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 viscosity for flow computation I
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
gravity
thermal expansivity
specific heat
Melting temperature
profile Tm (Wang, 1999;
Zerr and Boehler, 1994;
Yamazaki and Karato, 2001)

8. In the lower mantle, use strain-stress relationship
Mantle viscosity for flow computation II
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
Viscous rheology inappropriate for lithosphere
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)

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. Optimize model to fit observational
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.