. Byerlee’s law offrictional brittle failure, which characterises defor-mation in the uppermost part of the lithosphere,suggests that strength linearly increases with pres-sure and, hence, depth. According to this law, theminimal brittle rock strength in the absence of£uid pressure is at least 65% of the lithostaticpressure at the corresponding depth. Near the sur-face, the strength is V10^20 MPa while at depthit may theoretically reach a few GPa. For thisreason, the Earth’s uppermost layers will failmore easily than its lowermost layers even forthe same amount of strain. In the oceans, wherethe crust is only V10 km thick, this leads to aconcentration of seismicity in the crust and upper-most mantle. In the continents, however, wherethe crust is thicker, seismicity is concentrated inthe uppermost parts of the crust, in contrast tothe lowermost part of the crust and uppermostmantle that may never fail due to the lack of asu⁄cient stress. Indeed, at typical Moho depths(i.e. V35 km), the theoretical brittle rock strengthreaches 0.6 GPa (tension) to 2.0 GPa (compres-sion). To exceed these stresses by, for example,tectonic strain, a ¢bre force of at least V1013 Nis required, which is an order of magnitude higherthan any previous estimates of the body and platedynamics forces for the whole lithosphere [56].

The signi¢cance of Te in the continents is not asclear as it is in the oceans. This is because thecontinents may comprise more than one brittlelayer that is de-coupled from an underlying layerby an intermediate ductile layer. As Burov andDiament [2] have shown for thermally ‘young’continental lithosphere, a weak ductile layer inthe lower crust does not allow bending stresses



to be transferred between the strong brittle layersthat ‘sandwich’ it and this leads to a mechanicalde-coupling between them. Nevertheless, stresslevels are reduced for the same amount of £exureand so each brittle layer is involved in the supportof a load. Te re£ects the strength of each elasticlayer and the combined strength of all the brittleand ductile layers. It is not simply a sum of thethickness of these layers (h1, h2Thn), however, butis given by the following Kircho¡ relation [2] :

T eðYSEÞWðh31 þ h32 þ h33TÞ1=3 ¼Xnl¼1

h3l

!1=3ð3Þ

In the case of equally strong layers(h1 = h2 = h3T= h) : T eðYSEÞWn1=3h, which yieldsTeW1.25h for two strong layers (n=2). Themeaning of Te(YSE) in the continents is nowclearer. It re£ects the integrated e¡ect of all thecompetent layers that are involved in the supportof a load, including the weak ones.

As in the case for the single-rheology-layer oce-anic lithosphere, if the multi-layered continentallithosphere is subject to large loads, it £exes,and the curvature of the deformed plate, K, in-creases. Te(YSE) is again a function of K and isgiven [2] [9] by:

T eðYSEÞ ¼ T eðelasticÞCðK ;T ; h1; h2TÞ ð4Þ

where C is a function of the curvature, K, thethermal age, T, and the rheological structure. Aprecise analytical expression for C is bulky,although Burov and Diament [9] provide a ¢rst-order approximation for a ‘typical’ case of conti-nental lithosphere with a mean crustal thicknessof 35 km, a quartz-dominated crust, and an oliv-ine-dominated mantle which they indicate is validfor 1039 6K6 1036 m31. Te(YSE) then simpli¢esto:

T eðYSEÞWT eðelasticÞ

13ð13K=KmaxÞ1=2� �ð1=2þ1=4ðTeðelasticÞ=TeðmaxÞÞÞ ð5Þ

where Kmax (in m31) = (180U103 (1+1.3Te(min)/Te(elastic))6)31, Te(max) = 120 km, Te(min) = 15km, and Te(elastic) is the initial elastic thicknessprior to £exure and can be evaluated from Eq. 3.

The considerations above are based only on¢rst-order approximations. It is therefore di⁄cult

to precisely track Te and, particularly, Ts, both ofwhich would be expected to change as a result ofloading.

We show in Fig. 5, therefore, how Te and Tswould be expected to change using the more pre-cise analytical formulations of Burov and Dia-ment [21]. The ¢gure illustrates how the thick-nesses of the brittle and ductile layers evolvewith di¡erent loads and, hence, curvatures. Onbending, brittle failure and, hence, the potentialfor seismicity preferentially develops in the upper-most part of the crust. The onset of brittle failurein the mantle is delayed, however, and does notoccur until the amount of £exure and, hence, cur-vature is very large.

