1. Modeling the size spectrum of mantle heterogeneities
Chris Huber; Brook Peterson; Liran Goren; Martin Collier; Jan Verhoeven; Edwin Kite; Louise Kellogg; Michael Manga
CIDER 2008 plenary, 7 Aug 2008
SNORCLE team, 1994

2. Recap of motivation Seismology Geochemistry Tomography
Noise tomography (?)
Scattering
Observations
Controlled source
 SCOPE OF OUR MODEL 
MORB, OIB isotopes
Mantle outcrops
Atomic diffusion
Processes
Convective stirring
k (m^-1)

3. Recap of objectives Geochemistry group (Peterson, Collier, Manga):
MORB data  spherical harmonics
Geodynamics group (Verhoeven, Kite, Kellogg):
Mixing mechanism as function of Ra
Initial wavelength as function of Ra
Thermal history
Modeling group (Goren, Huber):
Incorporate results in simple model of size spectrum evolution over geological time

4. Inclusion of thermal history
Schubert et al., 2001
Extraction of radiogenic elements to
form continents is not tracked;
Thermal (and Ra) evolution sensitive
to initial complement of radiogenic
elements.
Kite et al., unpublished

5. Insensitivity to initial conditions; assumed scaling}
Hot starts quickly converge
Coltice 2005, EPSL
Kite et al., unpublished

8. Sticky slabs We use a viscosity ratio of 100
(Regenaeuer-Lieb & Kohl 2003,
Min. Mag.)
If viscosity ratio > 4, shear strain
becomes unimportant (effective
C_s is 1).
Manga 1996, GRL

10. Varying Constant to within an order of magnitude (neglecting magma
ocean processes / ‘primordial blobs’)
Diffusion times for λ(ini) -
τ(thermal) ~ τ(overturn) << τ(Earth)
τ(He) ~ τ(Earth) Hart et al. 2008, EPSL
τ(X) >> τ(Earth)
Korenaga 2006, ‘Archean geodynamics and environments’

11. Seismological observations are consistent with λ(typical) ~ 101-2 km
‘Precursor coda shapes are consistent with 1 per cent fluctuations in P velocity in the wavenumber band 0.05–0.5 km−1 extending to 1000 km above the core–mantle boundary’ – Cornier 1999, GJI
Cornier 2000, JGR

12. Results

13. Cs varying with Ra: results
2D CitCOM, box with aspect ratio 1 x 1, reflecting sidewalls, free slip top and bottom, isoviscous, bottom heated.

14. transition to chaos

15. Cs varying with Ra: effect on model

16. Effect of Cs and λ(ini) combined

17. 4.5 Ga simulation

18. Aside: Cs with strongly T-dependent viscosity (‘stagnant lid’)
Cs shows no systematic trend with Ra; Citcom runs have not reached steady state so are not ready for inclusion in heterogeneity model

19. 130 Sr isotope data from Mid-Atlantic Ridge basalts
130 Sr isotope data from Mid-Atlantic Ridge basalts. Compiled by Martin Collier, processed by
Michael Manga using code supplied by Ved Lekic and Guy Masters

20. Next steps?
Consider depth variability in heterogeneity spectrum – active (dense) tracers.
This might be tested against power spectra of MORB and OIB geochemistry…
…to interpret these power spectra we will need to quantify the homogenizing effects of melting.