Testing hypotheses on plate-driving mechanisms with global

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. B5, PAGES 10,115-10,129, MAY 10, 1998 Testing hypotheses on plate-driving mechanisms with global lithosphere models including topography, thermal structure, and faults Peter Bird Department of Earth and Space Sciences, University of California, Los Angeles Abstract. A popular concept of plate tectonics is that the most important density anomalies are in oceanic plates, which descend from rise to trench while subducting slabs act as velocity regulators and the drag on the base of the lithosphere is resistive. This hypothesis has been shown to be consistent with velocities of rigid plates and to approximately predict stress directions in a global elastic shell. Here I test whether the hypothesis leads to correct plate velocities and stress directions in models of laterally heterogeneous plates of nonlinear rheology separated by faults with low friction. All models have bottom boundary conditions based on simple shear in an olivine asthenosphere extending to the transition zone, where various patterns of lower mantle flow are assumed. These models show that topography alone is not sufficiento drive plate motion at actual rates over a or sluggish transition zone. If the forward component of velocity of each subducting slab is also imposed, then velocities are improved, but errors in stress direction become unacceptable. Better models are found by assuming that at least some parts of the transition zone have velocities greater than surface velocities, leading to active or forward basal drag. In the most plausible model, this forward drag acts only on continents, while oceanic lithospherexperiences negligible basal shear tractions. Probably the dense descending slabs of oceanic lithosphere not only pull the oceanic plates, but also stir the more viscous lower mantle, and this in turn helps to drive the slower drift of continents. 1. Introduction When the concepts of convection and plate tectonics were first developing, many thought of mantle convection as a process heated from below, which in turn exerts driving tractions on the base of a relatively stagnant "crust"(later, "lithosphere") to cause continental drift [e.g., Holmes, 1965, pp ]. Griggs [1939] epitomized this view with his scaled models in which flow was driven by embedded horizontal cylinders which stirred a viscous model "mantle" and in turn deformed a model "crust." In the early 1970s, more sophisticated understanding of convection led to the opposite view. It was realized that only a fraction of the Earth's heat flow originates in the core, while most results from radioactivity and/or secular cooling of the mantle. Computer models showed that internally heated (and/or surface cooled) systems have no upwelling sheets or plumes and that all concentrated flow originates in the upper cold boundary layer, which stirs the interior as it sinks. Thus it became natural to regard plates of lithosphere as driving themselves and, incidentally, stirring the rest of the mantle. The most certain part of this autonomous plate concept is the "ridge push" effect. Assuming general isostasy and a break in the lithosphere at the center of spreading rises, it is easy to show [Frank, 1972; Artyushkov, 1973] that rises must Copyright 1998 by the American Geophysical Union. Paper number 98JB /98/98 JB cause excess horizontal compression (in excess of local vertical compression) in adjacent deeper seafloor. On an idealized flat Earth with an inviscid asthenosphere and a linear rise, the vertical integral of the excess horizontal compression would be approximately equal to the excess pressure of rise topography times its mean depth of compensation. Since depths of compensation inferred from seismology and from thermal models are in rough agreement, this has become the best quantified term in the plate-driving system. Of course, a real plate might be subjecto resistance along its margins and possibly on its base, both of which would "consume" the "driving force" in the sense that they would cause the horizontal compression in old lithosphere to become less. Since many plates of oceanic lithosphere are destroyed at deep-sea trenches and since some trenches are deeper than old seafloor by several kilometers Oust as rises are shallower by several kilometers), it is masonable to expect a comparable topographic driving effect on oceanic plates due to trenches: "trench pull." However, since the subducting plate is very strong, the state of stress in the shallow part of any subducting slab is an enormous unknown in the force balance. Forsyth and Uyeda [ 1975] created an idealization in which rigid plates move with respecto a hot spot reference frame, with resistive drag tractions on their bases and on subducting slabs which are proportional to velocity. In contrast, ridge push, transform drag, trench pull, and slab pull were considered independent of velocity. Then they solved for the magnitudes of these assigned tractions necessary to best approximate a balance of torques on each plate. Their result 10,115

2 10,116 BIRD: GLOBAL MODELS OF THE FAULTED LITHOSPHERE was that slab weight and subduction resistance are both very large but nearly balanced, so that subducting slabs act as velocity regulators for their attached plates. Harper [1975] performed a similar calculation, in which plates are driven by ridge push and slab pull and resisted by basal and transform drags. He found the best match to plate velocities when the slab pull was about 7 times as strong as ridge push. In both of these models, it was not possible to test the implied stresses within the plates, because they had been indealized as rigid. Richardson et al. [1979] tested how similar boundary that their "driving forces" were never defined, except procedurally as model parameters in highly idealized models. For example, ridge push can be defined in the case of an infinitely long straight ridge bounding a plate of iso oceanic lithosphere on a flat Earth with frictionless transform faults and an inviscid asthenosphere: in this case it is the vertical integral through the lithosphere of the difference between horizontal and vertical principal stresses, and it varies with the age and depth of the lithosphere where the integral is performed. However, no general definition appropriate to real spherical planets has been published. tractions might cause internal stresses in the lithosphere. Similarly, trench pull is widely understood to be a deficit of They modeled the lithosphere as an elastic shell of constant thickness, in which spreading and subducting plate boundaries (but not transforms) were approximated by horizontal compression (with respecto vertical compression) in an oceanic plate which is somehow caused by the proximity of a deep trench, but there is no formal definition. elements of lower rigidity. Testing predicted principal stress Rather than devoting more energy to semantics, I hoped to directions against earthquake fault plane solutions, they concluded that ridge push and net slab pull (the net of trench create models including the most essential features of the three-dimensional density and strength distributions in the pull, slab weight, frictional resistance, and viscous resistance) actual lithosphere. In such models, ridge push, trench pull, were of comparable size and that shear tractions on the base of the plates were backward or resistive. Unfortunately, their mechanical idealization made it impossible to predict and check the velocities of the plates. Largely as a result of these benchmark studies, the modem consensus developed that plates drive themselves and drive most flow in the deeper mantle (except for plumes). That is, and continental collision resistance would arise naturally from the inclusion of actual topography/bathymetry and its compensation, without any need for definitions or adjustable model parameters. This goal dictated the use of the finite element method, which lacks algebraic generality, but is unexcelled in its ability to represent three-dimensional structure. angular velocity ( /r) decreases with depth, so that Another advantage of finite elements is their ability to everywhere work is being done on the