Observations of curvature in the region of largeloads help constrain the strength of continentallithosphere. Curvatures range from 1038 m31 forthe sub-Andean [41] to 5U1037 m31 for the WestTaiwan [57] foreland basins. The highest curva-tures are those reported by Kruse and Royden[58] of 4^5U1036 m31 for the Apennine and Di-naride forelands. Fig. 5 shows, however, that cur-vatures this high may still not be large enough tocause brittle failure in the sub-crustal mantle, un-less the £exed plate is subject to an additional in-plane tectonic stress. In the case illustrated in Fig.5, the tectonic stress that is required to cause fail-ure in the sub-crustal mantle for a plate curvatureof 7U1037 m31 is 0.7 GPa. This is already closeto the maximum likely value for tectonic bound-ary loads [59], suggesting that brittle failure and,hence, earthquakes in the mantle will be rare. In-stead, seismicity will be limited to the uppermostpart of the crust where rocks fail by brittle defor-mation, irrespective of the stress level. This limitdoes not apply, of course, to Te. For curvatures ofup to 1036 m31, Fig. 5 shows that Te is alwayslarger than Ts. Only for the highest curvatureswill TeCTs and, interestingly, will the case thatTs sTe arise.

The YSE in Fig. 5 is based on a relatively weakdry quartz and quartz diorite continental crust.The question is raised, therefore, of how Te andTs would change if a weaker or stronger crust hadbeen assumed. We know, for example, that £uidsmay reduce not only the frictional strength, butalso the ductile strength of rocks by a signi¢cant



amount. As a result, a rock may £ow rather thanbreak in response to bending stresses and Tewould be expected to decrease. The e¡ect on Tsis less clear, but a reduction in brittle strength by

£uids is not, by itself, the only possible explana-tion of seismicity in the mantle. As Te decreases,curvature increases, and so the likelihood thatbending stresses will exceed the brittle strength

Fig. 5. Te and Ts for a multi-layered continental lithosphere as a function of plate curvature, K. (a) Te and Ts. Note that thereare two main seismogenic layers: one in the uppermost crust and the other in the uppermost mantle. The two layers are sepa-rated by an aseismic region. (b) Evolution of the brittle and ductile deformation ¢elds. The observed K values are from the sub-Andean [41], West Taiwan [57], Dinarides [85] and Apennines [58] foreland basins and the Australian plate in the Timor region[86]. (c) YSE showing the stress di¡erence for a load that generates a curvature of K=7U1037 m31. The calculations are basedon the semi-analytical models of Burov and Diament [21][2] and assume a thermal age of continental lithosphere of 400 Ma, athermal thickness of 250 km, a mean crustal thickness of 50 km (i.e. an orogenic belt setting), a ¢xed background strain rate of10315 s31, a dry quartzite upper crust (A=1.26U1037 MPa32:7 s31 and Q=134 kJ/mol [81]), a dry quartz or quartz diorite lowercrust (A=5.01U10315 Pa32:4 s31, Q=212 kJ/mol [87]), an olivine mantle (A=7U10314 Pa33 s31, Q=212 kJ/mol), densities ofthe upper crust, lower crust, and mantle of 2650, 2900, and 3330 kg/m3 respectively, thermal di¡usivities of the upper crust, low-er crust, and mantle of 8.3U1037, 6.7U1037, 8.75U1037 m2/s respectively, and a thermal conductivity of the upper crust, lowercrust, and mantle of 2.5, 2.0, and 3.5 W/m/‡K respectively. Elastic moduli, E and e, equal 80 GPa and 0.25, respectively. Byer-lee’s rock friction law [3] is assumed for the brittle portions of the lithosphere. Note that cataclastic £ow, pressure solution andsome other ‘atypical’ mechanisms may signi¢cantly reduce the frictional rock strength and hence Ts.



of mantle rocks and cause seismicity also in-creases. We also know that more ma¢c rocks,such as diabase, would have a higher ductilestrength. As a result, the lower crust is less likelyto £ow and Te would be expected to increase.However, we found that when the quartz dioritelower crust in Fig. 5 is replaced by diabase there islittle change in Te, so long as the lower crust is de-coupled from the mantle. This is because diabaseis weaker than the mantle and so the mantlestrength still dominates the rheology of the entirelithosphere. The main in£uence, we found, of adiabase lower crust is to Ts which can now extendfrom depths of 20^30 km, although not as deep asthe Moho itself.

