Lithospheric Strength and Its Relationship to the Elastic and Seismogenic Layer Thickness

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Earth and Planetary Science Letters 213 (2003) 113^131 www.elsevier.com/locate/epsl

Lithospheric strength and its relationship to the elastic and seismogenic layer thickness

A.B. Watts a;, E.B. Burov b

a Department of Earth Sciences, University of Oxford, Parks Road, Oxford OX1 3PR, UK b 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 plate models it has been possible to estimate the effective elastic thickness of the lithosphere, Te. In the oceans, Te is the range 2^50 km and is determined mainly by plate and load age. The continents, in contrast, are characterised by Te values of up to 80 km and greater. Rheological considerations based on data from experimental rock mechanics suggest that Te reflects the integrated brittle, elastic and ductile strength of the lithosphere. Te differs, therefore, from the seismogenic layer thickness, Ts, which is indicative of the depth to which anelastic deformation occurs as unstable frictional sliding. Despite differences in their time scales, Te and Ts are similar in the oceans where loading reduces the initial 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 in cratons, many convergent zones, and some rifts. Most rifts, however, are characterised by a low Te that has been variously attributed to a young thermal age of the rifted lithosphere, thinning and heating at the time of rifting, and yielding due to post-rift sediment loading. Irrespective of their origin, the Wilson cycle makes it possible for low values to be inherited by foreland basins which, in turn, helps explain why similarities between Te and Ts extend beyond rifts into other tectonic regions such as orogenic belts and, occasionally, the cratons themselves. ß 2003 Elsevier Science B.V. All rights reserved.

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

1. Introduction remained rigid for long periods (i.e. s 105 yr) of geological time. One manifestation of plate ri- Plate tectonics is based on the observation that gidity is the £exural response of the lithosphere the Earth’s outermost layers, or lithosphere, can to surface loads such as ice, volcanoes, and sedi- be divided into a number of plates which have ments, sub-surface loads such as those associated with tectonic emplacement and magmatic intru- sions, and tectonic boundary loads such as slab

* Corresponding author. Tel.: +44-1865-272032; pull and ridge push. By comparing the £exure Fax: +44-1865-272067. observed in the vicinity of these loads to the pre- E-mail address: [email protected] (A.B. Watts). dictions of simple elastic, plastic, and viscous

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart 114 A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 plate models, it has been possible to determine the layer. Indeed, the brittle and ductile ¢elds also £exural rigidity of the lithosphere and its spatial contribute to the apparent strength of the litho- and temporal variation. sphere. In the oceans, the depth of the brittle^ Both continental and oceanic lithosphere are ductile transition (BDT) falls approximately modi¢ed by £exure. The two types of lithosphere, mid-way in the elastic portion of the lithosphere. however, have had a distinct physical and chem- As a result, the brittle and ductile deformation ical evolution. As a result, they respond to long- ¢elds are roughly equally involved in the support term loads in fundamentally di¡erent ways. The of loads. In the continents, there may be more oceanic lithosphere, for example, is relatively than one BDT and so the relationship of the brit- young, has a single-layer rheology and, as a con- tle and ductile ¢elds to the elastic portion of the sequence, its e¡ective £exural rigidity (which is lithosphere is more complex. determined by the elastic thickness, Te) depends Plate £exure studies [2,10,11] have shown that mainly on thermal age [1]. The continental litho- Te corresponds to, or indeed exceeds, the strong sphere, in contrast, is relatively old, has a multi- portion of the lithosphere, the thickness of which layer rheology, and its £exural rigidity does not ranges from 2to 50 km for oceanic lithosphere depend on a single controlling parameter such as and as high as 100+ km for the continental lith- thermal age, but is an integrated e¡ect of a num- osphere. ber of other factors that include the geotherm, Probably the best known manifestation of brit- crustal thickness, and composition [2]. tle deformation is seismicity data. It has been Rock mechanics data suggest that the £exural known for some time [12], for example, that con- rigidity of the lithosphere is determined by the tinental earthquakes are con¢ned to a seismogenic brittle and ductile properties of the constitutive layer, Ts, in the uppermost brittle part of the rocks that comprise it. Since brittle behaviour, crust. More recent studies, using improved hypo- as described by Byerlee’s law, is only possible at centre location techniques [13], have shown that relatively low con¢ning pressures and depths, it is in regions such as California, the Aegean, Tibet likely that this deformation type will determine and the Zagros mountains, Ts is remarkably uni- the strength of only the uppermost part of the form in thickness and rarely exceeds 20 km. Seis- lithosphere [3^5]. Ductile strength, in contrast, micity extends to depths as great as 40 km in old only slowly increases with con¢ning pressure, shield areas such as the Tien Shan, the Indian but strongly decreases with temperature [6]. The shield, and in the vicinity of the East Africa and transition to brittle, elastic or ductile behaviour is Lake Baikal rift systems, but is usually less intense mainly determined by the weakest rheology at the than it is in the upper crust. respective depth [4,5]. However, brittle frictional Rock mechanics data help constrain the mech- sliding is improbable at great depths (i.e. s 50^70 anisms that control the distribution of earth- km), irrespective of the ductile strength. quakes. These data suggest, for example, that de- As ¢rst shown by Goetze and Evans [7], loads spite its usual representation as pressure- on the lithosphere are supported by a quasi-elastic dependent Byerlee behaviour, frictional sliding in layer that separates the brittle and ductile defor- continental rocks is controlled by other factors mation ¢elds. This competent layer is the strong such as geotherm, strain rate, mineralogical inclu- portion of the lithosphere that is capable of sup- sions, and £uid content. In general, frictional slid- porting loads for long periods (i.e. s 105 yr) of ing is limited to a depth of V15 km (and 6 6^8 geological time. Watts et al. [8] and Burov and km depth on large faults). Beginning at this Diament [9] dubbed this layer the elastic ‘core’ depth, a semi-brittle/semi-ductile strain rate-de- and it has become popular to associate Te with pendent plastic £ow occurs, with a frictional com- its thickness. It is important to point out, how- ponent that is no longer signi¢cant at depths ever, that the Te revealed by £exure studies is the s 40^50 km [14^16]. This helps explain why seis- depth integral of the bending stress, which is not micity in the oceanic lithosphere is actually lim- necessarily associated with a particular competent ited to this depth range. It also accounts for why