asthenosphere and represent faults. Zhong and Gurnis [1995] have lower mantle by the lithosphere. However, this concept has demonstrated that weak faults naturally lead to platelike never been tested in a model simulation with realistic behavior in their two-dimensional (vertical plane) models of rheology and lateral heterogeneity, including actual time-dependent convection. In contrast, models of the topography, heat flow patterns, and plate boundary fault geometry. More important, the concept has been shown to be consistent with plate velocities under one mechanical lithosphere without faults [e.g., Wen and Anderson, 1997] predict smooth velocity fields which can only be compared with reality in the form of truncated spherical harmonic idealization and to be roughly consistent with stress directions expansions. In this study, I incorporate all the major plate under a different idealization, but it has never been tested for boundary faults of the Earth' surface but do not attempt any the ability to predict both velocity and stress within a single time evolution or finite strain. In these neotectonic model. The closest approach to such a test was the computation of Bai et al. [1992]. They assumed a Newtonian viscous mantle in order to permit solution of most equations in the spherical harmonic domain. Beginning with a low-resolution ( _< 8) model of mantle density anomalies, they computed the velocities of 11 rigid plates so as to balance the torques on each (assuming no interaction along plate margins). Then they relaxed the assumption of plate rigidity and converted the patterns of shear tractions on the bases of plates into maps of internal plate stress, adding in stresses due to crustal thickness and topography variations. This was one of the first calculations the positions and dips of faults are known; so there is no need to choose any evolution rules for the formation and weakening of new faults. The spherical shell modeling method used in this study has already been described by Kong [1995], Kong and Bird [ 1995], and Kong and Bird [ 1996]. This in tum was based on a flat-earth modeling method for continua of realistic nonlinearheology described by Bird [ 1989], and methods for adding faults detailed by Bird and Kong [1994]. Consequently, this discussion will be brief and qualitative. The method is a two-dimensional or thin-shell method in the sense that only the horizontal components of the computations to show the importance of sublithospheric momentum equation are solved (in a radially integrated weak density anomalies on the surface stress field, through the soft form) using a two-dimensional finite element grid, and only linkage of mantle flow. However, their predicted principal the horizontal components of velocity are predicted. Angular stress directions appear to be uncorrelated with actual stress direction data. Unfortunately, with a single negative result of this kind it is never possible to tell whether the defects are in velocity is assumed to be independent of radius within the lithosphere. The radial component of the momentum equation is represented by the iso approximation. the model or in our understanding of the Earth. The present Therefore vertical normal stress at any point is assumed to be study may be subjecto the same criticism, but at least it uses completely different modeling methods. equal to the weight of overburden per unit area. Bending stresses such as those occurring in the outer rises of subduction zones are not represented in the models. This 2. Finite Element Model Construction approximation is probably adequate for studies of what drives the plates; noniso topography is supported by local self- As the introduction may have suggested, one of the difficulties with the preceding highly idealized models was equilibrating stress loops, which only affect the balance of torques on a plate when they cross over plate boundary faults.

3 BIRD' GLOBAL MODELS OF TIlE FAULTED LITHOSPHERE 10,117 (This happens in some subduction zones, but by using the 'actual bathymetry of these zones, I think I have represented the anomalous forces on the lithosphere, at least to first order.) In other cases, noniso topography can only induce modest local rotations of principal stress directions. On the other hand, the method has some characteristics of three-dimensional or thick-shell methods in the sense that volume integrals of density and strength are performed numerically in a lithosphere model with laterally varying crest and mantle lithosphere layer thicknesses, laterally varying heat flow, and laterally varying topography. First, vertical integrals are performed using 1-km-depth steps at each of seven Gauss integration points in each finite element (continuum or fault). Application of a Gauss integration formula on the Earth's surface to these selected vertical integrals then gives a good approximation of threedimensional integrals. Thus it might be called a "2V2- dimensional" method. It may be useful to briefly contrast my models with those already published. Unlike Hager and O'Connell [1981], I allow the plate velocities to arise as part of the solution instead of being imposed as boundary conditions. Unlike Ricard and Vigny [1989], I use the actual topography of the Earth and include plate-plate interactions; I also compute intraplate stresses for testing and score velocity predictions on a point-by-point basis (not in spherical harmonic expansion). Deparis et al. [1995] and Lithgow-Bertelloni and Richards [1995] also omitted topography and all interactions between plates along their boundary faults. (Since they did not include the shallow density anomalies which many believe to drive plate motions, they could not definitively conclude that driving forces from below are required.) The rheology of my models has the same mathematical form at all points. Given the current strain rate tensor, the deviatoric stress tensor is evaluated separately for each of three flow laws: cohesionless frictional faulting, dislocation (power law) creep, and Newtonian (linear) creep. The mechanism giving the lowest maximum shear stress is presumed to dominate at that point. Then the total stress tensor is found by adding a pressure to the deviatoric stress that makes the vertical stress litho. Elastic strain, earthquake cycles, and other transient phenomena are not included in the model. crustal rheology is based on the California models of Bird and Kong [1994], where it was calibrated agains the depth of the brittle/ductile transition. The mantle rheology is based on olivine deformation studies summarized by Kirby [1983]. The Newtonian viscosity in the linear creep law is not intended to give an accurate representation of diffusion creep; rather, it is a numerical device by which I insure against excessive stiffness in cold lithosphere, which might lead to an ill-conditioned linear system and large solution errors that would prevent convergence. This value is typically 8x 10 TM Pa s. The finite element grid used in this study was relatively coarse, with 595 nodes, 796 continuum elements, and 185 fault elements (Figure 1). The starting grid was based on the second triangular subdivision of the icosahedron, for uniform coverage of plate interiors. Then plate boundary faults were added manually with an interactive utility program (ORBWEAVE; see below for its availability) that prevents clerical errors and detects topological errors. Spreading rises were represented by normal faults with 65 ø dip, transforms were represented by strike-slip faults of 90 ø dip, and subduction zones were represented by thrust faults of 25 ø dip. (In nature, subduction zones have a smoothly varying dip to accommodate the flexural rigidity of the subducting plate. But my model lacks any flexural rigidity; so this refinement is not necessary.) The diffuse boundary that allows slow relative rotation between the "India plate" and the "Australia plate" portions of the former Indoaustralia plate [DeMets et al., 1990] was not represented by a fault, as it seemed more appropriate to let the models undergo continuum deformation if the local stresses so dictate. Since most spreading boundaries are interrupted by numerous short transforms, some approximation of these boundaries was