These considerations have implications for therelationship between Ts and Te and, importantly,the strength of the mantle. In low-curvature re-gions, the mantle may be devoid of earthquakes,but still involved in the support of long-termloads. In high-curvature regions, however, themantle may have earthquakes, but long-termloads appear to be supported by the crust. Thisapparent ‘duality’ of role is explicable in terms ofa model in which the strength of the lithosphereresides more in the mantle than the crust. Thepresence or absence of seismicity depends on thecurvature and stress level and so by itself is not anindicator that the mantle is weak or strong. Theobservations of £exure together with the results ofanalytical modelling, however, indicate that themantle is strong and that, irrespective of curva-ture, the thickness of the strong competent layerin the mantle is always greater than that of itscounterpart in the crust. This is consistent withthe general observation that seismic instabilitiesmay have little or no relation to the long-termstrength of rocks that deform in a more stablebrittle and ductile regime.

Fig. 6 summarises the expected relationship be-tween Ts and curvature for di¡erent thermal ages,coupled and de-coupled continental lithosphere,and oceanic lithosphere. The circles show themaximum observed curvatures and, hence, themaximum likely value of Ts. In the de-coupledcontinental cases, Ts does not exceed 15 km,which corresponds well with observations. More-over, there is no obvious correlation between Te

and Ts. Te always exceeds Ts, irrespective of thethermal age and curvature. High Te values limitthe amount of curvature due to £exure and,hence, the ratio of Te to Ts increases with thermalage. Interestingly, it is the coupled continentaland oceanic lithosphere cases that have the poten-tial to yield the highest values of Ts. The reason isthat in both these cases, Byerlee’s friction law ex-tends, uninterrupted by a ductile lower crust,from the uppermost part of the crust into theunderlying mantle. Observed curvatures, however,still limit Ts in the continents. In contrast, Ts inthe oceans could extend to depths of V30 km.

The models discussed thus far are limited inthat they are based on thin-plate theory and thesmall-strain approximation. Moreover, we havefollowed previous studies and assumed that duc-tile deformation is controlled by uniform, ratherthan varying, strain rate. We have therefore car-

Fig. 6. The relationship between Ts and K for di¡erent ther-mal ages and coupled and de-coupled continental lithosphere.The ¢lled circles show Kmax and the corresponding Ts(max).Thin lines show de-coupled continental lithosphere of ther-mal age of 50, 500 and 1000 Ma. Dashed line shows thecoupled case which is based on a diabase rather than aquartz diorite lower crust. It is assumed that the Dinaridesare representative of the deformation of a de-coupled conti-nental lithosphere while the Australian plate (Timor) is repre-sentative of the deformation of a coupled lithosphere. Thickline shows the case of old, strong, oceanic lithosphere as itapproaches a deep-sea trench^outer rise system (thermalage= 175 Ma, Te = 55 km).



ried out numerical modelling using the ¢nite-ele-ment code PAROVOZ [60]. This code solves theforce, mass and energy balance equations for eachelement of a £exed plate and takes into accountlarge strain deformation. It also allows brittlestrain to be localised, thereby simulating faulting.Importantly, there is no limit on the strain rate¢eld. The model accounts for brittle, elastic, and

ductile deformation and is similar in formulationto that used by Burov and Molnar [61] and Burovet al. [62]. The main di¡erence is that we considersurface rather than buried loads, as were assumed,for example, by Burov and Diament [2] in theirstudy of orogenic loading.

Fig. 7 shows a numerical model for the £exureof continental lithosphere of thermal age 400 Myr

Fig. 7. ‘Snapshots’ of a numerical large-strain simulation of the response of the continental lithosphere to vertical loading, 0.5, 4,8, and 11 Myr following the load emplacement. The rheological parameters, crustal structure, and the thermal structure are thesame as assumed in Figs. 5 and 6. The ¢gure shows the strain (left-hand panel), viscosity (middle panel), and strain rate (right-hand panel). The strain shows that the potentially active seismic zones are con¢ned to the brittle uppermost part of the crust.The thickness of the seismic zone corresponds approximately to the depth of the BDT. The red dots at V40 km depth indicatea potential for seismicity in the lower crust. The presence or absence of seismicity in the lower crust would depend, of course, onthe applicability of Byerlee’s law to such great depths. The viscosity (as determined from the ratio of stress to strain rate) showsthe evolution of weak (blue-black) and strong (blue-white) zones in the lithosphere. Those zones in which the viscosity exceeds1023 Pa s can be considered e¡ectively elastic and their thickness would correspond roughly to that of the strong competent layer.The resulting Te is shown with yellow dashed line using the same vertical axes as depth. Note that there is no apparent correla-tion between Te and the thickness of the uppermost brittle layer. The strain rate, which reaches its maximum values in the ductilelowermost part of the crust, shows that the continental lithosphere responds rapidly to loading.



