SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION DOI: /NGEO2525 Cratonic root beneath North America shifted by basal drag from the convecting mantle Supplementary Materials SM1. Construction of a 3D density model of the upper mantle. The 3D density model of the compositional variations in the upper mantle is based on the inversion of the residual gravity field and residual topography. They are obtained after removing the following three effects from the observed fields: (1) the effect of the crust, (2) the effect of temperature variations in the upper mantle 7, (3) the effect of deep density variations below 325 km as estimated by a recent instantaneous mantle flow model 10. It is important to estimate uncertainties in the corrections that have been made. The effect of deep density variations represents a very long-wavelength trend over North America 10, and therefore its uncertainty cannot influence the principle result concerning the deep geometry of the cratonic root. The impact of the first two factors is analyzed in detail by Mooney and Kaban 9. It has been demonstrated that the uncertainty of the crustal correction may vary from 35 mgal for the well-studied regions of North America to about 70 mgal for the regions with thick crust and poor seismic coverage. The corresponding uncertainty of the residual topography ranges from 0.3 km to 0.6 km. The lower value of uncertainty is more appropriate for the main part of the study area. The maximal gravity effect of the uncertainty for the thermal correction could be up to mgal ( km for the residual topography) depending on a quality of the tomography model 7,9. The residual topography is additionally biased by isostatic disturbances of the lithosphere. The short wavelength anomalies associated with the non-compensated load can be filtered out to a large extent by considering only mid- or large-scale anomalies (>400 km), while long-wavelength disturbances, e.g. related to postglacial deformations, have relatively low amplitudes 31. Therefore, the total uncertainty is within 100 mgal for the residual gravity field and within 1 km for the residual topography 9. We analyze the anomalies with amplitudes that are about 3 times larger than these values (Figure 1), therefore the principal results are sufficiently well constrained. Calculations based on the joint inversion of the residual gravity and residual topography provide much improved constraints on the 3D density structure of the upper mantle in comparison with inversions of gravity data alone. The residual gravity and topography depend on density heterogeneity but in fundamentally different ways depending on size and depth of the density anomalies. This is clearly demonstrated by gravity and topography kernels showing a response from a single density anomaly, NATURE GEOSCIENCE 1

2 considered as a function of the wavelength (spherical harmonic number). Two examples corresponding to different depths are demonstrated in Figure S1. It is clear that for the upper mantle the amplitude of the dynamic topography decreases much more slowly than that of the gravity field when increasing both depth and spherical harmonic degree/order (decreasing wavelength). This difference opens the possibility for using a joint inversion of these fields to constrain depth of the principal anomalies in the upper mantle. Figure S1. Normalized gravity and topography kernels 26 for a typical continental viscosity profile 27 (Figure S2). The gravity kernels reflect a direct effect of the density variations since the effect of all surface perturbations is removed from the observed gravity field before hand and the residual mantle anomalies reflect the effect of mass anomalies below Moho. The topography response is negative with respect to the initial density anomaly; positive values are shown for comparison with the residual gravity. The inversion is performed in a spherical harmonic domain, where the solution can be found separately for each spherical coefficient 27. The maximal spherical harmonic degree is limited to 90, which corresponds to the horizontal resolution 2 x 2. The damping factor in equation (1) is α=2πghd n, where D n is the normalized damping, h - the thickness of the elementary cells used in the inversion and 2

3 G is the gravitational constant. The dynamic topography is calculated for a predefined viscosity structure as explained below. In the inversion we employ only radial viscosity variations (black line in Figure S2). The effect of lateral variations of viscosity, including weak plate boundaries, on the dynamic topography is insignificant for North America 28 and represents a very long-wavelength trend that won t affect the modeled anomalies in the upper mantle. Figure S2. Vertical viscosity distribution. (Black): reference radial viscosity 27 ; (Grey): limits of viscosity variations in the model with LVV 10,28 ; (Red): simplified radial viscosity model used for comparison (see text). The inversion technique has been validated with numerical tests. A density model with several density patterns that are representative of the real Earth (Figure S3) has been implemented in a spherical shell and the model s effect on the gravity field and topography has been computed. Realistic noise (RMS is 30% of the signal) has been added and both fields have been inverted in order to reproduce the density structure. It is found that in most cases it is possible to reconstruct initial density patterns including various combinations of positive and negative anomalies (Figure S3). The most difficult case is 3