necessary. I chose to reduce the number of "stair steps" along each spreading boundary by using a few long strike-slip faults and a few long normal faults. This preserves the natural constraint(s) on the location of the relative Euler pole (if both plates are rigid) and the total lengths of rise and transform (respectively) along the boundary. Using a utility in ORBWEAVE, the azimuth of each strike-slip fault element was adjusted to within 1 o of the actual azimuth of transforms in that region, as reported in Table 3 of DeMets et al. [1990]. (Note that these are the Frictional faulting stress is evaluated under an assumption actual azimuths observed in the field, not the theoretical of hydro pore pressure. The coefficient of friction is the azimuths from their best fitting NUVEL-1 rigid-plate model.) same (f = 0.85 ) in the continuum (intraplate) parts of the Naturally, higher grid resolution (smaller elements) would be crest and mantle lithosphere layers, but it is assigned a lower desirable as well, in order to better representhe gradation of value in fault elements; numerous local studies have shown increasing plate strength with distance from a spreading rise. that this is necessary for a realistic simulation [Bird and The present large elements require the spatial variation of heat Kong, 1994; Kong, 1995; Bird, 1996; Kong and Bird, 1996]. flow near the rises to be linear, whereas most boundary layer The dislocation creep parameters are constant (but distinct) in models predict an inverse square-root-of-age relationship. It each layer; so it is common to have one brittle/ductile is likely that some of the local failures of these models to transition in the crustal layer and a second one in the mantle match spreading rate data are due to artificial breakage of hot lithosphere. In the power law dislocation creep formula for plate comers that would be eliminated with higher resolution. the maximum possible shear stress o s, The elevations (depths) of plate interior nodes were obtained from the ETOPO5 data set, after smoothing it with a Gaussian low-pass filter of 250-km radius to remove short- Icrsl-< Alslmn r wavelength features, which tend to be flexurally supported. (where s is shear strain rate, z is depth, and T is absolute However, elevations of plate boundary nodes were readjusted temperature), the assumed constants for crest/mantle are as by hand to actual local elevations, because spatial filtering follows' n = 3 (in both layers); A = 2.3x109/9.5x104 Pa s 1/3' tends to underestimate rise heights and trench depths, and it is B = 4,000/18,314øK; C = 0/0.017øK m -1. The maximum important to have the correct elevations along plate edges so shear stress at any point (plasticity limit) is 500 MPa. This as to accurately representhe topographic driving forces. The

4 10,118 BIRD: GLOBAL MODELS OF THE FAULTED LITHOSPHERE o o ILl o LONGITUDE Figure 1. Mercator projection of most of the spherical finite element grid "2N." Dashed lines are boundaries of continuum elements with no geological significance. Heavy lines are fault elements, with ticks indicating dip: no tick means 90 ø, straightick means 65 ø, rectangle tick means 45 ø, triangle tick means 25 ø. These fault elements are used to outline all the major plates. heat flow values for continental nodes were based on the 5 ø- mean compilation of Pollack et al. [1993]. Heat flows for oceanic nodes (those with depths of >2.5 km) in some models were derived from their depths according to the boundary layer cooling model of Stein and Stein [1992]. Heat flow along all spreading rises was set to a uniform 300 mw/m 2. This is admittedly arbitrary, but higher values would be associated with lithosphere thicknesses of under 10 km, and in practice this leads to local landslides in the model which are due to local imperfections (especially low spatial resolution) in the finite element grid. Once the elevation and heat flow were set for each node, the thicknesses of the crust and mantle lithosphere layers were computed by an iterative process to achieve both relative isostasy and a common temperature (1300øC) at the base of the lithosphere (which is defined here as the depth of transition from a conductive to an adiabatic geotherm). This resulted in crustal thicknesses which range from 5 km in the ocean basins to a maximum of 63 km in Tibet. Total lithosphere thicknesses range from 11 km at spreading rises to 200 km in some cratons, with a modal value of about 80 km. (At most points, the mantle lithosphere layer of the model contains a brittle/ductile transition, corresponding to the "elastic thickness" of some authors. However, the thicknesses mentioned here are the greater thicknesses over which all density anomalies and deviatoric stresses are integrated.) The intensive parameters used in these calculations were crust/mantle densities of 2816/3332 kg m -3 at 0øK, volumetric thermal expansion coefficients of 2.4x10-5/3.9x10-5 øk-i, thermal conductivities of 2.7/3.2 W m-løk - 1, and radioactive heat productions of 7.27x10-7/3.2x10-8 W m-3. The surfaces of the land and sea are obviously traction-free boundaries. Because the models are global, they might be expected to have no lateral boundary conditions. However, the model domain only includes subducting slabs down to the depth (~100 km) where the subduction thrust fault merges into a horizontal triangular prism of convecting asthenosphere. Therefore the subducting slabs are cut off arbitrarily, and a boundary condition is required for those surface nodes which represent the footwall side of each subduction zone (thrust fault) element. A "stress" boundary condition specifies the tractions on the "cut" surfaces of the slabs (at 100-km depth) which form part of the surface enclosing the model volume. In some models the cut surface is only subjected to litho normal tractions, and the horizontal velocities of these nodes are left free; I call them "free slab" models. In other models, these nodes have a velocity boundary condition. (The velocity reference frame for all absolute velocities in this paper is Africa-fixed.) I specify the NUVEL 1 parallel component of velocity to be the NUVEL 1 value, while the perpendicular component is left free. (In this case, the parallel component of boundary tractions need not be specified.) Of course, such nodes are still connected to thrust fault elements which transmit some frictional (shear) and topographic (normal) tractions between plates. In all subduction zones, the downdip integral of the shear traction

5 BIRD: GLOBAL MODELS OF THE FAULTED LITHOSPHERE 10,119 on the thrust fault is limited to 2.5x10 2 N/m, to represent of the lithosphere; (2) the speed of this assumed deep flow; the lubricating effects of subducted seawater [Bird, 1978]. Some earlier models (not presented here) did not have this limit, but their behavior was qualitatively similar, except that their stress direction errors were larger. The base of the lithosphere is subjected to a traction boundary condition in the vertical direction and a mixed boundary condition (traction is a function of model plate (3) the temperature assumed in the intervening olivine-rich asthenosphere, which controls how strongly the surface flow is linked to the assumed deep flow; (4) the treatment of footwall nodes in subduction zones, either with free or fixedvelocity boundary conditions; and (5) the friction of the brittle upper parts of plate boundary faults. As mentioned before, all of the models were constructed velocity) in the two horizontal directions. Consistent with the with actual topography/bathymetry and its iso iso approximation, vertical normal tractions are computed from the weight of the overburden, including topography or bathymetry and seawater. As was explained above, layer parameters were adjusted so that in most places compensation (or, locally, with anomalous vertical tractions arising deeper than the lithosphere). Therefore all models include ridge push, trench pull, and continental collision resistance effects without the need for arbitrary boundary these vertical tractions are equal to the radially varying conditions or variable intensities. This means that the pressure in a uniform inviscid asthenosphere of density 3139 (elusive) proper definition of