A lithosphere‐dynamics constraint on mantle flow:Analysis of the Eurasian plate

K. N. Warners‐Ruckstuhl,1 P. Th. Meijer,1 R. Govers,1 and M. J. R. Wortel1

Received 21 June 2010; revised 5 August 2010; accepted 10 August 2010; published 29 September 2010.

[1] We present a method to estimate the poorly understoodmechanical coupling between lithosphere and underlyingmantle, and apply it to the Eurasian plate. Mechanical equi-librium of tectonic plates requires the torque from mantletractions (TM) to be balanced by the torques from edge forces(TE) and lithospheric body forces (TB). The direction ofTE proves tightly constrained by plate boundary nature butTB is affected uncertainties in the density structure ofcontinents. We consistently find that the non‐zero torquerequired from mantle tractions does not agree with the ori-entation of any published absolute motion model. We con-clude that mechanical balance of the Eurasian plate requiresan actively convecting mantle, which should result in atorque on the Eurasian plate located in the southwest Pacific.Citation: Warners‐Ruckstuhl, K. N., P. Th. Meijer, R. Govers,and M. J. R. Wortel (2010), A lithosphere‐dynamics constrainton mantle flow: Analysis of the Eurasian plate, Geophys. Res. Lett.,37, L18308, doi:10.1029/2010GL044431.

1. Introduction

[2] In recent years it is increasingly being realized that thelithosphere and underlying deeper mantle are intrinsicallycoupled parts of the dynamic Earth which should be jointlyaddressed [Becker and Faccenna, 2009]. Nevertheless, withonly a few exceptions [e.g., Ghosh et al., 2008; Iaffaldanoand Bunge, 2009] model analyses of forces driving platemotion or producing the lithospheric stress field generallyadopt either a lithosphere‐based or a mantle‐flow‐basedperspective. In the former the coupling with the underlyingmantle is taken into account through boundary conditions,often in a simplified manner, e.g., through uniform basal drag[Forsyth and Uyeda, 1975;Meijer et al., 1997; Liu and Bird,2002; Copley et al., 2010]. In the latter approach the litho-spheric plates are usually taken to be rigid with simplifiedplate boundaries (review article by Becker and Faccenna[2009]).[3] In this study we aim to interface the two modeling

approaches by using a detailed analysis of forces acting onthe lithosphere as a basis for determining a dynamic con-straint on the tractions exerted by the convecting mantle ontothe lithosphere.[4] Our analysis is based onmechanical equilibrium, which

requires that the sum of all torques on a tectonic plate van-ishes [Forsyth and Uyeda, 1975]. The forces acting on a platecan be divided in three categories: 1) edge forces due tointeraction with neighboring plates (FE), 2) lithospheric

body forces (FB) and 3) mantle tractions at the bottom ofthe plate (FM). For a total force‐set including NE edge forcetypes iFE (with i = 1,..NE) and similarly NB lithospheric bodyforce types iFB:

XNE

i¼1

ZSr � i FE dS þ

XNB

i¼1

ZVr � i FB dV þ

ZAr � FM dA ¼ 0

ð1Þ

where the integration is over the boundary area S, the bottomarea A, or the volume V, while r is the position vector fromthe center of the earth.[5] In this study we carefully assess the orientation, and

when possible the magnitude of the first two terms ofequation (1). This provides constraints on the balancingtorque arising from mantle tractions. We focus on the Eur-asian plate. Due to its large size the ratio between total basalarea and total boundary length is high, making it likely thatmantle flow is a major contributor to the plate’s dynamics.

2. Eurasian Plate Model Boundaries

[6] Torque calculations are performed on a spherical thinshell representing the Eurasian plate (Figure 1). Our modelboundaries follow the major plate boundaries [Bird, 2003]where iFE are more clearly defined. The model domainincludes several regions exhibiting non‐rigid behavior, e.g.,SE Asia, Okinawa, Birma, Aegean and Anatolia. This doesnot affect our torque calculations: Eurasia can be considered aclosed system in which forces across internal faults opposeeach other and do not contribute to the torque.[7] We determine the type of FE based on tectonic setting

(Figure 1). Focusing on the overall dynamics of the Eurasianplate, features smaller than a few hundred kilometers areneglected. We distinguish five categories representing theaverage boundary characteristics: 1) ridge and transform (redline), 2) continental collision (black triangles), 3) trench roll‐back subduction [Schellart et al., 2008] (purple triangles),4) non‐roll‐back subduction (orange triangles), 5) unknownboundary (black boundary segment); the boundary betweencontinental North America and Eurasia is unclear both inlocation and nature due to the absence of seismicity and recenttectonic features; relative velocities are negligible.

