thermo-chemical convection: a comparison of numerical methods, and application to modeling planetary...
TRANSCRIPT
![Page 1: Thermo-chemical convection: A comparison of numerical methods, and application to modeling planetary evolution Paul J. Tackley with help from Takashi Nakagawa](https://reader035.vdocuments.site/reader035/viewer/2022062515/56649d055503460f949d92f5/html5/thumbnails/1.jpg)
Thermo-chemical convection: A comparison of numerical methods, and application to modeling
planetary evolution
Paul J. Tackley
with help from
Takashi Nakagawa Shunxing Xie
John Hernlund
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Plan
• Numerical: benchmarks of methods for treating chemical field
• Scientific: results of Earth thermo-chemical evolution models
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Benchmark 1: van Keken et al, JGR 1997
• Transient Rayleigh-Taylor instability with different viscosity contrasts, or fairly rapid entrainment of a thin layer
• Challenging. No two codes agree perfectly for long-term evolution.
• Show example results for my code (FV multigrid, tracers hold composition)
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BM2: Tackley and King, Gcubed 2003
• Model layer with long-term stability: test how convective pattern and entrainment varies with numerical details
• Compare two underlying solvers: STAG3D (FD/FV multigrid) and CONMAN (FE)
• Compare two tracer methods with field-based methods
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Two tracer methods• ‘Absolute’: tracers represent dense material,
absence of tracers represents regular material. ‘C’ proportional to #tracers/cell– Pro: C is conserved– Con: C can exceed 1
• ‘Ratio’: two types of tracer, one for dense material one for regular material C=#dense/(#dense+#regular)– Pro: C cannot exceed 1– Cons: C not perfectly conserved, need tracers
everywhere
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Grid-based advection methods
• STAG: MPDATA with or without ‘Lenardic filter’
• CONMAN: FE with or without ‘Lenardic filter’
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Initial condition (thermal)
• Composition: layer 0.4 deep
2-D 3-D
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Tracer results: STAG
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Findings
• Absolute method: considerable settling unless #tr/cell>40. Improved by truncation.
• In contrast, ratio method gives visually correct solution with only 5 tracers/cell
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• Similar to STAG results
Tracer results: CONMAN
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Diagnostics
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3-D results (STAG3D)
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Grid-based methods:
STAG and CONMAN
• ‘Lenardic’ filter helps a lot. Thanks Adrian.
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Diagnostics for grid-based methods
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Long-term layering BM: Conclusions
• Tracer ratio method allows fewer tracers/cell than tracer absolute method
• Grid-based methods can be competitive with enough grid points
• Not clear that all methods are converging to the same solution as resolution is increased!
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Need melting+eruption benchmark?
• Melt=> surface crust, but what about compaction?– Place crust tracers in upper 8 km, ignore compaction
(Christensen & Hoffman 1994)– Use inflow free-slip boundary condition (unreasonable high
stresses)– Place crust at free-slip top, assume stress-free vertical
compaction– Place crust at top, use free surface with viscoelastic rheology
(best?)
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Part 2- Science : Main points• C highly heterogeneous - a mess
– Not much ‘pyrolite’- mostly strips of basalt and residue – Not much difference between the upper and lower mantles
• Chemical heterogeneity has a different spectrum from thermal and dominates at most wavelengths
• Post-perovskite transition anticorrelated with “piles”• The nature of chemical layering hinges on uncertain
mineral physics parameters (partic. densities) and must be resolved by better data or by observation+modeling
• Presence or absence of dense layering above the CMB has strong implications for core thermal evolution and mantle geotherm
• Convection models can generate synthetic geochemical data to act as a further constraint
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The mantle is chemically highly heterogeneous - “a mess”
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Cartoon models: different regions appear to be internally pretty homogeneous
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Numerical models often start with clean layering, each layer internally homogeneous
• Tackley, 1998
• (green=C)
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Heterogeneity continuously produced by melting-induced differentiation
• Differentiation by partial melting + crust production– Major elements (density differences)– Trace elements partition between
melt+solid• Radiogenic ones most useful• He, Ar outgassed on eruption
• Mixing/stirring by convection– Homogenizes material to lengthscale <
melting region on timescale=??Coltice & Ricard
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T phase C
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Trace element ratios heterogeneous!
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Most of the mantle has differentiated by MOR melting: how much?
• Outgassing of nonradiogenic noble gases: >90%
• Davies 2002: >97%
• => only a few % primitive unprocessed material left
• => at the grain scale, not much ‘pyrolite’ but rather strips of former MORB and depleted residue
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Metcalfe, Bina and Ottino, 1995
In Earth, ‘blobs’ are continuously introduced
Laboratory stretching
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How long does it take to get mixed together again?