these terms is not essential to kg m -3. However, the traction is more compressire above the correctness or longevity of these results. plumes (for example, Iceland, Afar, Galapagos) and less compressive above some subducting slabs, representing the To test the relative realism of the models, each was compared with three global data sets relevanto neotectonics. vertical traction anomalies of up to _+60 MPa locally exerted The first data set contained the vector velocities of 28 on the lithosphere by unmodeled deeper parts of the Earth. Shear tractions are computed from the velocity difference between the lithosphere and the top of the transition zone at geodetic benchmarks on seven plates as determined by Robaudo and Harrison [1993] in their merger of separate Very Long Baseline Interferometry (VLBI) and Satellite Laser 400-km depth (were a velocity pattern is assumed), using the Ranging results. (Another solution by Caprette et al. [1992] approximations of simple shear, an adiabatic geotherm (0.61 ø gives 50 velocities using only VLBI, but unfortunately these C/km), and an olivine dislocation creep rheology (the same as benchmarks are concentrated on only four plates.) Before in the mantle lithosphere layer). The assumption of simple comparing predicted model velocities to the geodetic shear probably cannot be improved except by performing velocities, the vertical components of the data were discarded, fully three-dimensional whole-earth models. However, other and model velocities were corrected by adding the rigid-body temperature or rheology profiles for the asthenosphere can Earth rotation which minimized the RMS discrepancy. The easily be imagined, and their results could be predicted: the remaining RMS discrepancy (in millimeters per year) is the single parameter which determines how the asthenosphere scalar error measure reported in the "geodesy" column of model affects these calculations is the ratio of the shear Table 1. The discrepancies between model predictions of traction on horizontal planes to the cube root of the velocity velocity and actual observations are large enough (>10 difference between lithosphere and the transition zone. mrn/yr) that detailed consideration of the accuracy and The many nonlinearities in the rheologies and the boundary covariance of the geodetic velocities is irrelevant. conditions are handled by iteration of each solution; in 50 Seafloor spreading rates determined from marine magnetic iterations the fractional velocity change typically drops to anomalies were also used to test the models, because this data ~0.04%, while the fractional stress change drops to -2% or set has more uniform geographi coverage than the geodetic less. Accuracy tests of such converged solutions were one. The complete list of 277 actual spreading rates summarized by Kong and Bird [1995] and detailed by Kong determined from analyses of magnetic anomaly 2A was taken [1995]. from Table 3 of DeMets et al. [ 1990]. The RMS discrepancy The FORTRAN77 program SHELLS which embodies (in millimeters per year) is the scalar error measure reported these methods, together with utility programs ORBWEAVE in the "spreading" column of Table 1. and ORBMAPAI and sample input and output files from this The third data set was a set of azimuths of the most study, is currently available by anonymous FTP from compressive horizontal principal stress at regularly spaced ftp ://element. ess. ucla. ed u/neotec/s h el Is/. grid points from [Bird and Li, 1996, Figure 5]. These 3. Model Tests and Results directions were derived by maximum likelihood interpolation from the 6700 entries of the World Stress Map data set of During , approximately 136 tests were conducted with various versions of this program and input Zoback [1992]. Interpolated stress was used in preference to the original data so as to mitigate the very strong bias of the data. As questionable features were noted and investigated, World Stress Map toward coverage of North America and small corrections were made to either the program or the data. To avoid lengthy explanation, I present here only the 70 most recent computations, all conducted with the final version of the program and with nearly the same finite element grid. Details of each model are contained in Table 1, and Figure 2 presents an overview of the misfits of the different classes of models attempted. Five parameters were varied in order to study their effects and to search for the best fitting model: (1) the pattern of horizontal flow assumed at the top of the transition zone when computing the boundary conditions applied to the base Europe; however, some remaining bias is unavoidable, since Bird and Li typically could not report a reliable interpolated direction in most oceanic regions. Discrepancies between the models and the interpolated azimuths were weighted only by the varying sizes of the 5 ø grid blocks but not by any measure of uncertainty. (Again, this is to mitigate the bias toward North America and Europe, where the uncertainties are least.) The mean value of the discrepancy (in degrees) is reported in the "0' h" column of Table 1. Since the discrepancy can never exceed 90 ø at any point, an average discrepancy of 45 ø is a very poor result, indicating no correlation between the

6 10,120 BIRD: GLOBAL MODELS OF THE FAULTED LITHOSPHERE Table 1. Input Parameters and Resulting Misfits of All Models Input Parameters Slab End Model Flow Pattern 400-km Speed Ta,o C Boundary Fault No. Depth Factor Condition Friction Grid mm/yr O11 95O statm free free free free NUVEL free free free free free free free free free free NUVEL NUVEL NUVEL free free free free NUVEL free free free free NUVEL NUVEL free NUVEL free NUVEL free free free free free free Geodesy, K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K M M N N N N N N N N N N N Misfit Measures Spreading, lh ' deg

7 BIRD: GLOBAL MODELS OF 2'FIE FAULTED LrrHOSPHERE 10,121 Table 1. (continued) Model No. Flow Pattern at 400-km Depth Baurngardner [1988] Baumgardner [1988] Baurngardner [1988] (continents) (continents) (continents) (continents) (continents) (continents) (continents) (continents) (continents) (continents) Input Parameters Slab End Speed Ta,o C Boundary Fault Misfit Measures Geodesy, Spreading, {Jlh, deg Factor Condition Friction Grid mm/¾r mm/yr N N N N N N N N N free N free N free N free N model and the data. However, the data set has large internal inconsistencies [Bird and Li, 1996, Figure 2], so it is doubtful whether any model will ever match it to better than mean error of ~25 ø. This compressed range means that variations of just a few degrees in the size of the mean misfit are probably significant. Unfortunately, information on stress magnitudes is not useful for scoring. This is because my models only make predictions of vertically integrated stress throughout the lithosphere. Actual stress has never been measuredeeper than 6 km. In order to compare the two, it would be necessary to make complex assumptions about how stress is distributed with depth. This is possible in the simple idealized model but very difficult in the real Earth. Time-averaged (anelastic) strain rates of plate interiors are also predicted by these models. These values are typically low (for example, <10-6/s in 95% of elements). These model predictions are not currently used for scoring. First, sufficient t- O o 0 40 ø- anticorrelated correlated NUVEL-1 continental d only ' r.ner,o 30 LU 0 I I I I,I mm/a Average of RMS Misfits for Geodesy and Spreading Figure 2. Results of all 70 modelsummarized in a two-dimensional misfit space. Ordinate is mean error in the velocity predictions; abscissa mean error in predicted horizontal principal stress directions. Circular open symbols indicate models with free subducting slabs; solid square symbols indicate models with slabs forced to subduct at NUVEL 1 velocities. (All models include topographic "driving forces.") Letter S indicate lower mantle (at 400 km). Letter B indicates the convection pattern of Figure 7 of Baurngardner [1988]. Letter N indicates an artificial flow pattern based on the NUVEL 1 surface model. Letter C indicates that only continents interact with the assumed NUVEL 1 deep flow. Groups of models are outlined and labeled for clarity.