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 115 earthquakes are so rare in the continental sub- responds to loads of variable spatial and temporal crustal mantle. This is because these depths typi- scales and, therefore, while both parameters are cally correspond to the lowermost part of the con- indicative of strength, they are not the same. tinental crust where ductile creep is dominant. There are, of course, regions where earthquakes extend to depths s 40 km, for example, in sub- 2. Observations of £exure duction zones. However, it is generally agreed [4,5] that deep seismicity is not related to friction- There have been a number of studies that have al sliding, at least not in the form expressed by focussed on the estimation of Te and Ts. Fig. 1 Byerlee’s law, but to various other metastable shows a histogram plot of Te derived from £exure mechanisms. These mechanisms are only weakly studies and Ts as revealed by the depths of intra- related to absolute rock strength. For example, it plate earthquakes. Although there are currently has been known for some time that unlike shallow debates about the reliability of both Te [20] and (i.e. depths 6 50^70 km) earthquakes, deep earth- Ts [13] estimates, we believe that the distributions quakes produce very few aftershocks. Shallow shown in Fig. 1 are representative and will not earthquakes, on the other hand, are characterised change signi¢cantly as more direct measures of by numerous aftershocks that decay exponentially the surfaces of £exure are used to constrain Te with time. This aftershock behaviour is a strong and improved earthquake hypocentral location argument that the earthquake-generating mecha- techniques are used to de¢ne Ts. nism di¡ers between shallow and deep earth- Fig. 1 shows that Te and Ts are similar in the quakes. oceans with the large majority of values 6 50 km. Because both Te and Ts re£ect the strength of Moreover, both Te and Ts clearly exceed the aver- the lithosphere, Jackson and White [17] assumed age thickness of oceanic crust. Therefore, not only that the two parameters are the same. While there do earthquakes occur in the sub-oceanic mantle, is some similarity between Te and Ts in the oceans but it is also involved in the support of long-term [18], their relationship in the continents is unclear. loads. The continents, by way of contrast, show a Recently, Maggi et al. [19] suggested that the Ts that is con¢ned to the crust and, interestingly, strength of the lithosphere is determined by the a Te that sometimes exceeds Ts. extent of the brittle deformation and therefore While Te and Ts are similar in the oceans and that Ts is the same as Te. Hence, Te, like Ts, in some continents, we believe that they have fun- should be low ( 6 20 km), except perhaps in old damentally di¡erent meanings. Ts re£ects the shield regions where it might extend to depths as great as 40 km. Such an assertion, which implies that the crust, rather than the mantle, is mainly involved in the support of long-term loads, raises serious questions concerning the observations of £exure, the extrapolations of data based on experimental rock mechanics, and the results of analytical and numerical modelling of £exure. The purpose of this paper is to consider the relationship between the elastic thickness, Te, and the seismogenic layer, Ts. We begin by re- viewing the results of £exure studies. The physical meaning of Te and Ts is then discussed in the light of analytical and numerical models for plate £ex- Fig. 1. Histograms of global compilations of elastic thickness, Te, and seismogenic layer thickness, Ts. (a) Oceans. ure with both a single- and multi-layer rheology. (b) Continents. The compilation is based on data in tables We conclude that Te and Ts re£ect the fundamen- 6.1 and 6.2of Watts [80], tables 1^6 of Chen and Molnar tally di¡erent ways that the Earth’s lithosphere [12], and table 1 of Wiens and Stein [18].

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart 116 A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 strength of, or more precisely the stress level in, tions at deep-sea trenchôuter rise systems. Be- the uppermost brittle layer of the lithosphere cause of the high curvatures that are experienced while Te is indicative of the strength of the elastic by the oceanic lithosphere as it approaches a portion of the lithosphere that supports a partic- trench, Te is less than it would otherwise be on ular load and, importantly, the brittle and ductile the basis of plate age because of yielding. Judge strength of the entire elastic layer. The di¡erence and McNutt [22], for example, have shown that in is most obvious in un£exed lithosphere when Ts is the high-curvature region of the seaward wall of zero and Te takes on its highest possible value [2]. the northern Chile trench (curvature 36 31 Di¡erences persist into £exed lithosphere where K = 1.3U10 m ) Te is 22 þ 2 km, which is Te slowly decreases with increasing curvature less than the Te of 34 km that these workers ex- and, hence, bending stress [11,21] while Ts simply pected on the basis of the thermal age of the sub- re£ects the local stress level. Yield strength enve- ducting oceanic lithosphere. lope (YSE) considerations (e.g. Fig. 2) suggest Fig. 3 compares Te and Ts at northern Chile as that in the case of the oceans, with their single- well as other di¡erent deep-sea trenchôuter rise layer rheology, the BDT just happens to fall ap- systems in the Paci¢c and Indian oceans. The ¢g- proximately mid-way in the strong elastic portion ure shows that Te and Ts are similar, at least for of the lithosphere. Therefore, Te and Ts may well ages of the oceanic lithosphere 9 100 Ma. For be similar. greater ages, there is a suggestion of a ‘threshold’ These conclusions are in accord with observa- beyond which Te exceeds Ts. This is attributed to the fact that as the lithosphere ages, its strength increases, and so the curvature and, hence, the bending stress associated with the same load decreases. Therefore, Te, which mainly re£ects the integrated strength of the lithosphere, increases while Ts, which depends more directly on the stress level, decreases. We have based the discussion thus far on a YSE that only considers the stresses generated in a £exed plate by bending. We have not, therefore, taken into account the e¡ect of any in-plane Fig. 2. Te and Ts for an idealised case of £exure of the oceanic lithosphere. Thin solid line shows the YSE for 80 Ma stresses that act on the plate due, for example, to oceanic lithosphere. The brittle behaviour is described by tectonic boundary loads. It is di⁄cult to concep- Byerlee’s law, the ductile behaviour by an olivine power law tualise Te and Ts from a YSE in the presence of U 314 33 31 (stress constant, A,of7 10 Pa s ; creep activation such stresses. However, we can say that Ts will be energy, Q, of 512kJ/mol [81]), and the thermal structure by conditioned by the brittle failure due to these the cooling plate model [82]. Thick solid line shows the stress di¡erence for a load which generates a moment, M,of stresses and, as a consequence, will be even less 2.2U1017 N/m and curvature, K,of5U1036 m31. The ¢gure related to the bending stress and, hence, the local shows that the load is supported partly by a strong elastic Te. layer or ‘core’ and partly by the brittle and ductile strength The oceanic Te estimates plotted in Fig. 1 are of the lithosphere. The dashed lines show the cases of K of based on more than 48 individual studies and so 1U1037 m31 and 1U1036 m31 which bracket the range of observed values at deep-sea trenchôuter rise systems can be considered a reliable measure of the long- 5 [7,11,22]. The ¢gure shows that Ts corresponds to the depth term ( s 10 yr) £exural properties of oceanic lith- of the intersection of the moment^curvature curve with the osphere. The continental Te estimates, in contrast, brittle deformation ¢eld, but could extend from the surface, are based on fewer studies (16) and some authors Ts (min), to the BDT, Ts (max). Te, in contrast, could ex- [20] have recently questioned their validity, espe- tend from the thickness of the elastic ‘core’, T (min), to the e cially estimates that are in excess of 25 km. thickness of the entire elastic plate, Te (max). Both Ts and Te depend on the moment generated by the load and, hence, The evidence for high continental Te is based the plate curvature. on forward models in which observations of £ex-