3. Torque Analysis of Edge Forces

[8] Directions of FE’s can be estimated with some con-fidence but their magnitudes are unknown, prohibiting fullquantification of TE. However, we can constrain its orienta-tion using the geometrical distribution and orientation of thevarious iFE. Each boundary force is factorized into a con-stant magnitude per unit length of boundary, iFE, and a unit

1Department of Earthsciences,Utrecht University, Utrecht, Netherlands.

Copyright 2010 by the American Geophysical Union.0094‐8276/10/2010GL044431

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orientation vector ei [Forsyth and Uyeda, 1975]. iFE re-presents the average contribution of processes beyond theboundary domain averaged along each boundary segment;

iTE ¼ZSr � i FE rð ÞdS ¼ iFE

ZSr � ei rð ÞdS ¼ iFE iT

0E ð2Þ

iT0E will be referred to as geometrical torque.[9] Transform fault resistance, continental collision and

forces at non‐roll‐back subduction segments arise fromfriction at the plate contact and are modeled anti‐parallelto the direction of motion relative to the adjacent plate(NUVEL‐1a [DeMets et al., 1994]). The force at subductionroll‐back segments is expected to be dominated by suction ofthe retreating slab and is modeled outward and perpendicularto the boundary. No force is applied on the unknown North‐America Eurasia boundary segment.[10] We use the various iT

0E to constrain the orientation

of the total torque TE. Figure 2 illustrates the geometricalproperties of the vector sum of torques by representing torqueorientations as the location where a semi‐line of that directionintersects the globe. For positive scalar magnitudes, the sumof any number of torques is confined to the area enclosed bythe connecting great circles.[11] The calculated iT

0E are represented by black dots in

Figure 3. As a continuous variation of the (positive) scalarsiFE is possible, TE may lie anywhere inside the red line. Thisregion can be refined by imposing constraints on the rela-tive magnitudes of the iFE. Based on the larger contact areaper meter boundary we require 1) continental collisionboundaries to have a larger resistance per meter boundarythan transform fault boundaries and, 2) continental collisionresistance to be strongest on the contact segment with theIndian plate. Within these two constraints a continuousvariation of the relative force magnitudes remains possible,which limits T

0E to the red zone in Figure 3.

[12] The robustness of the solution space for T0E is decisive

for the robustness of the resulting constraint on lithosphere‐mantle interaction. Overall, torque directions are well con-strained by plate boundary geometry and relative motion.We tested the sensitivity of T

0E to boundary conditions on

the unknown North‐America Eurasia boundary segment bytreating it as a continental collision boundary and found theeffect limited. Force directions oppose along this segment

Figure 1. Topography and boundary types of our model Eurasian plate. Arrows denote relative motion of adjacent plate withrespect to Eurasia according to NUVEL‐1a, rate of motion is indicated in mm/yr. Thin black lines outline major tectonic units.

Figure 2. Illustration of the summation of geometrical tor-ques. Positive torque vectors are represented by the intersec-tion of the globe by a corresponding semi‐line in an upperhemisphere stereographic projection. aT1 is parallel to T

01.

For positive scaling factors a and b aT01 + bT

02 lies on the con-

necting great‐circle. Sum vector aT01 + bT

02 + cT

03 lies inside

the area (grey zone) enclosed by the connecting great circles.

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so that its torque contribution remains small and does notinfluence our findings regarding T

0E.

4. Torque Analysis of Lithospheric Body Forces

[13] FB’s result from gradients in gravitational potentialenergy (GPE) [Artyushkov, 1973]. In oceanic domains, FB’sconsist of slab pull, which is insignificant on the Eurasianplate, and ridge push, which can be quantified for a giventhermal cooling model and age distribution [Lister, 1975].We use the boundary layer model with constant basal heatflux [Crough, 1975] and oceanic age distribution fromMülleret al. [1997]. The ridge push torque is well constrained in bothorientation and magnitude.[14] FB’s arising in the continents and passive margins