8 10,122 BIRD: GLOBAL MODELS OF THE FAULTED LITHOSPHERE geodetic data are only available in a few small regions (California, Aegean), each of which is poorly resolved by the large elements of my grid. Second, the models predict large strain rates in a few elements with high heat flow which form the convex comers of oceanic plates at ridge/transform intersections, but because these strain rates are high in only a single element, I suspecthat they are artifacts of the limited spatial resolution of the grid. between a rise at 2.7-km depth and a trench at 8-km depth. If the subduction thrust fault was eliminated (locked), then the vertical integral of the difference between horizontal and vertical compression in 6-km-deep seafloor was 1.75x1012 N/m, in agreement with most estimates of ridge push. If the normal fault at the ridge was eliminated and the subduction zone was free to slip, then the topographic trench pull effect was 3.3 lx1012 N/m in 6-km-deep seafloor. This suggests that the topographic driving effects are correct. Then I tested how 3.1. Models With a Static Lower Mantle In one class of models the transition zone and lower mantle fast these plates would be driven against basal drag and subduction shear zone drag; a rectangular plate with the area were approximated as. (In these calculations, of the Pacific plate and no transform resistance moves at 140 convection at rates much lower than surface plate rates would mm/yr if asthenosphere temperature is 1400øC, but at only 16 hardly be different from inactivity.) Therefore the drag on the mm/yr if the temperature is 1300øC. base of the lithosphere is uniformly passive or resistive. Plate I also made one additional test (not included in Table 1 or motion is driven, as in all models, by topography (including Figure 2) to see if the Pacific plate in the Earth model was the effects sometimes called ridge push, trench pull, and continental collision resistance) Models with free subducting slabs and lower being unreasonably restricted by discretization errors in modeling its transform margins. I created a finite element grid in which I reset the azimuths of each transform to lie mantle. Within this class there is a subset of models where along small circles abouthe absolute rotation pole of the real the truncated ends of subducting slabs were treated as "free" (subject only to litho normal tractions); these models essentially test the hypothesis of Richardson et al. [ 1979] that the only important driving forces are topographic. Unfortunately, within this class there are no models with plate velocities over a few millimeters per year! Because these models have almost no plate motion, they all have about the same velocity error (-50 mm/yr) and similar stress errors ( ø) and form a tight cluster in Figure 2 (open circles marked "S"). This immobility persisted even though plateboundary fault friction was reduced to only 0.03, which is even lower than that reported in California ( [Bird and Kong, 1994]) and Alaska (0.17 [Bird, 1996]). It persisted even though the limit on the downdip integral of the shear traction in subduction zones was reduced to 2.5x 10 2 N/m, the lower limit found for two Pacific subduction zones by Pacific plate. However, the slow Pacific plate velocity was nearly unchanged in this model. With hindsight, the failure of these topography-driven models is understandable. If a spreading rise contributes 1.7xl 012 N/m of driving force (as loosely defined above) and an 8-km trench contributes 3.3x1012 N/m, it is also true that even a minimum estimate of subduction-zone friction [Bird, 1978] consumes 2.5x1012 N/m, or half of the total. As transform margins consume part of the remainder, the nonlinear (n = 3 ) rheology of the asthenosphere causes the plate velocity to drop below 140 mm/yr (for 1400øC asthenosphere) in proportion to the cube of the fraction remaining. Furthermore, the Pacific plate is the only plate on Earth which has these ideal driving forces. The Nazca and Cocos plates also descend from the East Pacific Rise to trenches, but these trenches are much more shallow. All other Bird [1978]. It also persisted even though the asthenospheric plates are either overriding plates or are involved in adiabatemperature / (at a reference depth of 100 km) was increased to an implausible 1400øC. For example, in model 95043, the maximum spreading velocity on the East Pacific Rise was 6 mm/yr, where it should be over 150 mm/yr. The fastest motion in these loosely constrained models was in the form of local landslides, principally around the Iceland and Afar hot spots and in the Japan area. (Such landslides are a common feature of neotectonic models with low strengths. In some cases they may disqualify a model. However, when they are only one element wide, it is never clear whether they are caused by incorrect model parameters or simply by inadequate spatial resolution.) In an attempt to stop these continental collisions along their leading edges. 3.1,2 Models with velocity boundary conditions on slabs and a lower mantle. Another group of models have velocity boundary conditions applied to the nodes on the footwalls of well-developed subduction zones. Specifically, in all subduction zones with a seismic Benioff zone, I require the velocity component of footwall nodes in the direction predicted by the NUVEL 1 model to have the NUVEL 1 value. (There is no constraint on the orthogonal component of velocity and no velocity constraint on the nodes of the overriding plate.) This set of models tests the hypothesis of Forsyth and Uyeda [1975] that while topographic driving landslides and to increase the accuracy of the topographic forces and basal drag are roughly balanced, it is the driving force model, I tried two modifications of the nodal subducting slabs which regulate the velocity of their attached input data. Whereas finite element grid "2K" had been computed using oceanic heat flow values from Pollack et al. [1993], the oceanic heat flow values for grid "2M" were obtained from ocean depths and the boundary layer cooling model of Stein and Stein [1992]. This was tested in model 95060, with no improvement. Then I hand-edited the grid data in the Iceland and Afar regions to alleviate the landslides (creating grid "2N") and ran model 95069; however, the problem of plate immobility was unchanged. Suspecting possible errors in the finite element code, I performed some tests on idealized rectangular oceanic plates plates by applying either forward or backward forces, which can be very large. As is shown in Figure 2 (solid squares marked "S"), the addition of these velocity boundary conditions reduces the velocity error by 24-68% by forcing most of the plates to move at roughly the right velocities. (This is natural, since velocity boundary conditions are now applied to all plates except Caribbean Sea and Eurasia!) However, the velocity error is never reduced below 17 mm/yr, because resistive basal drag causes the subducting plates to stretch, and their trailing edges move less rapidly than their subducting edges.