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the use of the free-air admittance instead since this technique takes into account what are considered the only known loads: surface loads. There is persuasive geological evidence, however, that subsurface or buried loads are also present in the continents [33] and, possibly, the oceans [34]. Such loads, which include intra-crustal thrusts [35], dynamically induced viscous stresses [36], and buoyant magmatic underplate [37], contribute to both the gravity anomaly and the topography. As Forsyth [33] has shown, however, increasing the ratio of buried to surface loading shifts the isostatic ‘roll-over’ in the free-air admittance to short wavelengths while increasing Te shifts it to long wavelengths. It is always possible, therefore, to interpret a free-air admittance that has been attributed to surface loading of a lithosphere Fig. 3. Summary of T and T estimates for deep-sea trench^ e s with low T by a model of combined surface outer rise systems. (a) Plot of Te and depth of earthquakes e as a function of the age of the oceanic lithosphere approach- and buried loading of a high-Te lithosphere. ing the trench. Data based on table 6.1 of Watts [80] and ta- McKenzie and Fairhead [20] are correct when ble 1 of Seno and Yamanaka [83]. The Te estimates have they state that there is no advantage in using been corrected for curvature. Solid lines show the YSE based the Bouguer coherence over the free-air admit- on the same rheological structure as assumed Fig. 1, a stress di¡erence of 10 MPa, and thermal ages of oceanic litho- tance if surface loads are the only ones that are sphere of 0^200 Ma. (b) Summary of Te and depth of earth- operative. However, if buried loads are also quakes for age of oceanic lithosphere of 85^115 Ma. Note present, then the coherence is better because it is the similarity between Te and the depth to which earth- less sensitive to the amount of buried loading and quakes extend. more sensitive to Te than is the admittance [33]. McKenzie [38], in a recent paper, has taken into ure are compared directly to predictions, and account buried loading. His focus, however, is on spectral, or inverse, methods in which the rela- the buried loads that because of the modifying tionship between gravity anomalies and topogra- e¡ects of erosion and sedimentation generate phy is analysed as a function of wavelength. For- gravity anomalies, but no topography. The e¡ect ward modelling of late-glacial rebound in North of such loads is to reduce the Bouguer coherence America, for example, reveals Te values as high as ^ in much the same way as would a surface load 80^90 km [23]. These estimates are in accord with which is emplaced on a su⁄ciently rigid plate that forward modelling of some of the foreland basins there is no £exure and, hence, Bouguer anomaly. that form by £exure in front of migrating thrust McKenzie [38] showed that in the region of the and fold loads. The Ganges basin, for example, is US Mid-Continent gravity ‘high’ the free-air co- associated with values that are in the range 80^90 herence is nearly zero for wavelength, V, 6 200 km [24^27]. Similar high values have been re- km suggesting there is no topography that might ported from spectral studies of parts of Australia be caused by buried loading. The topography of [28], Siberia [29], Brazil [30], North America [31], the region is indeed subdued. However, it is by no and Africa [32]. means clear that erosion and sedimentation will McKenzie and Fairhead [20], however, have always reduce a landscape to a £at plane. To the criticised the results of spectral studies, especially contrary, erosion and sedimentation are part of those that are based on the Bouguer coherence an isostatic cycle that involves uplift and subsi- technique which they consider upper bounds dence, both of which would be expected to con- rather than true estimates. These workers suggest tribute to the gravity anomaly and the topogra-