(hereafter referred to as topography force) are more difficultto assess because the vertical density distribution of thelithosphere is not generally known. Warranted by the largehorizontal scale of our model we make the assumption ofisostatic equilibrium, which we use to infer the depth of majordensity interfaces from topography. However, as both crustalthickness and lithospheric depth vary laterally, additionalassumptions are necessary. These turn out to have a dominantimprint on the topography force. We bound the plausiblerange of the topography torque by using different lithospheric

density models that represent the extremes of what can beexpected.[15] We consider two classes of density models, one where

we calculate crustal thicknesses, and one based on observedcrustal thicknesses. In the first class, we assume Airy com-pensation through crustal thickness variations inside a litho-sphere of uniform (100 km) thickness (model Airyuni), orAiry isostatic compensation of homogeneously (i.e., uni-formly) thickened/thinned crust and lithospheric mantle at thebase of the lithosphere (model Airyvar). In the second class ofmodels we use crustal thicknesses from CRUST2.0 [Bassinet al., 2000]. Isostatic compensation follows by assumingeither density variations in the lithospheric mantle above100 km (model Crust2.0uni), or thickness variations of thelithospheric mantle (model Crust2.0var).[16] We calculate the topographic force for regions above

1000 m bathymetric depth to include the contribution ofcontinental margins, but to exclude areas where ridge pushacts and trenches where flexure dominates. Although plau-sible variations of the different parameters (e.g., densities,compensation depth) affect the magnitude of the forces,torque orientations are stable within a few degrees.[17] Force distributions for the four models (Figure 4) are

dominated by an outward pattern around the Tibetan plateau.However, whereas the Airymodels show low forcing outside

Figure 3. Analysis of torques acting on the Eurasian plate. Symbols represent the positive end of outward torques. Blackcircles represent iT

0E. Red line encircles theoretical solution space for the sum‐torque TE. Red zone represents physically

acceptable range for this torque. Green diamonds give torque orientations of ridge push and the various models for topographyforce, red triangles are the corresponding TB’s. The antipode of TE is confined to the blue zone, and antipodes of the TB’s arerepresented by blue triangles. They confine the orientation of TM to the shaded area (see text). Brown stars represent basal dragtorques, labeled according to used absolute velocity model. Closed/open stars correspond to driving/resistive drag. Key: tf:transform fault resistance, ccaf: continental collision (cc) Africa, ccar: cc Arabia, ccin: cc India, ccau: cc Australia, cctot: totalcc in case of equal forcing along entire continental collisional boundary, rb: force at roll‐back trenches, nrb: force at non‐roll‐back trenches, rp: ridge push, au: crustal Airy model, av: Airy model homogenous thickening entire lithosphere, cu: crust2.0model with uniform lithospheric thickness, cv: crust2.0 model with variable lithospheric thickness, HS3: HS3‐NUVEL‐1amodel [Gripp and Gordon, 2002], NNR: No‐net‐rotation reference frame [Argus and Gordon, 1991], DR: [Duncan andRichards, 1991], GJ: [Gordon and Jurdy, 1986], O’Neill: [O’Neill et al., 2005] in combination with NUVEL‐1a, Torsvik:global moving hotspot frame [Torsvik et al., 2008] in combination with NUVEL‐1a.

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the main mountain areas, the crust2.0 models induce hori-zontal forces in regions where crustal thickness variations arenot reflected by topography. These crustal thickness varia-tions have a long wavelength component (Siberian craton)that contributes significantly to the torque. This results inlarger and almost anti‐podal torques for the crust2.0 modelscompared to the Airy models (Figure 3). Figure 3 also shows

that torque orientations within each model class agree well.We find that torque magnitudes, however, are affected by thechoice of lithospheric mantle properties, and can vary by upto a factor four.[18] We conclude that the topography torque of Eurasia is

poorly constrained. However, the total TB is less variable dueto the large stable ridge push contribution. The red triangles in

Figure 4. Distribution of topography force for (a) Airyvar (black arrows) and Airyuni (red arrows) and (b) crust2.0var (blackarrows) and crust2.0uni (red arrows). Contour data show GPE for the models with constant lithospheric thickness (100 km).Areas below 1000 m bathymetric depth are not included in topography force calculations to exclude areas where ridge pushacts and trenches where flexure dominates.

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Figure 3 show TB for our four models. Differences in theirorientations demonstrate the uncertainty in TB.