by a gaussian-shaped load, 3 km high, 200 kmwide, and uniform density of 2650 kg/m3. The¢gure shows the evolution of the brittle layer,the e¡ective strength of the lithosphere (de¢nedhere as the ratio of the deviatoric stress to thestrain rate), and the strain rate. The thickness ofthe brittle layer and, hence, Ts remains small de-spite changes in stress levels as the lithosphereaccommodates the load. In particular, Ts is al-ways three to four times smaller than the thick-ness of the competent, high-e¡ective-viscosity‘core’ of the lithosphere that supports the loadfor long periods of time. We also note that themodel predicts a localisation of brittle strain atthe base of the crust as well as along other densityand rheological boundaries. The localisation atthe base of the crust is explained by a strainrate ampli¢cation due to intense ductile £owand strong shear deformation in the narrowlow-viscosity zone near the interface between therelatively weak lower crust and relatively strongmantle. In this zone, the £ow stress becomes com-parable to the brittle strength, thereby promotingoccasional brittle failure and, hence, seismicity inwhat is otherwise a ductile regime for loads oflong duration.

The relationship between Te and Ts predictedfrom numerical modelling for load ages of 0.5, 5and s 10 Myr, is illustrated in Fig. 8. Ts is thethickness of the uppermost brittle layer and Te isdetermined from the e¡ective £exural rigiditywhich, in turn, has been derived from a verticalintegration of the stress ¢eld. The ¢gure showsthat Ts is less than 20 km, even for the casethat Te s 80 km. Ts varies with load-inducedstress relaxation such that if there is any changein Ts, it is a decrease which increases even furtherthe contrast with Te.

4. Discussion

These considerations of £exure observationsand model predictions have clari¢ed, we believe,our understanding of the mechanical behaviour ofthe Earth’s lithosphere. Ts, as de¢ned by thedepth of earthquakes, re£ects the extent of fault-ing in the uppermost, competent, part of the lith-osphere. The seismogenic layer potentially extendsto the BDT. The level of stress, however, may notbe su⁄ciently large to cause failure at suchdepths. Byerlee’s law predicts that Ts in the con-tinents is unlikely to exceed 20 km. Earthquakesmay extend deeper, into the brittle part of thesub-crustal mantle on major faults, in regions ofhigh curvature or high bending stress. In this case,there will be two seismogenic layers with an aseis-mic layer in between.

There is evidence from seismic re£ection pro¢ledata that the continental Moho is sometimes o¡-set by faults [63], although the signi¢cance of thisobservation is not entirely clear. Despite this,earthquakes in the continental sub-crustal mantleare rare. We interpret this as the consequence ofthe increase in brittle strength of rocks with con-¢ning pressure and the absence of a su⁄cientlylarge stress in these regions to overcome thestrength of the mantle. This is not to claim thatfrictional sliding may not give way to a di¡erent,aseismic, mechanism at great depths. Rather, ifbrittle frictional sliding is possible in the regionof the Moho, the stresses at these depths are toosmall to activate such sliding.

Ts re£ects current stress levels in the litho-

Fig. 8. Relationship between Te and Ts derived from numeri-cal experiments based on equilibrium equations, an explicitbrittle^elastic^ductile rheology, and a variable strain rate.Other model parameters are as given in Fig. 4. The modelingassumes a gaussian-shaped orogenic load (200 km wide, 3 kmhigh). Note that there is no apparent relationship between Teand Ts. The time dependence of Ts arises because of a load-induced stress relaxation in the lithosphere.



sphere. We have shown (Fig. 5), from the obser-vations of curvature and its associated bendingstress, that continental Ts is likely to be limitedto the uppermost 10^15 km of the crust. Ts mayextend deeper, depending on the level of the bend-ing and/or in-plane tectonic stress. Irrespective,we note that Ts correlates with a part of the geo-therm that is strongly in£uenced by crustal heatproduction (up to 50% of the surface heat £ow)[54]. Radiogenic heat production in granites, how-ever, exponentially decreases with depth and be-comes negligible at Moho depths. Continental Tsmay therefore be limited, in some way, by crustalheat production.