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart 118 A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 phy. The contributions may, because of the only the £exure and gravity anomaly to one side strength of the lithosphere, be small and so we of a load is used to derive Te. This is di¡erent agree with McKenzie [38] that it is always impor- from the approach of Lyon-Caen and Molnar tant to determine whether the coherence (free-air [25] and Karner and Watts [24] who used the to- or Bouguer) is high enough to yield a reliable Te pography to de¢ne the load. In this approach, the estimate. This is now possible using techniques £exure and gravity anomaly to one side of and, such as the maximum entropy method (MEM) importantly, beneath a load is used to estimate [39,40] where spectral estimates are calculated in Te. boxes that are moved step-wise across a study Fig. 4 compares the Te derived using the two area. approaches along a composite of ¢ve closely Signi¢cantly for this discussion, spectral tech- spaced pro¢les of the Ganges foreland basin. niques are not the only means of estimating con- The ¢gure shows that they yield similar results. tinental Te. The large majority of these estimates Te is high and V60 km. However, the minimum are based on forward modelling methods in which in the root mean square (RMS) error between observations are compared directly to the predic- observed and calculated Bouguer gravity anomaly tions of elastic plate models. Forward modelling is broad. This makes it di⁄cult to resolve the has the advantage that it is not sensitive as to actual value of Te. We can say though that Te is whether the free-air or Bouguer gravity anomaly high since application of the same approaches to is used. Indeed, many forward modelling studies a pro¢le of the Hawaiian ridge shows that if Te are not based on the gravity anomaly at all, but was lower, as it is in this tectonic setting, then the on direct observations of the surfaces of £exure minimum would be sharper. such as those derived from seismic re£ection and These considerations of spectral and forward refraction pro¢le, stratigraphic, and deep well modelling results suggest there is no reason to data. Where ¢eld geological data exist for buried query high continental Te, especially those esti- loads (e.g. in the region of the US Appalachian mates that are based on the MEM technique gravity ‘high’), they can be explicitly taken into where a coherence criterion is applied and for- account in forward modelling [41]. ward modelling which takes into account the pos- One way to verify the Te derived from spectral sibility of both surface and sub-surface loading. analysis is to compare it to the results of forward While a majority of the Te estimates are, indeed, modelling. Although only a few such comparisons low, there are values of up to 80+ km. Hence, Te have been carried out, they show [42^44] good in the continents can be signi¢cantly larger than agreement between the Te estimated using the the crustal thickness and, importantly, Ts. two di¡erent approaches. Armstrong and Watts Unfortunately, there are still only a few conti- [44], for example, used the MEM method of ana- nental regions where Te and Ts have been com- lysing Bouguer anomaly and topography data and pared directly. The main reason is that seismicity showed that Te in the southern Appalachians is in in the continental plate interiors is limited in its range 50^60 km. This is in agreement with the spatial extent. Seismicity, ¢rst of all, implies some mean estimate of 57.5 km based on the forward level of tectonic stress. These stresses would be modelling of pro¢les [41]. expected to be higher in the oceans, where the However, McKenzie and Fairhead [20] have displacement rates, and probably strain rates, also queried the high Te values determined from are typically an order of magnitude higher than forward modelling. They obtained, for example, a they are in the continents [45]. Moreover, stresses best ¢t Te for the Ganges foreland basin of 42 decrease away from plate boundary zones [46] km, which is about a factor of 2smaller than and the tectonic strains may be insu⁄ciently large the previous estimates by Lyon-Caen and Molnar in the slowly deforming interior regions of the [25] and Karner and Watts [24]. Their forward cratons to cause seismicity. Indeed, Byerlee’s law modelling followed a ‘no-load’ approach (D.P. (e.g. Fig. 2) implies that in order to produce seis- McKenzie, written communication) in which micity below depths of 25 km, a di¡erential stress

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many cases of TeETs. Two examples are Fenno- scandia and the Baikal Rift. In Fennoscandia, the thickness of the seismogenic layer based on an earthquake data set that spans 1965^1995 and a magnitude threshold of 3.0 is 25^30 km whereas YSE considerations [47] and Bouguer coherence studies using both periodogram [48] and MEM [49] methods suggest a Te that is locally in excess of 60 km. In the Baikal Rift, historical seismicity peaks 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 forward modelling of free-air and Bouguer gravity anomaly data along west^east topographic pro¢les of the rift.

3. Analytical and numerical models

Mechanical models that take into account both Fig. 4. Comparison of observed and calculated Bouguer brittle and ductile deformation provide additional gravity anomalies along a pro¢le of the Ganges foreland ba- insight into the manner that the lithosphere re- sin, north-central India. (a) Topography and £exure. Thick sponds to long-term loads. Moreover, they are line = topography. Thin lines show the calculated £exure due to surface (topographic) loading of a semi-in¢nite (i.e. bro- capable of predicting the relationship that would ken) plate with a plate break at x = 0 and Te of 30, 60 and be expected between parameters such as Te and 90 km. Thick grey horizontal bar shows the estimate of Bur- Ts. bank [84] for the depth to the base of the foreland basin se- Consider ¢rst the £exure of a thin elastic plate quence. Curved half-arrow indicates the approximate location that overlies an inviscid £uid, a well-known prob- of the main boundary thrust. (b) Bouguer anomaly. Solid dots = observed based on a 5U5 min grid of GETECH’s lem in mechanical engineering. As has been South-East Asia Gravity Project (SEAGP) data (J.D. Fair- shown by Turcotte and Schubert [54],among head, personal communication). Thin lines show the cal- others, the thickness of such a plate, Te(elastic) culated anomaly based on the £exure pro¢les in panel a. is given by: (c) RMS di¡erence between observed and calculated Bouguer 2 1=3 anomalies. Upper plot = Ganges basin. Lower plot = Ha- Melastic12ð13e Þ T ðelasticÞ¼ ð1Þ waiian Ridge. The two curves for each plot compare the e EK RMS based on McKenzie’s ‘no load’ (lowermost plot) case to the ‘load’ (uppermost plot) case for the Ganges basin where Melastic = the bending moment, K = curva- [24,25] and the Hawaiian Ridge [1]. Note: the RMS in the ture, and E and e are the Young’s modulus and ‘no load’ case is based only on the Bouguer anomaly to one Poisson’s ratio respectively. Melastic and K are in- side of the load whereas in the ‘load’ case the RMS is based on the Bouguer anomaly both beneath and to one side of dicative of the total amount of £exure and, hence, the load. are directly related to the stress and strain that accumulates in a deformed plate. Theoretical considerations suggest that, with some modi¢cation, Eq. 1 is valid for any rheology on the order of 0.4 GPa (tension) to 1.4 GPa (e.g. elastic, ductile, or viscous) that is capable of (compression) is required. maintaining stresses over a su⁄cient (for a quasi- We concur with Maggi and co-workers [19] that static approximation) amount of time. YSE con- continents, like oceans, show cases where TeWTs siderations suggest, however, that only in the case and, indeed, where Te 6 Ts. However, there are of a single-layer, elastic rheology, high Te, and