5. Implications for Mantle Contribution

[19] The constraints on TE and TB allow us to limit theorientation of TM, which, from equation (1), is the sum of theantipodes of the two:

TM ¼ �TE

� �þ �TB

� � ð3Þ

[20] TM represents the total effect of the mantle consistingof two contributions: 1) horizontal shear 2) the effect ofnormal pressure at the base of the lithosphere due to activemantle flow, which will alter GPE based on isostaticequilibrium.[21] In Figure 3, the antipode of TE is confined to the blue

zone, and antipodes of the TB’s are represented by blue tri-angles. As magnitudes iFE are unknown, the solution spacefor TM follows from a linear combination of the blue zonewith any one TB (as in Figure 2). Considering the solutionspaces derived with the different TB’s, we confine the ori-entation of TM to the shaded area of Figure 3.[22] Additional assumptions regarding relative magnitudes

of the involved torques can considerably tighten the solutionspace. Previous studies have globally found TM to be of thesame order as, or stronger than TB [Bird et al., 2008]. Thisrestricts TM to the southwest Pacific part of the shaded area, inor just outside the blue zone. The overall effect of the mantlethen forces Eurasia’s center southward.[23] A common simplification in lithospheric based studies

is to model mantle tractions (anti)‐parallel to the direction ofabsolute motion [Forsyth and Uyeda, 1975; Meijer et al.,1997; Liu and Bird, 2002; Copley et al., 2010]. We evalu-ate this approach in the light of our torque analysis. Absolutemotion of Eurasia is low and directions vary considerablydepending on the chosen reference frame. We therefore usedifferent velocity models to calculate the resulting geomet-rical torque for uniform basal shear (Figure 3). Although it isoften seen as resistive to plate motion, its nature, being eitherresistive or driving, is ambiguous and we consider bothoptions. The torques fall well outside the shaded areaimplying that uniform shear (anti)‐parallel to absolute platemotion does not give a good average of lithosphere‐mantleinteraction under Eurasia. Due to the strong dominance ofcontinental lithosphere, results obtained with a shear stresscontrast between oceans and continents are very similar anddo not alter this finding. Incorporation of active mantle flowin a direction other than absolute plate motion proves indis-pensable for equilibrium of the Eurasian plate. As the mantledoes not force Eurasia towards or against its direction ofmotion it can not be seen as a truly driving or resistive force.

6. Discussion

[24] Our result for TM is independent of the magnitudesiFE, on which we have not made assumptions, and considersGPE uncertainties. Although FB are often thought to be welldetermined, systematic assessment of isostatic models for thelithospheric density structure shows that they are, in truth,poorly constrained on continents.[25] Our analysis concentrates on torque orientations and

does not quantify TM . The fact that none of the TB’s falls into

the antipodal area of TE, however, illustrates that FB and FE

alone do not balance the Eurasian plate and a net contributionfrom the mantle is required. Calculations of plate velocitiesfrom mantle flow models are commonly based on theassumption of balance of torques arising from two sets oftractions: 1) shear due to relative motion of the plates over thepassive mantle, and 2) tractions due to active mantle flow.This assumption is inconsistent with our findings: the sum ofthe two torques should be non‐zero.[26] For other large continental plates (South‐America

[Meijer et al., 1997], India [Copley et al., 2010]), basal shearin the absolute plate motion direction, or opposite to it, doesallow for mechanical balance. Our conclusion that, on aver-age, lithosphere‐mantle coupling must act in a differentdirection is therefore either unique to the Eurasian plate, or ismade possible by a more tightly constrained TM.

7. Conclusions

[27] Throughmechanical equilibrium of the Eurasian plate,analysis of lithospheric forces has brought us insight on thenet effect of mantle tractions. We find that:[28] 1. The orientation of the mantle torque required to

balance the Eurasian plate is constrained to the southwestPacific.[29] 2. A first‐order representation of mantle tractions

as uniform shear (anti‐)parallel to absolute plate motionis inadequate for the Eurasian plate. Therefore activemantle flow should be taken into account when modelinglithosphere‐mantle interaction.

[30] Acknowledgments. Constructive reviews by two anonymousreviewers are greatly appreciated. Figures were produced with theGMT software by Wessel and Smith (1991). Work supported in part bythe EUROMARGINS Programme of the European Science Foundation,project 01‐LEC‐EMA22F WESTMED.

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R. Govers, P. Th. Meijer, K. N. Warners‐Ruckstuhl, and M. J. R. Wortel,Department of Earthsciences, Utrecht University, Budapestlaan 4, NL‐3584CD Utrecht, Netherlands. (ruckstuh@geo.uu.nl)

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