4 represented by separate anomalies of the same sign. In this case it is hardly possible to divide the anomalies in the inversion, however the general configuration is adequately determined. Due to damping, the inverted amplitudes are generally lower up to ~30% than the initial ones, which should be taken into account while interpreting the results. Figure S3. Cross-sections showing the initial and reproduced density structure: (A) The initial and adjusted gravity field (D n = 0.5). The misfit of the dynamic topography is equivalent to the misfit of the gravity anomalies since the weighting for both parameters is normalized (Equation 1); (B) Initial density model; (C-D) Inverted densities for different values of the normalized damping factor (D n ). The value of the damping factor is assigned based on the amplitude of the inverted densities (Figure S4). In the initial stage, an increase of the damping factor rapidly reduces the impact of the noise. Further increase of the damping leads to smearing of the amplitude of the inverted density model. The transition point, which corresponds to a change of the slope (Figure S4), may be considered as an optimal solution. It is clear from the Figure S3 that the solution remains stable within a wide range of the damping factor, therefore its precise selection is not critical. 4

5 Figure S4. Amplitude of the inverted density model versus damping factor. The steep part is chiefly associated with the noise reduction while the flatter one is associated with smearing of the solution. The transition point corresponds to the optimal solution. The assumed viscosity of the mantle, required for the estimation of the dynamic topography, is the most uncertain parameter in the inversion. However, the topography kernels are not very different for reasonable alternative viscosity models for the upper mantle 26. To assess this effect, we perform inversion for an alternative viscosity model (Figure S2, red line) that can be considered as oversimplified relative to the reference model based on various studies 27 (Figure S2, black line). Notably, viscosity is not decreased within the transition zone in this model, in contrast with the reference model, which is an important factor for global convection models 27. The results for both models for the 1 st transcontinental profile (Figure 2) are compared in Figure S5. The maximum difference between the models is less than 3 kg/m 3 and the geometry of the main anomaly is changed insignificantly. Therefore, uncertainty of the mantle viscosity doesn t affect robustness of these results. 5

6 Figure S5. Compositional density variations in the upper mantle along the 1 st transcontinental profile (Figure 2). Solid lines correspond to the reference viscosity model and the dashed ones correspond to the oversimplified alternative model (see text). The maximum difference between the two models is less than 3 kg/m 3. We also estimate effect of the shifted depleted root under the Superior craton on the gravity field and topography (Figure S6). This provides a quantitative evaluation of whether this effect is large enough to be modelled with the existing data. The effect of the shifted root turns to be strong, especially for the dynamic topography (Figure S6-b) which reaches 1 km, the amplitude that is sufficiently resolved by the initial data. Therefore, an alternative model without the shifted root would lead to an unacceptable discrepancy with the residual gravity field and residual topography. 6

7 Figure S6. Effect of the shifted depleted root under the Superior craton on the gravity field (a) and dynamic topography (b). (c): Compositional density variations in the upper mantle along the 1 st transcontinental profile (Figure 2). The black line shows the part of the root, which effect is estimated (a and b). See text for discussion. SM 2. Calculation of mantle flow velocities and dynamic topography. We use the numerical code ProSpher 10 to calculate instantaneous flow velocities in the mantle and dynamic topography. The code is based on the decomposition of all physical parameters into spherical harmonics that permits a semi-analytical solution of the Navier-Stokes and Poisson equations 32. Because of its high computational efficiency, this method has been widely used for decades 33,34,35. However, with its classical formulation this method was not able to operate with a three-dimensional distribution of viscosity. To employ strong lateral variations of viscosity (LVV), which are typical for the upper mantle and the lithosphere, a new numerical approach 10 has been developed, based on a substantially revised iterative method of Zhang and Christensen 36. The ProSpher code offers the advantages of both spectral-based and FD/FE numerical methods, taking into account strong LVV 7

8 (about 5 orders of magnitude in each layer), self-gravitation and compressibility. The new code has been extensively tested with various benchmarks from both theoretical estimates and models computed with other numerical codes (i.e. CitcomS) 37,38. The discrepancy of flow velocities with all benchmarks are within 3% RMS 10, which is easily sufficient for this study. Importantly, the code can tackle the large viscosity contrast between lithospheric plates and weak plate boundaries. The numerical model is global, and is based on the S-wave tomography model S40RTS 25 supplemented with the high-resolution data for North America 12. Density variations (Δρ) are derived from V s variations by applying the velocity-to-density scaling factor = d(lnδρ)/d(lnδv s ) = ,28. Next, the procedure involving conversion of the homologous temperature variations to viscosity (η) is used to obtain a 3D viscosity model 39 : ( r,, ) 0( r)exp E( r) T a T m ( r) (S1) ( r) T ( r,, ) The homologous temperature is the ratio of the actual temperature to the melting point. The depthdependent melting temperature T m (r) is calculated according to Yamazaki and Karato 40. The coefficient E(r) scales the amplitude of lateral viscosity variations (LVV). The pre-exponential term η 0 (r) calibrates the viscosity according to the predefined radial viscosity profile (Figure S2) 28. Temperature variations T ( r,, ) are derived from the density anomalies by applying a depthdependent thermal-expansion coefficient 39, which in combination with the adiabatic temperature profile 42 T a (r) gives a 3D temperature distribution. Tectonic plates are introduced as shells with constant viscosity of Pa s, and with a thickness of 50 and 100 km for the oceanic and continental plates, respectively. The weak plate boundaries (WPB) are implemented based on an integrated global model of plate boundary deformations GSRM 41. They have the viscosity 4 orders of magnitude less than the tectonic plates, which is sufficient to provide an efficient mechanical decoupling between them 28. Additionally, to improve resolution of the tomography-based density and viscosity models along narrow subduction zones, a global model of slab geometries has been used 29. Densities in the continental lithosphere are also corrected taking into account depletion of the cratonic lithosphere. For North America the model of Mooney and Kaban 9 is employed, whereas for other continents we use the results from the global study 43. The resolution of the grids is 2 x 2 in the horizontal direction and 50 km in the vertical direction. 8