9 BIRD: GLOBAL MODELS OF THE FAULTED LITHOSPHERE 10, ',,,. f ( 5E+12 N/m Iv/ ,, normal faulting STRESS REGIMES'. strike-slip faulting --- thrust faulting Figure 3. Vertically integrated stress anomalies in the lithosphere predicted by an unsuccessful model (95058) which was driven by slab velocity boundary conditions and topography, moving the lithosphere over a lower mantle. (top) Principal axes of vertically integrated stress anomaly shown by diverging arrows (relative tension) or converging arrows (excess compression); vertical axis shown by triangle (relative tension) or circle (excess compression). Some symbols have been omitted for clarity, and others have been slightly displaced. The standard for defining the stress anomaly is a model profile of isotropic pressures under a mid-ocean rise. Mercator projection, but symbol sizes are not exaggerated at high latitudes. (bottom) Directions of the most compressive horizontal principal stress ( t51h ) at the same points.

10 10,124 BIRD: GLOBAL MODELS OF THE FAULTED LITHOSPHERE This effect is severe at the lower asthenosphere temperatures (1100 ø and 1200øC) and less important at the high 3.2.l. Models superimposed on a constant-viscosity mantle convection solution. The first convection pattern tested was from Figure 7 of Baurngardner [ 1988]. His model was of a constant-viscosity compressible mantle with Rayleigh number of 106 and 50% internal heating, without any crust. He initialized the model with higher temperatures at the sites of present rises and lower temperatures present subduction zones. After computing six overturns, he found that the overall pattern of flow remained about the same. This pattern has seven broad plumes, four of which are located near Iceland, Afar, Kerguelen, and Hawaii. In between them are linear downwellings in the NW Pacific, SW Pacific, Andean, Scotian, and African regions. Baumgardner noted that absolute velocities at the surface were about 10x too low as would beexpected. These Baurngardner [1988] models are more successful than the -mantle model, but still have stress direction errors of >_32 ø and kinematic errors of >_17 temperatures (1300 ø and 1400øC). However, as the slab boundary condition reduces the velocity errors, it increases the stress errors. Every one of the models in this group has a stress direction error which is at least 10 ø greater than that of any one of the immobile group mm/yr Models superimposed on an artificially plate-like lower mantle flow. I was interested in investigating just how much these errors could be reduced by other patterns of active with free slabs (Figure 2). One reason is that the combination mantle flow and whether forcing a reduction in kinematic of slab driving with basal and transform drag creates errors would exacerbate or improve the stress errors. horizontal tension in the direction of motion of most However, in creating a flow pattern for the lower mantle, I subducting plates (Figure 3). However, Wiens and Stein was conscious that its own internal strain rates would have a [1984] showed that the stress state of oceanic lithosphere is much more complex and includes considerable thrust faulting in the older parts of the plates. All the models of this group tendency to "read through" as surface strain rates within the lithospheric plates, thereby biasing the predicted directions of intraplate stress. This would fatally compromise the use of have mean stress direction errors of over 48 ø, which suggests stress directions to score and compare models with different that they are weakly anticorrelated with the true stress field. lower mantle flows. For that reason, I computed another set of models with a lower-mantle flow pattern that is not a 3.2. Models Superimposed on Active Mantle Convection solution of the convection equations but which has no strain At this point there seemed to be no alternative but to reject rate within plates to read through: the angular velocities the conventional wisdom of the last 20 years and return to the assumed for the lower mantle are exactly those of the NUVEL view that the plates may be partially driven from below by 1 model of surface plate flow, except slightly faster or slower, active convection. That is, in the asthenosphere the radially by a uniform velocity factor for each computation. (As was normalized or angular velocity might increase rather than mentioned above in discussing velocity boundary conditions, decrease with depth, and work might be done on the the NUVEL 1 model of relative plate motions was converted lithosphere (at least locally) by density anomalies deeper in to a model of absolute motions by fixing Africa.) the Earth. It was immediately obvious (Figure 2, circles and squares marked "N") that this was a way to obtain solutions with lower kinematic and stress errors than those seen before. The reduction in velocity errors is a natural result of strongly forcing every part of the lithosphere through the stiff basal boundary condition and does not mean that these models are -e- Stress direction (deg.) I SGPer;edtiinc reti (reflecting a Rayleigh number about 30x less than the Earth's); so I scaled all of his computed velocities up by an order of magnitude. (Further velocity factors listed in Table i were compounded with this basic adjustment.) Twelve models were computed with this flow pattern assumed at 400 km: both with and without the NUVEL 1 velocity boundary 10 condition on subducting slabs and at six different velocity factors. Asthenosphere temperature was held at 1200øC because previous experience suggested that coupling at 1300 ø o 1 2 or 1400 ø might be too weak to give a qualitatively different solution and because 1100 ø is probably too low to be Angular Velocity of Flow/NUVEL-1 consistent with adiabatic melting beneath mid-ocean rises. Fault friction was held at a very low 0.03 in order to let the Figure 4. Misfit measures of 10 models with different mantle convection pattern have a strong influence on the surface flow. Figure 2 (circles and squares marked "B") shows that the velocity factors for the assumed lower-mantle flow. All had the NUVEL 1 flow pattern, asthenosphere temperature of 1200øC, plate boundary fault friction of 0.03, and subducting stress direction errors in this group of 12 models were slabs constrained to move at NUVEL 1 velocities. The uniformly much lower than those of the previous mantle class: 320~39 ø. This gives a strong suggestion that an active lower mantle is an important part of the plate-driving system. The models with velocity boundary conditions on slabs mostly have lower kinematic errors than those with free slabs, geodetic error indicator weakly prefers velocity factors of , but this may be a provincial effect. The stress direction and seafloor-spreading error measures are parallel and indicate a strong preference for deep flow with angular velocities higher than those at the surface. 5O.,-, 40 ß g

