1. Bernhard Steinberger Deutsches GeoForschungsZentrum, Potsdam and Centre for Earth Evolution and Dynamics, Univ. Oslo Geodynamic relations between subduction, plume generation, LLSVPs and true polar wander

2. Model ingredients: Thermal boundary layer caused by heat from the core Numerical model: Flow field computed in spherical harmonic domain (Hager and O'Connell, 1979, 1981) (l_max=127; 57 radial layers) Radial viscosity structure based on constraints from mineral physics and modelling geoid and other observations (Steinberger and Calderwood, 2006) Viscous incompressible; free-slip boundary conditions Time stepping on grid (128 x 256 grid points per layer) includes terms corresponding to (a) advection (with upwind differencing scheme) (b) diffusion --> radially only --> assign thermal density anomaly at CMB and surface --> thermal diffusivity 30 km 2 /Myr (c) heat production Model initiated at 300 Ma with small random fluctuations

3. 100 Ma Viscosity structure from Steinberger & Calderwood, 2006

4. 50 Ma

5. 0 Ma Plumes rather stable Relevance for Venus? Application to specific hotspots with seeding at specific locations

6. Margins of Large Low Shear Velocity Provinces (LLSVPs) of Lowermost mantle (here: smean tomography model by Becker and Boschi) are overlain by Most Reconstructed Large Igneous Provices (Torsvik et al., 2006) A large fraction of reconstructed Kimberlites (Torsvik et al., 2010) Many present-day hotspots (Thorne et al., 2004) Figure from Torsvik et al., Nature, 2010 Goal: Devise a numerical model that can explain (a) long-term stability of LLSVPs (b) plumes forming along their margins

7. Torsvik et al. (2006) LLSVPs often seen as chemically distinct: → anti-correlation of shear wave and bulk sound speed in lowermost mantle → explicit density models → steep and sharp edges

8. Evidence that LLSVPs are chemically distinct Anti-correlation of shear wave velocity and bulk-sound velocity v c =(K s /  ) 1/2 in lowermost mantle (Masters et al., 2000)

9. Explicit density model (based on free oscillations) indicates high densities beneath Pacific and Africa in the lowermost mantle Figure from Ishii and Tromp (2004)

10. Wang and Wen (2004) – waveform modelling and travel time analysis „VLVP (Very Low Velocity Province) has rapidly varying thicknesses from 300 to 0 km, steeply dipping edges … structural and velocity features unambiguously indicate that the VLVP is compositionally distinct.“

11. → True polar wander corrected (Steinberger & Torsvik, 2008) → Longitude shifted (van der Meer et al., 2010) Color = age; Darkness = amount of subduction Subduction history (compiled by Trond Torsvik):

12. Model ingredients: Thermal boundary layer caused by heat from the core Subducted lithospheric slabs sinking to the bottom of the mantle (Discontinuous) chemically dense layer at the base of the mantle Numerical model: Flow field computed in spherical harmonic domain (Hager and O'Connell, 1979, 1981) (l_max=127; 78 radial layers) Radial viscosity structure based on constraints from mineral physics and modelling geoid and other observations (Steinberger and Calderwood, 2006) Viscous incompressible; free-slip boundary conditions Time stepping on grid (128 x 256 grid points per layer) includes terms corresponding to (a) advection (with upwind differencing scheme) (b) diffusion --> radially only --> assign thermal density anomaly at CMB --> thermal diffusivity 30 km 2 /Myr (c) heat production (d) Insertion of slabs into the mantle --> Following Steinberger and Torsvik (2010) --> Longitude shifted (van der Meer et al., 2010) Model initiated at 300 Ma with small random fluctuations and a dense layer (32 kg/m 3 denser, 70 km thick) at the base

13. Numerical model I → Results from Steinberger and Torsvik (G-Cubed, 2012) → Based on spherical harmonic approach (Hager and O'Connell, 1979, 1981); only radial viscosity variations → initially flat thermochemical layer; 70 km thick

14. Shortcomings of numerical model I → Only radial viscosity variations; resulting plumes quite thick → Low resolution (l max =128) → Numerical diffusion, leading to entrainment of basal layer (ad-hoc fix: “push” chemical layer to bottom at each time step more appropriate: use tracers, but: in this model, chemical layer mixes with overlying mantle, becomes eventually buoyant unless higher above CMB, negative chemical buoyancy becomes stronger → Model initiated with flat thermochemical layer at 300 Ma (temporary fix: rerun with present-day structure for another 300 Myr – pattern remains similar but becomes less clear; planned fix: use plate reconstructions further back in time)

15. CitcomS Model Setup Chemical Layer at CMB: Initial Thickness Various material properties Radiogenic Heating Plate movement at surface: 250 Ma of plate history (Seton et al 2012) Viscosity Profile: Z,T-dependent (Steinberger & Calderwood 2006) Used Software: Citcoms Mesh-Size: 3.15 Mln Elements Spatial Resolution: ~50 km Ra – Number: 7*10 7 - 9*10 7