In contrast to Ts, Te re£ects the integratedstrength of the entire lithosphere. This includesa signi¢cant contribution from the aseismic partof the lithosphere. In oceanic lithosphere, the po-tential brittle zone extends to the BDT which maybe as deep as 50 km. This is because there is nointermediate ductile layer that prevents stressesfrom being propagated into surrounding compe-tent layers. As a result, the stresses generated by£exure accumulate locally and, if they exceed thecon¢ning pressure, cause earthquakes. In the con-tinents, however, there are one or more ductilelayers which may de-couple the competent partsof the lithosphere and cause smaller stresses forthe same amount of £exure and, hence, curvature.Furthermore, the small £exures and long loadingtimes suggest that most continental lithospherewill deform at rates that are signi¢cantly smallerthan oceanic lithosphere, which further reducesstress levels. While the stresses generated by £ex-ure are large enough to cause earthquakes in theuppermost brittle part of the continental crust,they may not be su⁄cient to overcome the brittlestrength of the continental sub-crustal mantle. Itis precisely because of this ‘threshold’, we believe,that mantle earthquakes are rare and continentalTe usually exceeds Ts.

Another, more obvious, di¡erence between Tsand Te concerns their time scales. Ts re£ectsweakness on historical time scales in the upper-most competent layer of the lithosphere. Te, onthe other hand, is indicative of the integratedstrength of the lithosphere on time scales whichexceed V105 yr.

In the oceans, there is evidence [64] of a timedependence to Te as the thickness of the litho-sphere that supports a load thins from its short-term thickness to its long-term elastic thickness.Oceanic Te studies suggest that thermal coolingwhich strengthens the lithosphere dominatesover that of load-induced stress relaxation whichweakens it, such that the mantle becomes increas-ingly more involved in the support of loads withthermal age. There is no evidence of a similardominance in the continents. Nevertheless, the ex-istence of high Te values in old cratonic regionssuggests that the thermal age of the continentsplays some role. Certainly, we can say ^ withsome con¢dence ^ that the sub-crustal mantle isan important contributor to the support of long-term loads in both the oceans and the continents.

While we have emphasised in this discussion thedi¡erences between Te and Ts, there are tectonicsettings where Te is low and may, therefore, ap-proach or, on occasions, be less than Ts. Most riftbasins are associated with Te values that are lowwhen compared to that of surrounding terrains.Moreover, the Te values are in accord with Tswhich ranges from 5 to 15 km for most rifts[65]. This similarity does not indicate, however,that Te and Ts are the same. Rather, the low Teat rifts is a consequence of all the geological pro-cesses that have in£uenced these features throughtime. The low Te has been variously attributed,for example, to a young initial thermal age ofthe rifted continental lithosphere, heating duringrifting, and thermal blanketing and yielding dueto post-rift sediment loading [66].

In some rifts, notably East Africa, there is evi-dence of earthquakes that extend to depths asgreat as 25^40 km in the crust and, hence, thatTs sTe. It has been proposed [67] that the deepseismicity is indicative of a strong ma¢c lowercrust. However, the brittle failure criterion forsuch a crust must be di¡erent from that associ-ated with Byerlee’s law, which requires very highstresses at such depths. One possible contributorare £uids, which would reduce the brittle strength.Fluids, however, also lower the ductile strength.Another is temperature. The Basin and Range,for example, is associated with high heat £owwhich imply Moho temperatures of V600‡C.



There are only a few pyroxene-rich rocks, how-ever, that would remain brittle at such high tem-peratures. These di⁄culties lead us to other ex-planations. Most data from experimental rockmechanics are based on simple monophase rocks(e.g. feldspars), yet we know that monophaserocks are stronger than polyphase ones. Conse-quently, it may be di⁄cult to maintain high duc-tile strength in the complex geological terrainsthat are involved in extensional terrains. The brit-tle strength of the lower crust has therefore alsoto be low, in order to deform seismogenically.

One consequence of the Wilson cycle is that, asoceans open and close, rifts become the sites ofcompression. The Te structure of rifts may there-fore be ‘inherited’ during subsequent orogenicloading events. The reason for this is that the lith-osphere is e¡ectively elastic on long time scalessuch that the Te acquired at the time of loadingis ‘frozen in’ and will not change signi¢cantly withtime. We know this to be the case for the oceans[8] and it is probably also the case for the con-tinents. Although orogenic belts are associatedwith crustal thickening and high strains, both ofwhich would weaken the lithosphere, they arecharacterised at one or both of their edges byfold and thrust loads that £ex the £anking litho-sphere not involved in orogeny, forming forelandbasins. The stratigraphic ‘architecture’ of thesebasins may therefore re£ect the Te structure ofthe underlying rift basins. Indeed, low values ofTe have been reported for the Apennine and Di-naride foreland basins [58], which developed onthe ancient Tethys margin, and the West Taiwanforeland basin [57], which developed on thepresent-day South China Sea margin. Other lowvalues have been reported from forelands in theWestern USA [40], Caspian Sea [68] and, interest-ingly, the Superior province in the Canadianshield [69].