11 BIRD: GLOBAL MODELS OFTHE FAULTED LITHOSPHERE 10,125 dynamically superior. However, the reason for the temperatures. Thus drag might be forward and large under improvement in stress directions is less clear. This class of models was expanded to 32 tests, investigating many the slow moving, viscous continents but backward and small under the fast moving, well-lubricated oceanic plates. As a combinations of different basal velocity factors, test of this concept, I created a final set of models in which asthenosphere temperatures, and fault frictions, as well as testing these both with and without the velocity boundary condition on subducting slabs. In the two-dimensional misfit space of Figure 2, these models form two trends with positive slopes: one for the free NUVEL 1 angular velocities (xl. 1 ) were again assumed at 400 km, but all basal tractions (of either sign) were restricted to the continents (defined as areas with elevation above-2500 m and heat flow less than W/m2). This set of models is shown with circles and squares slab models and one for the models with velocity boundary marked "C" in Figure 2. The models with free slabs at conditions on slabs. In each trend the upper right (inferior) subduction zones are not very successful because in them the end is associated with high asthenosphere temperatures, oceanic plates are too sluggish. However, in the group with which imply weak coupling to the lower mantle. In fact, at 1400øC, one slab driven model gives almost identical results to a mantle model which is also slab driven. (This shows that it would be pointless to consider higher asthenosphere temperatures.) Along the two trends, at equal asthenosphere temperature, the addition of velocity boundary conditions on slabs decreases the velocity misfit but increases the stress direction error by 40-8 ø, as was seen previously in velocity boundary conditions on slabs, the best model scores almost as well as the best of the models in the previous group. As before, I tested the effects of fault friction in this group over the range , while holding the lower-mantle flow constant and the asthenosphere reference temperature constant at 1200øC. Figure 5 shows the variation in model misfits; as before, the lowest friction tested gives the best results. This very low friction confirms the surprising the mantle class of models. When asthenosphere weakness of major faults that has previously been found in temperature is as low as 1100ø-1200øC the two trends models of California [Bird and Kong, 1994], Alaska [Bird, converge, and velocity boundary conditions on slabs have 1996], and Eurasia [Kong and Bird, 1996]. It also almost no differential effect, presumably because their retrospectively confirms that the very low friction values that were used in most of these tests were reasonable and did not information is redundant with that coming from the stiff basal boundary condition. In this region of parameter space, two additional sets of tests were performed. I first tested 10 different values of the velocity factor for the lower-mantle flow, holding all other parameters constant (slab velocity boundary conditions, asthenosphere temperature 1200øC, fault friction 0.03). The geodetic misfit measure shows (Figure 4) a very weak preference for velocity factors However, both the seafloor spreading and the stress direction errors are smallest for velocity factors slightly over 1.0, that is, for lower-mantle flow at angular velocities slightly faster than the surface plates. I give greater weight to them because the error minima are clearer and because these two data sets are more voluminous and global. I also tested the effects of different values of plate boundary fault friction, from a high of 0.72 to a low of These tests were done at two different asthenosphere temperatures (1100 ø and 1200øC) because the optimal transform drag might depend on the strength of basal drag. Subducting slabs were left free to accentuate the differences between models. At 1100øC the variations in the various misfit measures caused by friction are very small, but is the best value of friction. At 1200øC, 0.03 is also the best friction Models with basal drag confined to continents. There are serious dynamic problems with the concepthat all lithosphere is driven by basal drag (discussed below). However, most of the stress azimuth data used for scoring these models come from the continents; so it seemed possible that such forward basal drag might be needed only under continents. Alvafez [1982] proposed such a model, in which only continents are strongly linked to the convection of the lower mantle. Higher viscosity in the upper mantle below continents was also proposed by Doin et al. [1997] as a way to explain the apparent stability of continental roots and bolstered by the argument that depletion in volatiles could explain such higher strength without requiring much lower bias the solutions. Figure 6 shows the predicted stresses from the best model in this class, This model had basal drag only under continents (NUVEL 1 pattern, velocity factor 1.1, asthenosphere temperature 1200øC) and weak faults (friction 0.03) and velocity boundary conditions on subducting slabs. Its misfits are 11 mrn/yr for geodetic velocities, 32 ø for stress directions, and 23 mrn/yr for spreading velocities. (Large spreading errors, up to 104 mrn/yr, occur along the short Cocos-Pacific segment of the East Pacific Rise. If these 'C= 25 c lrl, O.2O -e-- Stress direction (deg.) -1-- Spreading rate (mm/a) --o--geodetic velocity (mm/a) 0o_4,...-o o Friction of plate-boundary faults Figure 5. Misfit measures of six models with different values of plate boundary fault friction. All had continents interacting with the NUVEL 1 flow pattem (at velocity factor 1.1) in the lower mantle, no drag beneath oceanic lithosphere, asthenosphere temperature of 1200øC, and subducting slabs constrained to NUVEL 1 velocities. Each error measure favors the lowest friction tested (0.03).

12 10,126 BIRD: GLOBAL MODELS OF THE FAULTED LITHOSPHERE ( 3E+12 N/m STRESS REGIMES:,, normal faulting strike-slip faulting thrust faulting Figure 6. (top) Vertically integrated stress anomalies and (bottom) most compressive stress directions in the lithosphere predicted the preferred model (97001, with mean stress direction error 32 ø) which is driven by a combination of active basal drag on the base of continents (only), slab velocity boundary conditions, and topography. Conventions as in Figure 3. Except in the vicinity of the 90 ø East Ridge, stress anomaly magnitudes are small and comparable in range to topographic stresses, as inferred by Bird and Li [ 1996].