16. Model Plume positions and hot spots Hot Spots (Steinberger 2000), R=300 km 11 Selected Hot Spots (Torsvik et al 2006), R=1000 km Depth: 500 km

17. Plumes at Margins of LLSVPs Depth: 1890 km Shaded: Chemical Pile at CMB Black Line: -1% Vs (SMean) Isosurface: +200 K - Plumes tend to rise at edges of thermo- chemical piles

18. Statistics of the observed fit between model plumes and Earth's hotspots

19. Subduction zones Before formation of Pangea LLSVP Stability in space Reconstruction of LIPs and Kimberlites indicates long-term Stability (Torsvik et al., 2010) Back to at least 500 Ma Can a thermo-chemical “pile” survive subduction right above?

20. Figure from Zhang & Zhong (2010) - “degree 1 vs. degree 2”

21. LLSVP Stability in time → Long-term stability of “piles” “Primordial” or material continues to be added? (Basalt? Harzburgite?) → How much entrainment of material in plumes? Accurate model of advection and entrainment Is critical! From Trønnes, 2010

25. What is true polar wander? Motion of “Earth as a whole” relative to its spin axis

26. What is true polar wander? Motion of “Earth as a whole” relative to its spin axis

27. What is true polar wander? Motion of “Earth as a whole” relative to its spin axis

28. What is true polar wander? Motion of “Earth as a whole” relative to its spin axis Why distinguish between plate motions and true polar wander?

29. LIPs reconstructed in palaeomagnetic and global moving/fixed hotspot (for the Pacific) frame Need appropriate reference frame to link surface and deep mantle

30. geoid [m] smean lowermost mantle [%] Without geoid highs related to subduction (presently at ~equatorial position) axis of maximum non-hydrostatic moment of inertia could have possibly moved along blue circle ~ corresponds to rotation of continents relative to spin axis but not over lower mantle Center of mass African Pacific LLSVP

31. What are TPW episodes caused by? LLSVPs associated with geoid highs Spin axis expected at ~67 ° N, 96 ° E Earth orientation expected from LLSVPs Subduction zones also associated with geoid highs Distribution of recent subduction suitable to move spin axis towards observed poles Actual orientation

32. Reality more complex because Subduction changes through time Density anomalies and deformed boundaries contribute to geoid anomalies Effect of slabs on degree-2 geoid probably... positive in the upper mantle... negative in the lower mantle

33. → True polar wander corrected (Steinberger & Torsvik, 2008) → Longitude shifted (van der Meer et al., 2010) Color = age; Darkness = amount of subduction Subduction history (compiled by Trond Torsvik):

34. ... and the geoid... Younger slabs cause positive geoid...... and older slabs negative As qualitatively expected from recent subduction distribution, geoid highs in East Asia and South America Expected displacement of pole

35. ... which is combined with the geoid contribution due to LLSVPs, weighted...

36. Such that the modelled total geoid...... optimally agrees with the observed geoid

37. Geoid going up beneath South America Geoid going down beneath North America predicted change ofsince 50 Ma Areas where geoid is going up / down tend to move towards equator / towards poles corresponding to predicted motion of the pole towards Greenland Since 50 Ma

38. Geoid going down beneath East Asia Geoid going up beneath North America predicted change of100-50 Ma Areas where geoid is going up / down tend to move towards equator / towards poles corresponding to predicted motion of the pole towards Siberia 100-50 Ma

39. Geoid going down in polar regions Geoid going up in equatorial regions away from LLSVPs predicted change ofsince 120 Ma Since 120 Ma Corresponding to increasing difference between maximum and intermediate moment of inertia – slower TPW LLSVPs only

40. Predicted and observed TPW agree on Motion towards Greenland since ~50 Ma Motion towards Siberia before that Polar motion before 100 Ma faster than afterwards All three features can be explained based on subduction history! Maximum moment of inertia axis LLSVPs only Towards intermediate moment of inertia axis LLSVPs only

41. Long-dashed: changes in age at subduction zone not considered Short-dashed: neither consider changes in convergence rate Further back in time: Models match direction of observed TPW episodes but over-predict amplitude Given uncertainties, better agreement cannot be expected Observation Models

42. Maximum speed of true polar wander With realistic Earth parameters, maximum speed in case (2) about 1 degree / million years

43. Conclusions Plate motions and true polar wander can be distinguished, even in the absence of hotspot tracks; several episodes of true polar wander are identified (up to 18 degrees, at speeds not exceeding ~1deg/Myr) Earth’s orientation relative to its spin axis is a consequence of subduction history and stable Large Low Shear Velocity Provinces