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart 120 A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 small curvatures, will Te(elastic) approach the ac- than it would be if the material maintained its tual mechanical thickness of the lithosphere. For elastic behaviour and, importantly, is lower than a multi-layered structure, Te is determined by the it would be in the elastic portion of the plate that bending moment, MYSE, which is the sum of all separates these two regions. The level of stress in the moments associated with the brittle, elastic, the brittle and ductile region, however, is not and ductile parts of the YSE. The correspondence zero. A load emplaced on the oceanic lithosphere principle allows the behaviour of any competent will therefore be supported partly by the strength plate (elastic, plastic, or viscous) to be related to of the elastic ‘core’ and partly by the brittle and that of an ‘equivalent’ elastic plate. ductile strength of the plate. The signi¢cance of In oceanic lithosphere, the equivalent elastic Te that has been estimated in regions such as thickness, Te(YSE), that generates the bending trenches where yielding occurs is that it re£ects moment MYSE and has the same curvature of an this combined, integrated, strength of the plate. elastic plate, K,is: Ts has its own signi¢cance. Byerlee’s law of 2 1=3 1=3 frictional brittle failure, which characterises defor- MYSE12ð13e MYSE T eðYSEÞ¼ ¼ ð2Þ mation in the uppermost part of the lithosphere, EK D K 0 suggests that strength linearly increases with pres- 2 where D0 = E/12(13e ). Since D0 is determined by sure and, hence, depth. According to this law, the the elastic properties of the plate and MYSE is minimal brittle rock strength in the absence of determined by depth integration of the YSE, £uid pressure is at least 65% of the lithostatic Eq. 2 can be used to calculate Te(YSE) for di¡er- pressure at the corresponding depth. Near the sur- ent values of plate curvature, K. Again, Te(YSE) face, the strength is V10^20 MPa while at depth is not the actual thickness of the plate. Rather, it it may theoretically reach a few GPa. For this is a ‘condensed’ thickness that re£ects the ‘inte- reason, the Earth’s uppermost layers will fail grated’ strength of the £exed, competent, plate. more easily than its lowermost layers even for McAdoo et al. [55] used Eqs. 1 and 2 to calcu- the same amount of strain. In the oceans, where late the ratio of Te(YSE) to Te(elastic) for a plate the crust is only V10 km thick, this leads to a of thermal age 80 Ma, an olivine rheology, and a concentration of seismicity in the crust and upper- uniform strain rate of 10314 s31. They showed most mantle. In the continents, however, where that for low curvatures (i.e. K 6 1038 m31) the the crust is thicker, seismicity is concentrated in ratio is 1, indicating little di¡erence between the the uppermost parts of the crust, in contrast to elastic thickness values. However, as curvature in- the lowermost part of the crust and uppermost creases, the ratio decreases as Te(YSE) decreases mantle that may never fail due to the lack of a and the £exed plate yields. For K =1036 m31 the su⁄cient stress. Indeed, at typical Moho depths ratio is V0.5, indicating 50% yielding and a cor- (i.e. V35 km), the theoretical brittle rock strength responding reduction in the elastic thickness. reaches 0.6 GPa (tension) to 2.0 GPa (compres- The fact that the oceanic lithosphere yields can sion). To exceed these stresses by, for example, be understood in terms of simple mechanics. Ideal tectonic strain, a ¢bre force of at least V1013 N elastic materials support any stress level. In the is required, which is an order of magnitude higher case of real materials, however, stress levels are than any previous estimates of the body and plate limited to the rock strength at the corresponding dynamics forces for the whole lithosphere [56]. depth. Strains in a bending plate increase with The signi¢cance of Te in the continents is not as distance from the neutral surface. Consequently, clear as it is in the oceans. This is because the the upper and lowermost parts of a £exed plate continents may comprise more than one brittle are subject to higher strains and may experience layer that is de-coupled from an underlying layer brittle or ductile deformation as soon as the strain by an intermediate ductile layer. As Burov and can no longer be supported elastically. These de- Diament [2] have shown for thermally ‘young’ formed regions constitute zones of mechanical continental lithosphere, a weak ductile layer in weakness since the stress level there is lower the lower crust does not allow bending stresses

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 121 to be transferred between the strong brittle layers to precisely track Te and, particularly, Ts, both of that ‘sandwich’ it and this leads to a mechanical which would be expected to change as a result of de-coupling between them. Nevertheless, stress loading. levels are reduced for the same amount of £exure We show in Fig. 5, therefore, how Te and Ts and so each brittle layer is involved in the support would be expected to change using the more pre- of a load. Te re£ects the strength of each elastic cise analytical formulations of Burov and Dia- layer and the combined strength of all the brittle ment [21]. The ¢gure illustrates how the thick- and ductile layers. It is not simply a sum of the nesses of the brittle and ductile layers evolve thickness of these layers (h1, h2Thn), however, but with di¡erent loads and, hence, curvatures. On is given by the following Kircho¡ relation![2]: bending, brittle failure and, hence, the potential Xn 1=3 for seismicity preferentially develops in the upper- W 3 3 3 1=3 3 T eðYSEÞ ðh1 þ h2 þ h3TÞ ¼ hl ð3Þ most part of the crust. The onset of brittle failure l¼1 in the mantle is delayed, however, and does not In the case of equally strong layers occur until the amount of £exure and, hence, cur- 1=3 (h1 = h2 = h3T = h): T eðYSEÞWn h, which yields vature is very large. TeW1.25h for two strong layers (n = 2). The Observations of curvature in the region of large meaning of Te(YSE) in the continents is now loads help constrain the strength of continental clearer. It re£ects the integrated e¡ect of all the lithosphere. Curvatures range from 1038 m31 for competent layers that are involved in the support the sub-Andean [41] to 5U1037 m31 for the West of a load, including the weak ones. Taiwan [57] foreland basins. The highest curva- As in the case for the single-rheology-layer oce- tures are those reported by Kruse and Royden anic lithosphere, if the multi-layered continental [58] of 4^5U1036 m31 for the Apennine and Di- lithosphere is subject to large loads, it £exes, naride forelands. Fig. 5 shows, however, that cur- and the curvature of the deformed plate, K, in- vatures this high may still not be large enough to creases. Te(YSE) is again a function of K and is cause brittle failure in the sub-crustal mantle, un- given [2] [9] by: less the £exed plate is subject to an additional in- plane tectonic stress. In the case illustrated in Fig. T eðYSEÞ¼T eðelasticÞCðK; T; h1; h2TÞð4Þ 5, the tectonic stress that is required to cause fail- where C is a function of the curvature, K, the ure in the sub-crustal mantle for a plate curvature thermal age, T, and the rheological structure. A of 7U1037 m31 is 0.7 GPa. This is already close precise analytical expression for C is bulky, to the maximum likely value for tectonic bound- although Burov and Diament [9] provide a ¢rst- ary loads [59], suggesting that brittle failure and, order approximation for a ‘typical’ case of conti- hence, earthquakes in the mantle will be rare. In- nental lithosphere with a mean crustal thickness stead, seismicity will be limited to the uppermost of 35 km, a quartz-dominated crust, and an oliv- part of the crust where rocks fail by brittle defor- ine-dominated mantle which they indicate is valid mation, irrespective of the stress level. This limit 39 36 31 for 10 6 K 6 10 m . Te(YSE) then simpli¢es does not apply, of course, to Te. For curvatures of 36 31 to: up to 10 m , Fig. 5 shows that Te is always larger than T . Only for the highest curvatures T ðYSEÞWT ðelasticÞ s e e will T CT and, interestingly, will the case that e s 1=2 ð1=2þ1=4ðTeðelasticÞ=TeðmaxÞÞÞ T T arise. 13ð13K=KmaxÞ ð5Þ s s e The YSE in Fig. 5 is based on a relatively weak 31 3 where Kmax (in m ) = (180U10 (1+1.3Te(min)/ dry quartz and quartz diorite continental crust. 6 31 Te(elastic)) ) , Te(max) = 120 km, Te(min) = 15 The question is raised, therefore, of how Te and km, and Te(elastic) is the initial elastic thickness Ts would change if a weaker or stronger crust had prior to £exure and can be evaluated from Eq. 3. been assumed. We know, for example, that £uids The considerations above are based only on may reduce not only the frictional strength, but ¢rst-order approximations. It is therefore di⁄cult also the ductile strength of rocks by a signi¢cant