9 Modeling of the plate motion and mantle flow velocities is an ill-defined problem due to several parameters that are not well known. Therefore additional constraints should be used to find a proper solution. The most critical parameters are the viscosity distribution within the mantle and rheologically weak boundaries dividing lithospheric plates 44,45. The vertical viscosity profile (Figure S2) is based on global studies and is constrained by surface observables (geoid and global plate velocities) and mineral physics 27. For the lateral viscosity variations (Eqs. S1), the most critical is the parameter E (r). Modeling of the direction and amplitude of motion for the Northern America plate is very sensitive to its amplitude 44. We have adjusted E(r) in such a way to obtain the best-fit solution with global GPS values by varying this parameter in the range ±30% at each depth for the upper mantle 28. This parameter varies within for depths of 50 to 200 km; then it decreases to 5 down to 400 km and is equal to 10 at greater depths in the mantle. The corresponding lateral viscosity variations (Equation S1) reach ~4 orders of magnitude 28. The strength of the weak plate boundaries (WPB) is another critical parameter affecting plate motions. In a recent study 28 we carried out a sensitivity test of its value on the dynamics of lithospheric plates. This test demonstrates that the results become stable when the viscosity contrast at WPB exceeds orders of magnitude. Any further decrease of the strength has almost no effect on the plate velocities, geoid and dynamic topography 28. Since WPB are less viscous (by 4 orders of magnitude in our model); the possible uncertainty of this parameter doesn t affect the result significantly. After all the adjustments, the 3D viscosity model is very similar to the recent model of Ghosh and Holt 45 which, in turn, is also in a good agreement with the observed plate velocities. To evaluate the sensitivity of the dynamic model to the 3D viscosity structure, we calculate an alternative model based on purely radial viscosity distribution 27 (Figure S2, black line). However, the laterally uniform lithosphere is divided by weak plate boundaries (WPB) as described above. All other parameters are the same as in the more comprehensive model. Resulting velocities (Figure S7) differ significantly from those ones shown in Figure 3. The alternative model doesn t provide reasonable fit to the GPS values and the North American lithosphere moves in the opposite direction. However, even this simplified model demonstrates opposite flow patterns under the lithosphere (Figure S7). Although the surface plate velocities are wrong, westward mantle flow appears below 200 km under the Superior craton and increases with depth. Therefore, the direction of the basal drag is a stable characteristic of the mantle flow pattern, being a part of the Earth s global convection. 9

10 Figure S7. Calculated plate (a) and mantle flow (b) velocities for the 1 st transcontinental profile (Figure 3). Dotted line indicates the position of the profile. Black arrows show the mantle velocities for the more comprehensive model (Figure 3). Red arrows show the velocities for the alternative model of viscosity without lateral variations in the mantle (see text). Other parameters are as in Figure 3. Considering the principle results of this study, the most important output of the dynamic flow model is presence of the velocity gradient under the Superior Craton. We note that our instantaneous flow model provides an excellent fit to the independent results of Eaton and Frederiksen 8. SM 3. Evidence from kimberlites studies. Diamondiferous kimberlites are indicators of specific P-T conditions, which correspond to a diamond stability field, namely very high pressure (> GPa) and relatively low temperature ( C) 46. Such kimberlites have been found in several locations within the Superior craton (Figure 2). For example kimberlites in the northern field (Attawapiskat) might be associated with the Great Meteor hotspot passing beneath the area at 180 Ma 31,47. However, presently the depleted layer is too thin to fit the conditions required for diamond formation. Furthermore, thermo-barometry estimates from 10