13 ,, BIRD: GLOBAL MODELS OF THE FAULTED LITHOSPHERE 10,127 errors are excluded, the RMS spreading error in the rest of the model is only 5.1 mm/yr.) Despite these uncomfortably large remaining errors, its stress directions are clearly quite similar to the robust features of the World Stress Map data set [e.g., Bird and Li, 1996, Figure 5]. In eastern North America the ENE-WSW direction of O h results from a combination of compression radiating from Iceland and relative tension radiating from the Antillean subduction zone. In Europe, NW-SE compression results from combined basal driving tractions and ridge push forcing the continent into the Tethyan collision zone. Radial compression around Tibet results from its high topography and potential energy and gives little direct information about mantle convection. In South America, E- W compression results from basal driving tractions and ridge push forcing the continent westward against another high buttress in the Andes. Russo and Silver [1996] have also argued that the continued convergence of the South America plate with the Andes cannot result entirely from ridge push, but requires a large component of active basal drag. 4. Discussion These results show that the "conventional wisdom" about plate-driving mechanisms is incomplete. Hypotheses in which driving forces result only from elevation differences between rises and trenches (balanced by passive basal drag and fault friction) do not succeed because they cannot move the plates at actual rates. First, this is partly because most plates lack the simple geometry assumed in such idealizations; their leading edges are often the overriding plate in a subduction zone or are involved in a continental collision. For the Pacific plate the hypothesized forces are present but are insufficient to shear its huge area over an upper mantle with the laboratory creep law of olivine, at a reasonable asthenosphere temperature. I am also unable to find a successful model in which plates move over a resisting lower mantle at velocities dictated by their attached subducting slabs, which was the hypothesis of Forsyth and Uyeda [1975]. While such models can succeed kinematically (if all basal and edge drags are small), their predicted stress directions are bad: actually anticorrelated with data. Second, we see that even a simple model of present mantle convection in the Earth [Baurngardner, 1988] yields better predictions of stress directions than any model with a (or relatively ) lower mantle, as long as this convection is rapid enough to provide forward or active driving traction on the base of the slower plates ,, ' :-"1,... ' - -,, ', '...,,,..., 0...,,,... i,, based on olivine rheology - limited by maximum viscosity 0.5 MPa Figure 7. Horizontal shear tractions on the base of the lithosphere in the preferred model Drag acts only on continents, the angular velocities assumed at 400-km depth to compute continental drag are from the NUVEL 1 surface model times 1.1, and the reference temperature for the subcontinental adiabat is 1200øC. Most values are based on the same laboratory theology for olivine as used in the lithosphere. However, for numerical stability a limit must be placed on the ratio of basal traction to basal velocity discrepancy ((I) of Bird [1989]); values which were reduced to observe this limit are indicated by a crossbar. Mercator projection, but vector sizes are not exaggerated at high latitudes.

14 10,128 BIRD: GLOBAL MODELS OF THE FAULTED LITHOSPHERE Third, if plates are driven from below by an artificial pattern of lower-mantle flow that mimics plate tectonics, then expected improvements in the kinematics of the model are These amount of forward basal drag on continents required in this hypothesis is quite modest. Figure 7 shows the basal tractions in the preferred model 97001; they are only accompanied by unexpected improvements in predicted stress MPa in most places. Such shear stresses are consistent with directions. This is not a trivial result, because the lower mantle flow to which each plate is coupled is platelike and strain free and does not impose any particular strain rate or stress direction at the surface. Instead, the deviatoric stresses result from topography and/or plate interactions along boundaries. Could there be a dynamically complete model of mantle convection that would create forward basal drag on all plates? Recent work by Lithgow-Bertelloni and Richards [1995] and also by Deparis et al. [ 1995] has led to the suggestion that old subducted slabs stir the mantle as they sink and drive the the laboratory rheology of olivine (at -1200øC) and would probably not produce detectable dynamic topography or iso gravity anomalies. However, a basal traction of 0.5 MPa acting across a continent of 4000-km width produces a change of 2x10 2 N/m in the vertical integral of horizontal compressive stress from one side to the other, an amount comparable to most estimates of ridge push. It is not entirely satisfactory to divide the Earth into two systems, modeled separately, as I have here. Our long-term objective must be a single model of mantle convection incorporating a surface lithosphere complete with faults, plates through basal tractions. Each group used a layered continents, and other heterogeneities. Yet the obstacles are Newtonian viscous approximation of the mantle for formidable. In the mantle convection modeling community, it mathematical convenience. From plate tectonic is generally accepted that models must pass through several reconstructions extending back to 200 Ma, they estimated the present positions of all slabs in the mantle. Then they found overturns before they can be assumed to be relatively free of the effects of their arbitrary initial conditions. However, this the velocities of the surface plates (ignoring edge interactions) would require several generations of model plates to be which would be driven by such a deep flow; they are reasonably close to actual velocities. Deparis et al. [1995] also showed that velocity predictions roughly match data from three epochs in the past. However, an important point about these models is that they involve artificial truncation of the strain rate singularities at plate boundaries and do not consider the effects of laterally heterogeneoustrength (i.e., strong slabs and weak faults). Consequently, they are not able to connect the old sinking slabs directly to the surface plates with stress guides and can only drive the plate by distributed basal tractions. In a more realistic mechanical model, one would expect any driving force from slabs in the upper mantle to be concentrated and transmitted through the slabs themselves (a possibility which I have explicitly tested). formed and destroyed on the surface during the computation. In turn, this requires knowledge of the physics of formation of new faults and the physics of fault weakening. It would also mean that no model could be expected to conclude with the actual geometry of the Earth's present plates. Until such unified models are possible, one interim approach is to use thin-shell lithosphere models such as these to test any proposed model of mantle convection which has been customized (in any creative way) to representhe present Earth. As was described above, our code and my finite element grid are available to anyone who wishes to test alternative mantle convection models in the way that I have tested the model of Baumgardner [1988]. If such tests give lower misfits for both plate velocities and internal stresses, Whether slabs sinking through the lower mantle could that convection model would be established as the current contribute to driving plates would depend on the relative velocity magnitudes of the deep slabs and the surface plates in question. Much recent work on the viscosity structure of the mantle [e.g., Mitrovica and Forte, 1997] has led to a consensus that best approximation. However, these results strongly suggest that continental crust is (on average) more strongly coupled to the lower mantle than oceanic crust, and such lateral strength variations may play an important role in the dynamics of the. Earth at all depths, not only at the surface. viscosities are much higher below the transition zone than in the asthenosphere above. Consequently, subducting slabs would be expected to slow down at depth and to stir the lower mantle at only a fraction of the surface velocities of oceanic plates. If this is true, it is almost inconceivable that the lower mantle could exert forward basal tractions on the fast moving Acknowledgments. This work was supported by the Geophysics Program of the National Aeronautics and Space Administration under grant NAGW-3042 to the University of California Los Angeles. All opinions are those of the author and do not necessarily representhe position of NASA or the United States government. oceanic plates. However, it still remains a possibility that the lower mantle could exert forward basal tractions on the slowest plates: Africa, Eurasia, North America, South America, and Antarctica. These contain 91% of the Earth's land and probably a similar fraction of its continental crust. (The negative correlation of plate speed with continental area was first noted by Forsyth and Uyeda [1975].) If thermal or compositional differences can be invoked to make the asthenosphere more viscous under continents, then it is dynamically reasonable for slow moving continents to be driven from below, as first proposed by Alvarez [1982]. Long-standing teleseismic results point to such systematic differences between continental and oceanic upper mantle [Jordan, 1988], necessarily extending to at least 300- to 400- km depths. References Alvafez, W., Geologic evidence for the geographical pattern of mantle return flow and the driving mechanism of plate tectonics, J. Geophys. Res., 87, , Anderson, O. L., The Earth's core and the phase diagram of iron, Philos. Trans. R. Soc. London, Set. A, 306, 21-35, Artyushkov, E. 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