Modeling the size spectrum of mantle heterogeneities

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
10-6 10-5 10-4 10-3 10-2
10-1 100 101 102
103
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Kite et al., unpublished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Kite et al., unpublished
6
(No Transcript)
7
(No Transcript)
8
Sticky slabs
We use a viscosity ratio of 100 (Regenaeuer-Lieb
Kohl 2003, Min. Mag.) If viscosity ratio gt 4,
shear strain becomes unimportant (effective C_s
is 1).
Manga 1996, GRL
9
(No Transcript)
10
Varying
Constant to within an order of magnitude
(neglecting magma ocean processes / primordial
blobs) Diffusion times for ?(ini) - t(thermal)
t(overturn) ltlt t(Earth) t(He) t(Earth) Hart
et al. 2008, EPSL t(X) gtgt t(Earth)
Korenaga 2006, Archean geodynamics and
environments
11
Seismological observations are consistent with
?(typical) 101-2 km

• Precursor coda shapes are consistent with 1 per
  cent ?uctuations in P velocity in the wavenumber
  band 0.050.5 km-1 extending to 1000 km above the
  coremantle 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 ?(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. 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.