Predicted magnitudes and directions of lithospheric stresses, free plate motions and dynamic topography for some other tomographic models, and locations of hotspots are shown in Fig. 15 to 23. For simplicity, ``other'' topography h<sub>sc</sub> is disregarded for computing plate motions, i.e. we only compute the first step of the iteration outlined in section 3 of this background data. It was found that results only slightly change if ``other'' topography is included. Dynamic topography was computed for plates moving at half the speed of free motion in each case. For the p-wave models, p-wave anomalies were first converted to s-wave anomalies, assuming both are due to thermal anomalies (Calderwood, 1999). For the model Global_P+PKP, a conversion factor as for the Grand model was used. In all other cases, is used. This smaller value is still roughly in accord with mineral physics and other evidence (Karato, 1993; Forte et al., 1994) , and it is used in order to account for the higher amplitudes of these models. Again, anomalies above 220 km depth are excluded. In all other aspects, calculations are done as in Fig. 5 of the main text, i.e. for an elastic lithosphere, with the same parameters, with plates moving at half the speed of free motion and including all stresses.

We use an expansion of the flow field up to maximum degree l_max = 15 for the models S12WM13 (Su et al., 1994) and SAW12D (Li and Romanowicz, 1996) and up to l_max = 31 for all others. For some of the density models, the degree of expansion is less than l_max, which was chosen for technical reasons, as Fast Fourier Transform is applied and requires a degree l_max = 2ⁿ-1, e.g. 15 or 31. If the density field only has terms up to a degree l₀ < l_max, internally driven part of the flow field (assuming a fixed upper boundary) for l > l₀ also vanish. On the other hand, if there is a plate-like surface velocity, the flow field will always have terms up to any arbitrary degree. It has been pointed out by Hager and O'Connell (1981) that due to stress singularities computed in theory at plate boundaries, torques acting on plates depend on l_max with the torque magnitude roughly proportional to the logarithm of the degree of expansion. In practice, these singularities do not occur, because along plate boundaries the assumed rheology is no longer valid. Because of the finite degree of expansion, the singularities do not occur in our computations either.

Although the patterns of stress directions look similar for different tomography models in general, they are different in a few regions: For example, based on some of the other models no ring-shaped stress pattern but rather a uniform northwest- southeast stress direction is predicted in Eastern Europe and Scandinavia, in agreement with the interpolations. For the s-wave models S12WM13 (Su et al., 1994), SAW12D (Li and Romanowicz, 1996), S20A (isotropic part) (Ekström and Dziewonski, 1998), S20RTS (Ritsema and Van Heijst, 2000), SAW24B16 (Mégnin and Romanowicz, 2000), SB10L18 (s-wave) (Masters et al., 2000) and SB4L18 (Masters et al., 2000) mean azimuth errors are 31.47^°, 32.66^°, 26.58^°, 26.92^°, 30.41^°, 30.81^° and 30.09^° respectively, for Global_P+PKP (Kárason et al., 1997) and SB10L18 (p-wave) (Masters et al., 2000) it is 33.75^° and 29.70^°. Stress directions and mean azimuth errors for viscous and elastic lithosphere are very similar for all models. The effect of including density variations within the lithosphere, and of using different plate motion models was already shown for the Grand model in the main text, and it remains similar for these models: again, patterns of stress directions do not strongly depend on which plate motions are used, and are not strongly affected by including density variations within the lithosphere.

References

A.R. Calderwood, Mineral Physics Constraints on the Chemical Composition and Temperature of the Earth's mantle, Ph.D. thesis, University of British Columbia, 1999.

G. Ekström, A.M. Dziewonski, The unique anisotropy of the Pacific upper mantle, Nature, 394 (1998) 168-172.

A.M. Forte, R.L. Woodward, A.M. Dziewonski, Joint inversion of seismic and geodynamic data for models or three-dimensional mantle heterogeneity, J. Geophys. Res., 99 (1994) 21,857-21,877.

H. Kárason, R.D. van der Hilst, K. Creager, Improving seismic models of global p-wave speed by the inclusion of core phases (abstract), EOS Trans. AGU, 78 (46), Fall Meet. Suppl. (1997) F17.

S. Karato, Importance of anelasticity in the interpretation of seismic tomography, Geophys. Res. Lett. 20 (1993) 1623-1626.

X.D. Li, B. Romanowicz, Global Mantle Shear-Velocity Model Developed Using Nonlinear Asymptotic Coupling Theory, J. Geophys. Res., 101 (1996) 22245-22272.

G. Masters, G. Laske, H. Bolton, A. Dziewonski, The relative behavior of shear velocity, bulk sound speed, and compressional velocity in the mantle: implications for chemical and thermal structure, in: S. Karato (Ed.), Seismology and Mineral Physics, Geophys. Monogr. Ser., 117, AGU, Washington, D. C., 2000, pp. 63-87.

C. Mégnin, B. Romanowicz, The shear velocity structure of the mantle from the inversion of of body, surface and higher modes waveforms, Geophys. J. Int, 143 (2000) 709-728.

J. Ritsema, H.J. Van Heijst, Seismic imaging of structural heterogeneity in Earth's mantle: Evidence for large-scale mantle flow, Science Progress, 83 (3) (2000) 243-259.

W.-J. Su, R.L. Woodward, A.M. Dziewonski, Degree 12 model of shear velocity heterogeneity in the mantle, J. Geophys. Res. 99 (1994) 6945-6980.

Figures

Figure 15: Predicted dynamic topography and plate motions (above) and lithospheric stress anomaly (below) for the Harvard model S12WM13 (Su et al., 1994). Here and in the following figures, plate motions are expanded up to spherical harmonic degree 127 and arrow length 222 km (2 degrees at equator) corresponds to 1 cm/year.

Figure 16: Predicted dynamic topography and plate motions (above) and lithospheric stress anomaly (below) for Harvard model S20A (isotropic part) (Ekström and Dziewonski, 1998).

Figure 17: Predicted dynamic topography and plate motions (above) and lithospheric stress anomaly (below) for Berkeley model SAW12D (Li and Romanowicz, 1996).

Figure 18: Predicted dynamic topography and plate motions (above) and lithospheric stress anomaly (below) for Berkeley model SAW24B16 (Mégnin and Romanowicz, 2000).

Figure 19: Predicted dynamic topography and plate motions (above) and lithospheric stress anomaly (below) for CalTech model S20RTS (Ritsema and Van Heijst, 2000).

Figure 20: Predicted dynamic topography and plate motions (above) and lithospheric stress anomaly (below) for Scripps model SB4L18 (Masters et al., 2000).

Figure 21: Predicted dynamic topography and plate motions (above) and lithospheric stress anomaly (below) for Scripps model SB10L18 (s-wave) (Masters et al., 2000).

Figure 22: Predicted dynamic topography and plate motions (above) and lithospheric stress anomaly (below) for Scripps model SB10L18 (p-wave) (Masters et al., 2000).

Figure 23: Predicted dynamic topography and plate motions (above) and lithospheric stress anomaly (below) for MIT model Global_P+PKP (Kárason et al., 1997).