• Old estimates of mixing time of 100s Myr were based on thinning ‘blobs’ by a factor ~50
• But thinning to ~cm scale is necessary for remixing at the grain scale, which means thinning by factor ~10^5 for oceanic crust
• This takes at least 2 billion years to accomplish by convection! (see next graph)
• Perhaps 50% of processed material has been stretched to the cm scale (but still not ‘average mantle’)
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Age and stretching for 4.5 Gyr
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Chemical heterogeneity has a different spectrum from thermal heterogeneity and will dominate
at shorter wavelengths and perhaps at long wavelengths too
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Total vs spectrum
T spectrum
C spectrum
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Recent probabilistic seismic inversion finds that composition dominates long-wavelength seismic signal in lower mantle
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T phase C
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Post-perovskite transition anticorrelated with possible
‘piles’ of dense material
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Is there a chemical difference between upper and lower mantles?
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If ‘660’ assumes 100% olivine, there is an early layered phase
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1 Ga
Time
T
C
age
2 Ga 3 Ga
With both olivine and pyroxene systems, no early layered phase but…
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3.6 GaT
C
age
=238U/204Pb
206Pb/204Pb
147Sm/144Nd
Local stratification builds up around 660 because of…
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Different depths of perovskite transition in olivine and pyroxene
systems
• From Ita and Stixrude
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Experimentally-measured basalt densities: Ono et al 2001
• Becomes less dense at greater depth?
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More proof of this
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The nature of chemical layering hinges on uncertain mineral
physics parameters (e.g., densities) and must be resolved
by better data or by observation+modeling
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Approximation: 2 systems with different phase transitions
• Dense
• Neutral
• Less dense (buoyant)
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Effect of deep mantle crustal density
T
C
3He/4He
dense neutral buoyant
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Presence or absence of dense layering above the CMB has strong implications for core
thermal evolution and mantle geotherm
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For these 3 cases…
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CMB heat flow either drops to zero (global
layer) or inner core grows too
big!Nakagawa & Tackley, Gcubed in press
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K in core seems necessary
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Effect on mantle
geotherm
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Secular evolution:
melting important early on
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Mantle convection models can be used to generate synthetic
geochemical data, to further constrain the possible range of
mantle models
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He ratios in mid-ocean
ridge basalts
(MORB)
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Effect of deep mantle crustal buoyancy
T
C
3He/4He
dense neutral buoyant
Xie & Tackley 2004a
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By tracer By sampling cell Erupted
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Effect of He partition coefficient
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Pb diagrams: 4.5 Gyr evolution
• 3.4 Gyr isotopic age much too large!
Model Observed
‘age’=1.8 Gyr‘age’=3,4 Gyr
Xie & Tackley 2004b
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What if HIMU didn’t enter mantle earlier in history?
• No HIMU before 2.5 Gyr before present• Works very well in getting the correct slope!
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Main points• C highly heterogeneous - a mess
– Not much ‘pyrolite’- mostly strips of basalt and residue – Not much difference between the upper and lower mantles
• Chemical heterogeneity has a different spectrum from thermal and dominates at most wavelengths
• Post-perovskite transition anticorrelated with “piles”• The nature of chemical layering hinges on uncertain
mineral physics parameters (partic. densities) and must be resolved by better data or by observation+modeling
• Presence or absence of dense layering above the CMB has strong implications for core thermal evolution and mantle geotherm
• Convection models can generate synthetic geochemical data to act as a further constraint
![Page 62: Thermo-chemical convection: A comparison of numerical methods, and application to modeling planetary evolution Paul J. Tackley with help from Takashi Nakagawa](https://reader035.vdocuments.site/reader035/viewer/2022062515/56649d055503460f949d92f5/html5/thumbnails/62.jpg)
THE END
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Geochemistry: Example isotope diagrams
Slope”Age”
(White, 2003)
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Compositional variations are important in the mantle
• We know they’re there because– Subducted slabs are compositionally stratified– Seismologists “observe” compositional variations– Geochemists measuring isotope ratios in erupted
magmas find that several chemically-distinct components are required
• They affect mantle convection (through density and other physical properties) and are affected by mantle convection => study using thermo-chemical convection models
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Compositional variations are important in the mantle
• We know they’re there because– Subducted slabs are compositionally stratified– Seismologists “observe” compositional variations– Geochemists measuring isotope ratios in erupted
magmas find that several chemically-distinct components are required
• They affect mantle convection (through density and other physical properties) and are affected by mantle convection => study using thermo-chemical convection models
![Page 68: Thermo-chemical convection: A comparison of numerical methods, and application to modeling planetary evolution Paul J. Tackley with help from Takashi Nakagawa](https://reader035.vdocuments.site/reader035/viewer/2022062515/56649d055503460f949d92f5/html5/thumbnails/68.jpg)
Compositional variations are important in the mantle
• We know they’re there because– Subducted slabs are compositionally stratified– Seismologists “observe” compositional variations– Geochemists measuring isotope ratios in erupted
magmas find that several chemically-distinct components are required
• They affect mantle convection (through density and other physical properties) and are affected by mantle convection => study using thermo-chemical convection models
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Ingredients: Physics
• Compressible anelastic (physical properties depend on depth/pressure)
• Viscosity dependent on:– Temperature (factor 106)
– Depth (factor 10, exponential + jump @660)
– Stress (yielding gives “plate-like” behavior)
• Pyroxene-garnet phase transitions as well as olivine-system transitions
• Internal heating + isothermal, cooling CMB
• Cylindrical geometry (2-D)
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