Because of inheritance, low Te values may ex-tend beyond rifts into orogenic belts and, in somecases, to the interiors of the cratons themselves.Low Te values may therefore appear widespread.They should not be construed, however, as indi-cating that the sub-crustal mantle is weak in thecontinents. To the contrary, we believe that themantle beneath continents is strong. This is prob-

ably best manifest in wide foreland basins, such asthe Ganges and Appalachian/Allegheny, wherethrust and fold loads have been emplaced onhigh-Te cratonic interiors, beyond regions thatwere extensively heated and thinned during rifting[41].

Other considerations suggest that the conti-nents, despite appearing weak in some regions,are also capable of great strength. The loads as-sociated with thrust and fold belts are among thelargest to have been emplaced on the Earth’s sur-face, exceeding oceanic volcanic loads, for exam-ple, by a factor of 2 or more. Numerical model-ling [70^72] suggests that loads of this size areunlikely to be preserved for s 1 Myr, if Te ismuch less than 20 km. This is because loadingof weak continental lithosphere would result ina strong ductile £ow in the lower crust and, inthe case of very low Te, in the sub-crustal mantle.Such £ow will eventually lead to a £attening ofthe Moho and the collapse of topography. HighTe, on the other hand, inhibits such £attening andcollapse. Indeed, a strong sub-crustal mantle isrequired [73^76] to order to explain the greatheight of orogenic belts. Finally, the transmissionof tectonic stresses over large distances (which bythemselves may not be large enough to causeearthquakes), as con¢rmed by recent geodeticdata and observations of large-scale continentalfolding [77,78], implies high integrated strengthof most of the continental interiors.

5. Conclusions

1. The elastic thickness of the lithosphere, Te, isin the range 2^50 km for oceans and up to 80km and higher for continents.

2. The seismogenic layer thickness, Ts, is therange 0^40 km in the oceans. In the continents,Ts is generally in the range 0^25 km, but someearthquakes extend to greater depths.

3. Te and Ts are similar in young (6 100 Ma)oceans and in some rifts and orogenic belts.

4. The largest di¡erences between Te and Ts oc-cur in cratons, in the old, cold, interior of thecontinents.

5. Mechanical models that take into account the



strength of the brittle, elastic, and ductile partsof the YSE closely reproduce the observed dis-tribution of Te and Ts in a wide range of tec-tonic settings.

6. Both the observations of £exure and the pre-dictions of analytical and numerical models in-dicate that Te is only weakly correlated withTs.

7. Ts re£ects the thickness of the uppermost weaklayer that responds on historical time scales tostresses by faulting and earthquakes. Te, incontrast, re£ects the response of the litho-sphere to long-term (s 105 yr) geologicalloads.

8. Ts re£ects the strength of the uppermost brittlelayer of the lithosphere, or more precisely thestress level in this layer. Te, however, re£ectsthe integrated strength of the entire litho-sphere, a signi¢cant component of which maybe provided by an aseismic sub-crustal mantle.

9. The continental lithosphere, unlike its oceaniccounterpart, is associated with a multi-layerrheology and small plate £exures. Both factorsresult in stress levels that are unlikely to ap-proach the very high brittle strength limits be-low the Moho. The absence of deep mantleseismicity in the continents is therefore morea consequence of its strength, not its weakness.

Acknowledgements

We thank D. Forsyth and A. Lowry for theircritical review and helpful comments on an earlierversion of the paper, S. Lamb and C. Jaupart fordiscussions, and Y. Podladchikov and A. Polia-kov for sharing their PAROVOZ code. T. Jordanassisted with the analytical calculations in Fig. 4.Figs. 1^4 were constructed using GMT [79]. Thiswork has been supported by grants from NERC(NER/A/S/2000/00454) to A.B.W. and the INSU/CNRS IT program to E.B.B.[AC]

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Lithospheric strength and its relationship to the elastic and seismogenic layer thicknessIntroductionObservations of flexureAnalytical and numerical modelsDiscussionConclusionsAcknowledgementsReferences

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