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart 122 A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131

Fig. 5. Te and Ts for a multi-layered continental lithosphere as a function of plate curvature, K. (a) Te and Ts. Note that there are 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 based on the semi-analytical models of Burov and Diament [21][2] and assume a thermal age of continental lithosphere of 400 Ma, a thermal thickness of 250 km, a mean crustal thickness of 50 km (i.e. an orogenic belt setting), a ¢xed background strain rate of 10315 s31, a dry quartzite upper crust (A = 1.26U1037 MPa32:7 s31 and Q = 134 kJ/mol [81]), a dry quartz or quartz diorite lower crust (A = 5.01U10315 Pa32:4 s31, Q = 212 kJ/mol [87]), an olivine mantle (A =7U10314 Pa33 s31, Q = 212 kJ/mol), densities of the upper crust, lower crust, and mantle of 2650, 2900, and 3330 kg/m3 respectively, thermal di¡usivities of the upper crust, lower crust, and mantle of 8.3U1037, 6.7U1037, 8.75U1037 m2/s respectively, and a thermal conductivity of the upper crust, lower crust, 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 and some other ‘atypical’ mechanisms may signi¢cantly reduce the frictional rock strength and hence Ts.

amount. As a result, a rock may £ow rather than £uids is not, by itself, the only possible explana- break in response to bending stresses and Te tion of seismicity in the mantle. As Te decreases, would be expected to decrease. The e¡ect on Ts curvature increases, and so the likelihood that is less clear, but a reduction in brittle strength by bending stresses will exceed the brittle strength

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 123 of mantle rocks and cause seismicity also increases. We also know that more ma¢c rocks, such as diabase, would have a higher ductile strength. As a result, the lower crust is less likely to £ow and Te would be expected to increase. However, we found that when the quartz diorite lower crust in Fig. 5 is replaced by diabase there is little change in Te, so long as the lower crust is de- coupled from the mantle. This is because diabase is weaker than the mantle and so the mantle strength still dominates the rheology of the entire lithosphere. The main in£uence, we found, of a diabase lower crust is to Ts which can now extend from depths of 20^30 km, although not as deep as the Moho itself. These considerations have implications for the relationship between Ts and Te and, importantly, Fig. 6. The relationship between Ts and K for di¡erent ther- the strength of the mantle. In low-curvature re- mal ages and coupled and de-coupled continental lithosphere. The ¢lled circles show Kmax and the corresponding Ts(max). gions, the mantle may be devoid of earthquakes, Thin lines show de-coupled continental lithosphere of ther- but still involved in the support of long-term mal age of 50, 500 and 1000 Ma. Dashed line shows the loads. In high-curvature regions, however, the coupled case which is based on a diabase rather than a mantle may have earthquakes, but long-term quartz diorite lower crust. It is assumed that the Dinarides loads appear to be supported by the crust. This are representative of the deformation of a de-coupled continental lithosphere while the Australian plate (Timor) is repre- apparent ‘duality’ of role is explicable in terms of sentative of the deformation of a coupled lithosphere. Thick a model in which the strength of the lithosphere line shows the case of old, strong, oceanic lithosphere as it resides more in the mantle than the crust. The approaches a deep-sea trench^outer rise system (thermal presence or absence of seismicity depends on the age = 175 Ma, Te = 55 km). curvature and stress level and so by itself is not an indicator that the mantle is weak or strong. The observations of £exure together with the results of and Ts. Te always exceeds Ts, irrespective of the analytical modelling, however, indicate that the thermal age and curvature. High Te values limit mantle is strong and that, irrespective of curva- the amount of curvature due to £exure and, ture, the thickness of the strong competent layer hence, the ratio of Te to Ts increases with thermal in the mantle is always greater than that of its age. Interestingly, it is the coupled continental counterpart in the crust. This is consistent with and oceanic lithosphere cases that have the poten- the general observation that seismic instabilities tial to yield the highest values of Ts. The reason is may have little or no relation to the long-term that in both these cases, Byerlee’s friction law ex- strength of rocks that deform in a more stable tends, uninterrupted by a ductile lower crust, brittle and ductile regime. from the uppermost part of the crust into the Fig. 6 summarises the expected relationship be- underlying mantle. Observed curvatures, however, tween Ts and curvature for di¡erent thermal ages, still limit Ts in the continents. In contrast, Ts in coupled and de-coupled continental lithosphere, the oceans could extend to depths of V30 km. and oceanic lithosphere. The circles show the The models discussed thus far are limited in maximum observed curvatures and, hence, the that they are based on thin-plate theory and the maximum likely value of Ts. In the de-coupled small-strain approximation. Moreover, we have continental cases, Ts does not exceed 15 km, followed previous studies and assumed that duc- which corresponds well with observations. More- tile deformation is controlled by uniform, rather over, there is no obvious correlation between Te than varying, strain rate. We have therefore car-