11 samples obtained in the Wawa province (east shore of the Superior Lake, Figure 2) indicate at least km thick thermal lithosphere at Archean-Proterozoic. However, samples dated as Late Jurassic demonstrate significant thinning of the lithosphere up to 150 km 48. This finding provides evidence that the lower part of the lithosphere has been removed. Numerical modeling of the cratonic roots generally confirms stability of the depleted cratonic keels on a geological timescale, while some additional factors are required to destabilization them 49,50,51. The destabilization can be caused by a plume activity in the vicinity of the root 52. Therefore, appearance of the Great Meteor hot spot about 200 Ma 8 could have triggered the shift of the Superior craton. References (supplementary material). 31 Kaban, M. K., Schwintzer, P. & Reigber, C. A new isostatic model of the lithosphere and gravity field. J. Geod. 78, (2004). 32 Hager, B.H. & O Connell, R.J. A simple global model of plate dynamics and mantle convection. J. Geoph. Res. 86, (1981). 33 Ricard, Y., Fleitout, L., Froidevaux, C. Geoid heights and lithospheric stresses for a dynamic earth. Annales Geophysicae 2, (1984). 34 Forte, A.M., Peltier, W.R. Plate tectonics and aspherical earth structure: the importance of poloidaltoroidal coupling. J. Geoph. Res. 92, (1987). 35 Steinberger, B. & Torsvik, T.H. Absolute plate motions and true polar wander in the absence of hotspot tracks. Nature 452, (2008). 36 Zhang, S. & Christensen, U. Some effects of lateral viscosity variations on geoid and surface velocities induced by density anomalies in the mantle. Geoph. J. Intern. 114, (1993). 37 Zhong, S., Zuber, M.T., Moresi, L. & Gurnis, M. Role of temperature-dependent viscosity and surface plates in spherical shell models of mantle convection. J. Geoph. Res. 105, (2000). 11

12 38 Tan, E., Choi, E., Thoutireddy, P., Gurnis, M. & Aivazis, M. GeoFramework: Coupling multiple models of mantle convection within a computational framework. Geochemistry, Geophysics, Geosystems, 7(6), Q06001, doi: /2005GC (2006). 39 Paulson, A., Zhong, S. & Wahr, J. Modelling post-glacial rebound with lateral viscosity variations. Geoph. J. Int. 163, (2005). 40 Yamazaki, D. and Karato, S. Some mineral physics constraints on the rheology and geothermal structure of Earth s lower mantle. American Mineralogist 86, (2001). 41 Kreemer, C., Holt, W. E. & Haines, A. J. An integrated global model of present-day plate motions and plate boundary deformation. Geophys. J. Int. 154, 8 34 (2003). 42 Katsura, T., Yoneda, A., Yamazaki, D., Yoshino, T. & Ito, E. Adiabatic temperature profile in the mantle. Phys. Ear. Plan. Inter. 183, (2010). 43 Kaban, M.K., Schwintzer, P., Artemieva, I.M., Mooney, W.D. Density of the continental roots: compositional and thermal contributions. Ear. Plan. Sci. Let. 209, (2003). 44 Ghosh, A., Becker, T. W. & Humphreys, E. D. Dynamics of the North American continent. Geophys. J. Int. 194, (2013). 45 Ghosh, A. & Holt, W. E. Plate motions and stresses from global dynamic models. Science 335, (2012). 46 Kennedy, C. S. & Kennedy, G. C. The equilibrium boundary between graphite and diamond. J. Geophys. Res. 81, (1976). 47 Smit, K. V., Stachel, T. & Stern, R. A. Diamonds in the Attawapiskat area of the Superior craton (Canada): evidence for a major diamond-forming event younger than 1.1 Ga. Contrib. to Mineral. Petrol. 167, 1 16 (2014). 48 Miller, C., Kopylova, M. & Ryder, J. Vanished diamondiferous cratonic root beneath the Southern Superior province: evidence from diamond inclusions in the Wawa metaconglomerate. Contrib. to Mineral. Petrol. 164, (2012). 12

13 49 Beuchert, M. J., Podladchikov, Y. Y., Simon, N. S. C. & Rüpke, L. H. Modeling of craton stability using a viscoelastic rheology. J. Geophys. Res. Solid Earth 115, (2010). 50 Jurine, D., Jaupart, C., Brandeis, G. & Tackley, P. J. Penetration of mantle plumes through depleted lithosphere. J. Geophys. Res. 110, 1 18 (2005). 51 Lenardic, A., Moresi, L.-N. & Mühlhaus, H. Longevity and stability of cratonic lithosphere: Insights from numerical simulations of coupled mantle convection and continental tectonics. J. Geophys. Res. 108, 2303 (2003). 52 Griffin, W. L. et al. A translithospheric suture in the vanished 1-Ga lithospheric root of South India: evidence from contrasting lithosphere sections in the Dharwar Craton. Lithos 112, (2009). 13