Deep Earth dynamics – numerical and fluid tank modelling

1. Deep Earth dynamics – numerical and fluid tank modelling Bernhard Steinberger Center for Geodynamics, NGU, Trondheim, Norway

2. Part 1: Instantaneous mantle flow computations based on mantle density heterogeneities • Equations • What is the mantle viscosity structure • What are the mantle density heterogeneities • Observational constraints

6. Use mineral physics to infer viscosity profile based on • mantle temperature and melting temperature profile • Adiabatic temperature profile • T(z): integrate dT/dz = T(z) (z) g(z) / Cp Melting temperature profile Tm (Wang, 1999; Zerr and Boehler, 1994; Yamazaki and Karato, 2001) Mantle viscosity for flow computation I gravity thermal expansivity specific heat

8. In the lower mantle, use strain-stress relationship ˙~n exp(-gTm/T) hence (z)~exp(-gTm/nT) for constant strain rate Yamazaki and Karato (2001): g=12, n=1 • Absolute viscosity values • -->may be different in • upper mantle • transition zone • lower mantle • -->determined by • optimizing fit to various • observables (geoid, • heat flux profile, CMB • excess ellipticity) Mantle viscosity for flow computation II Viscous rheology inappropriate for lithosphere

10. Problem: Seismic velocity anomalies may have thermal or compositional origin Alternative: Density ”forward model” inferred from subduction history etc. (e.g. 3SMAC by Nataf and Ricard)

11. Mantle viscosity for flow computation III Optimize model to fit observational constraints (geoid, radial heat flux profile)

12. Include CMB excess ellipticity as further constraint • Allow for non-thermal • density variations in • lowermost mantle

13. Thermal boundary layer (TBL) thickness Steepness of adiabatic viscosity profile Correspondto viscosity drop in TBL

14. Lithosphere stress

17. Conrad and Lithgow-Bertelloni (2002, 2004)

18. Steiner and Conrad (2007): • Adding upwelling flow degrades fit • Downwelling flow more significant driver of plate motions • Low-velocity anomalies either do not couple effectively to plate motions • or represent chmeical differentiation and do not drive upwelling flow

19. Seismic anisotropy (Behn, Conrad, Silver, 2004) Best fit with plate-driven + density- driven flow

20. Becker (2006): Strain rate and temperature dependent viscosity: • Models based on laboratory creep laws for dry olivine are shown to be compatible with average radial viscosity profiles, plate velocities in terms of orientation and amplitudes, plateness of surface velocities, toroidal:poloidal partitioning • Including temperature-dependent variations increases the relative speeds of oceanic versus continental lithosphere, makes surface velocities more plate-like, and improves the general fit to observed plate motions.

22. Cadek and Fleitout (2003) predicted lateral viscosity variations

23. Geoid variance reduction increased from 76% to 92%

24. Part 2: Time dependent: • Advecting backward in time • Full convection computations – requires additionally solving conservation of energy equation, and corresponding boundary conditions (heat flux or temperature) • (a) Forward models (example from Paul Tackley – strain rate weakening gives plate-like surface motion)

25. (b) Adjoint method (e.g. Bunge et al., 2002, 2003)

26. Gonnermann et al.