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart 124 A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 ried out numerical modelling using the ¢nite-ele- ductile deformation and is similar in formulation ment code PAROVOZ [60]. This code solves the to that used by Burov and Molnar [61] and Burov force, mass and energy balance equations for each et al. [62]. The main di¡erence is that we consider element of a £exed plate and takes into account surface rather than buried loads, as were assumed, large strain deformation. It also allows brittle for example, by Burov and Diament [2] in their strain to be localised, thereby simulating faulting. study of orogenic loading. Importantly, there is no limit on the strain rate Fig. 7 shows a numerical model for the £exure ¢eld. The model accounts for brittle, elastic, and of 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 the same 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 indicate a potential for seismicity in the lower crust. The presence or absence of seismicity in the lower crust would depend, of course, on the applicability of Byerlee’s law to such great depths. The viscosity (as determined from the ratio of stress to strain rate) shows the evolution of weak (blue-black) and strong (blue-white) zones in the lithosphere. Those zones in which the viscosity exceeds 1023 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 correlation between Te and the thickness of the uppermost brittle layer. The strain rate, which reaches its maximum values in the ductile lowermost part of the crust, shows that the continental lithosphere responds rapidly to loading.

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 125 by a gaussian-shaped load, 3 km high, 200 km The relationship between Te and Ts predicted wide, and uniform density of 2650 kg/m3. The from numerical modelling for load ages of 0.5, 5 ¢gure shows the evolution of the brittle layer, and s 10 Myr, is illustrated in Fig. 8. Ts is the the e¡ective strength of the lithosphere (de¢ned thickness of the uppermost brittle layer and Te is here as the ratio of the deviatoric stress to the determined from the e¡ective £exural rigidity strain rate), and the strain rate. The thickness of which, in turn, has been derived from a vertical the brittle layer and, hence, Ts remains small de- integration of the stress ¢eld. The ¢gure shows spite changes in stress levels as the lithosphere that Ts is less than 20 km, even for the case accommodates the load. In particular, Ts is al- that Te s 80 km. Ts varies with load-induced ways three to four times smaller than the thick- stress relaxation such that if there is any change ness of the competent, high-e¡ective-viscosity in Ts, it is a decrease which increases even further ‘core’ of the lithosphere that supports the load the contrast with Te. for long periods of time. We also note that the model predicts a localisation of brittle strain at the base of the crust as well as along other density 4. Discussion and rheological boundaries. The localisation at the base of the crust is explained by a strain These considerations of £exure observations rate ampli¢cation due to intense ductile £ow and model predictions have clari¢ed, we believe, and strong shear deformation in the narrow our understanding of the mechanical behaviour of low-viscosity zone near the interface between the the Earth’s lithosphere. Ts, as de¢ned by the relatively weak lower crust and relatively strong depth of earthquakes, re£ects the extent of fault- mantle. In this zone, the £ow stress becomes com- ing in the uppermost, competent, part of the lith- parable to the brittle strength, thereby promoting osphere. The seismogenic layer potentially extends occasional brittle failure and, hence, seismicity in to the BDT. The level of stress, however, may not what is otherwise a ductile regime for loads of be su⁄ciently large to cause failure at such long duration. depths. Byerlee’s law predicts that Ts in the continents is unlikely to exceed 20 km. Earthquakes may extend deeper, into the brittle part of the sub-crustal mantle on major faults, in regions of high curvature or high bending stress. In this case, there will be two seismogenic layers with an aseismic layer in between. There is evidence from seismic re£ection pro¢le data that the continental Moho is sometimes o¡- set by faults [63], although the signi¢cance of this observation is not entirely clear. Despite this, earthquakes in the continental sub-crustal mantle are rare. We interpret this as the consequence of the increase in brittle strength of rocks with con- ¢ning pressure and the absence of a su⁄ciently large stress in these regions to overcome the

Fig. 8. Relationship between Te and Ts derived from numeri- strength of the mantle. This is not to claim that cal experiments based on equilibrium equations, an explicit frictional sliding may not give way to a di¡erent, brittle^elastic^ductile rheology, and a variable strain rate. aseismic, mechanism at great depths. Rather, if Other model parameters are as given in Fig. 4. The modeling brittle frictional sliding is possible in the region assumes a gaussian-shaped orogenic load (200 km wide, 3 km of the Moho, the stresses at these depths are too high). Note that there is no apparent relationship between Te and Ts. The time dependence of Ts arises because of a load- small to activate such sliding. induced stress relaxation in the lithosphere. Ts re£ects current stress levels in the litho-

EPSL 6700 9-7-03 Cyaan Magenta Geel Zwart 126 A.B. Watts, E.B. Burov / Earth and Planetary Science Letters 213 (2003) 113^131 sphere. We have shown (Fig. 5), from the obser- In the oceans, there is evidence [64] of a time vations of curvature and its associated bending dependence to Te as the thickness of the litho- stress, that continental Ts is likely to be limited sphere that supports a load thins from its short- to the uppermost 10^15 km of the crust. Ts may term thickness to its long-term elastic thickness. extend deeper, depending on the level of the bend- Oceanic Te studies suggest that thermal cooling ing and/or in-plane tectonic stress. Irrespective, which strengthens the lithosphere dominates we note that Ts correlates with a part of the geo- over that of load-induced stress relaxation which therm that is strongly in£uenced by crustal heat weakens it, such that the mantle becomes increas- production (up to 50% of the surface heat £ow) ingly more involved in the support of loads with [54]. Radiogenic heat production in granites, how- thermal age. There is no evidence of a similar ever, exponentially decreases with depth and be- dominance in the continents. Nevertheless, the ex- comes negligible at Moho depths. Continental Ts istence of high Te values in old cratonic regions may therefore be limited, in some way, by crustal suggests that the thermal age of the continents heat production. plays some role. Certainly, we can say ^ with In contrast to Ts, Te re£ects the integrated some con¢dence ^ that the sub-crustal mantle is strength of the entire lithosphere. This includes an important contributor to the support of long- a signi¢cant contribution from the aseismic part term loads in both the oceans and the continents. of the lithosphere. In oceanic lithosphere, the po- While we have emphasised in this discussion the tential brittle zone extends to the BDT which may di¡erences between Te and Ts, there are tectonic be as deep as 50 km. This is because there is no settings where Te is low and may, therefore, ap- intermediate ductile layer that prevents stresses proach or, on occasions, be less than Ts. Most rift from being propagated into surrounding compe- basins are associated with Te values that are low tent layers. As a result, the stresses generated by when compared to that of surrounding terrains. £exure accumulate locally and, if they exceed the Moreover, the Te values are in accord with Ts con¢ning pressure, cause earthquakes. In the con- which ranges from 5 to 15 km for most rifts tinents, however, there are one or more ductile [65]. This similarity does not indicate, however, layers which may de-couple the competent parts that Te and Ts are the same. Rather, the low Te of the lithosphere and cause smaller stresses for at rifts is a consequence of all the geological pro- the same amount of £exure and, hence, curvature. cesses that have in£uenced these features through Furthermore, the small £exures and long loading time. The low Te has been variously attributed, times suggest that most continental lithosphere for example, to a young initial thermal age of will deform at rates that are signi¢cantly smaller the rifted continental lithosphere, heating during than oceanic lithosphere, which further reduces rifting, and thermal blanketing and yielding due stress levels. While the stresses generated by £ex- to post-rift sediment loading [66]. ure are large enough to cause earthquakes in the In some rifts, notably East Africa, there is evi- uppermost brittle part of the continental crust, dence of earthquakes that extend to depths as they may not be su⁄cient to overcome the brittle great as 25^40 km in the crust and, hence, that strength of the continental sub-crustal mantle. It Ts s Te. It has been proposed [67] that the deep is precisely because of this ‘threshold’, we believe, seismicity is indicative of a strong ma¢c lower that mantle earthquakes are rare and continental crust. However, the brittle failure criterion for Te usually exceeds Ts. such a crust must be di¡erent from that associ- Another, more obvious, di¡erence between Ts ated with Byerlee’s law, which requires very high and Te concerns their time scales. Ts re£ects stresses at such depths. One possible contributor weakness on historical time scales in the upper- are £uids, which would reduce the brittle strength. most competent layer of the lithosphere. Te,on Fluids, however, also lower the ductile strength. the other hand, is indicative of the integrated Another is temperature. The Basin and Range, strength of the lithosphere on time scales which for example, is associated with high heat £ow exceed V105 yr. which imply Moho temperatures of V600‡C.

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There are only a few pyroxene-rich rocks, how- ably best manifest in wide foreland basins, such as ever, that would remain brittle at such high tem- the Ganges and Appalachian/Allegheny, where peratures. These di⁄culties lead us to other ex- thrust and fold loads have been emplaced on planations. Most data from experimental rock high-Te cratonic interiors, beyond regions that mechanics are based on simple monophase rocks were extensively heated and thinned during rifting (e.g. feldspars), yet we know that monophase [41]. rocks are stronger than polyphase ones. Conse- Other considerations suggest that the conti- quently, it may be di⁄cult to maintain high duc- nents, despite appearing weak in some regions, tile strength in the complex geological terrains are also capable of great strength. The loads as- that are involved in extensional terrains. The brit- sociated with thrust and fold belts are among the tle strength of the lower crust has therefore also largest to have been emplaced on the Earth’s sur- to be low, in order to deform seismogenically. face, exceeding oceanic volcanic loads, for exam- One consequence of the Wilson cycle is that, as ple, by a factor of 2or more. Numerical model- oceans open and close, rifts become the sites of ling [70^72] suggests that loads of this size are compression. The Te structure of rifts may there- unlikely to be preserved for s 1 Myr, if Te is fore be ‘inherited’ during subsequent orogenic much less than 20 km. This is because loading loading events. The reason for this is that the lith- of weak continental lithosphere would result in osphere is e¡ectively elastic on long time scales a strong ductile £ow in the lower crust and, in such that the Te acquired at the time of loading the case of very low Te, in the sub-crustal mantle. is ‘frozen in’ and will not change signi¢cantly with Such £ow will eventually lead to a £attening of time. We know this to be the case for the oceans the Moho and the collapse of topography. High [8] and it is probably also the case for the con- Te, on the other hand, inhibits such £attening and tinents. Although orogenic belts are associated collapse. Indeed, a strong sub-crustal mantle is with crustal thickening and high strains, both of required [73^76] to order to explain the great which would weaken the lithosphere, they are height of orogenic belts. Finally, the transmission characterised at one or both of their edges by of tectonic stresses over large distances (which by fold and thrust loads that £ex the £anking litho- themselves may not be large enough to cause sphere not involved in orogeny, forming foreland earthquakes), as con¢rmed by recent geodetic basins. The stratigraphic ‘architecture’ of these data and observations of large-scale continental basins may therefore re£ect the Te structure of folding [77,78], implies high integrated strength the underlying rift basins. Indeed, low values of of most of the continental interiors. Te have been reported for the Apennine and Di- naride foreland basins [58], which developed on the ancient Tethys margin, and the West Taiwan 5. Conclusions foreland basin [57], which developed on the present-day South China Sea margin. Other low 1. The elastic thickness of the lithosphere, Te,is values have been reported from forelands in the in the range 2^50 km for oceans and up to 80 Western USA [40], Caspian Sea [68] and, interest- km and higher for continents. ingly, the Superior province in the Canadian 2. The seismogenic layer thickness, Ts, is the shield [69]. range 0^40 km in the oceans. In the continents, Because of inheritance, low Te values may ex- Ts is generally in the range 0^25 km, but some tend beyond rifts into orogenic belts and, in some earthquakes extend to greater depths. cases, to the interiors of the cratons themselves. 3. Te and Ts are similar in young ( 6 100 Ma) Low Te values may therefore appear widespread. oceans and in some rifts and orogenic belts. They should not be construed, however, as indi- 4. The largest di¡erences between Te and Ts oc- cating that the sub-crustal mantle is weak in the cur in cratons, in the old, cold, interior of the continents. To the contrary, we believe that the continents. mantle beneath continents is strong. This is prob- 5. Mechanical models that take into account the

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