thorsten w. becker - geodynamics · platetectonic anisotropy in a simple world, both ridges and...
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Thorsten W. BeckerUniversity of Southern California, Los Angeles
CIG Mantle Convection WorkshopBoulder, June 21 2005
Seismic anisotropy:
enough already?
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Nope.
CIG? ... gotta love itthanks to the people
who contribute software
and
geoframework.org
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Goal of this talk
provide a brief review of seismic anisotropy as a constraint for mantle convection and lithospheric deformationdiscuss some of the previous modeling efforts on global and regional scalespresent work in progress on evaluating the remaining problems
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Message
applied geodynamics useful for understanding plate tectonics (AGUPT)need to widen the realm of quantitative model predictions to reduce ambiguities (QUMRA)seismic anisotropy can yield a useful measure of flow and tectonic deformation (SAMFT)improved grip on many modeling issues, but imperfect data remains a big limitation (IHMBID)
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Collaborators
Donna Blackman (UCSD)
Jules Browaeys (USC)
Sebastien Chevrot (CNRS)
Boris Kaus (USC)
Jamie Kellogg (UCLA)
Rick O'Connell (Harvard U)
Vera SchultePelkum (CU Boulder)
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USC HPCC
1716 nodes, 1.4TB7th fastest academic supercomputer as of 2004I haven't been able to properly edit files for six months nowHunters and farmers
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Roadmap
dataanisotropy (azimuthal, 2φ) modelingmantle flow modelingcombining the two
previous workregional tectonicsglobal statisticsglobal specifics
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Applied geodynamics
construct “realistic” (i.e. bestguess) models of mantle flow to make predictions for our Earthbuoyancy forces ∼ viscous flowstress = viscosity strainrateexamples of constraints:
velocities: plate motions, past and presentstrainrates: GPS, earthquakes, upliftstress: WSM, geoidintegral of strainrates: anisotropy, geochemistry
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Data and models
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Constraints on mantle structure from seismic waves
δt > 0
δt > 0 δt' > 0
δt' < 0
isotropic anomalies
anisotropic anomalies
temperature,composition strainrates
seismology
geodynamics
δv>0
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Isotropic tomography: upper mantle
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Azimuthal anisotropy: Rayleigh wave phase velocity maps
Ekstrom (2001) Trampert & Woodhouse (2002)100 s
150 s
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Shear wave splitting
after Crampin (1981), from garnero.edu
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SKS splitting data coverage
data compilation from Matt Fouch's ASU database
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Regional anisotropy: splitting at trenches
water?arcparallel flow?
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At what depths do we detectseismic anisotropy?
Montagner (1998) McNamara et al. (2002)
dislocation creep (high σ, low T) needed for LPO (what about climb?)
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Laboratory studies:LPO in the multianvil
subcrustal anisotropy likely caused by lattice preferred orientation (LPO) of intrinsically anisotropic olivine crystals in flowfor olivine, the seismically fast, slow, and intermediate axes are a [100], b [010], c [001], respectivelya and b align with the largest and smallest axes of the finite strain ellipsoid (FSE) for small strainsfor large strains, a rotates into the shear plane by dynamic recrystallization (subgrain rotation and grain boundary migration)
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Pole figures
uniaxial compression experiment by Nicolas et al. (1974)
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High τ and high H20 regime
type A: normal anisotropy, a [100] in shear planetype B: High τ and high H20 regime, a [100] normal to shear plane (Jung & Karato, 2001)
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Platetectonic anisotropyin a simple world, both ridges and trenches should show a in plate motion directionridges: ridgeparallel fast a
due to melt/crack alignment (Kendall et al., 1994)due to melt segregation (Holtzman et al., 2003)small scale, so far not observed
subduction zones: arcparallel alignment of aarcparallel flow (e.g. Hall et al., 2000; Mehl et al., 2003)presence of water (Mitsukami et al., 2004)
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Quantitative links between LPO and flow: theories
kinematic constraint theory of Ribe (1991): grains rotate to minimize the mismatch between local and global strain rate
predicts alignment of a, b, c with FSEcritical ξ = log (e1/e2) ~ 0.5 overprints texture
VPSC theory of Wenk & Tome (1999)computationally intensivesix free parameters
kinematic theory of Kaminski & Ribe (2001, 2002); DREX (Kaminski et al., 2004) (freely available...)
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Kinematic recrystallizationKaminski & Ribe (2001, 2002) method includes stress dependent recrystallization
volume fraction of grains controlled by dislocation density, ρnonrecrystallized fraction of grain = exp ( − λ ρ2)large (small) strain energy grains shrink (grow) by grain boundary migrationtwo free parameters from lab:
strainfree subgrain nucleation λ grain boundary mobility M
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KR and the lab: a axes
Kaminski & Ribe (2001); Kaminski et al. (2004)
simple shear
uniaxialcompression
Zhang & Karato lab KR method
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Saturation of LPO anisotropy under simple shear: olivine
C tensor norms anisotropydln v ~ ½ dln C
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Saturation of LPO anisotropy: GBS, olivine and enstatite
C tensor norms anisotropydln v ~ ½ dln C
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LPO: an integral measure!
Kaminski & Ribe (2001)
red: fast ablue: velocitiesred blue!need mantle flow as f(t)
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ξ = 2 texture for simple,subPacific streamlines
regular slip
system
water slip
system
[010][100] [001]
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Trench LPO
simple flow modelLPO not so simple
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Advection rules for global models
here: assume steadystate flow (backward convection was used in Becker et al., 2003)follow tracers backward until ξ = log (e
1/e
2) ∼0.5
(OK for FSE) or ξ ∼ 2 (OK for LPO)erase texture if tracers rise from below 410km, maximum advection time ~43 Macompute full elastic tensor (21 components) at each depth layer
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From LPO to wiggles,
how?
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Surface wave anisotropy: Rayleigh wave phase velocities
D2=BC ,S
AC ija z
H C , S
FC ij f z
GC ,S
LC ij l z
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Body wave anisotropy: SKS splitting, for example
can compare largest FSE axes with bestfit transverse anisotropy (TI) axes for the hexagonal component of stiffness tensorany tilt will lead to backazimuth dependence of fast splitting axes, so will nonhexagonal tensors
SchultePelkum & Blackman (2003)
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From flow to SKS splittingcompute elastic tensors from LPO fabrics using the Kaminski et al. (2004) method for olivine/enstatite mix using DREX (with fixed enstatite handling)compute elastic tensors (using dP and dT derivatives, both P and T are here f(z) only) compute synthetic seismograms using reflectivity methodmeasure splits by crosscorrelation
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Backazimuth variations
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Global flow models
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What's going on?
solve conservation of mass, momentum, (& energy)infinite Prandtl number, incompressible fluidconstitutive relationships:1)
2)
3) (only for upper 410 km, should use mixed rheol.)
=2̇
= f z
=A f zexp E T 0−T ' 1n ̇II
1n−1
= f zexp E T 0−T '
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Numerical tools
finite elements:Citcom (Moresi, Tan, Conrad, Gurnis, ...)CitcomS (Zhong, Moresi, ...)all old versions from geoframework.org, slightly modified
Hager & O'Connell (1981) semianalytical, spectral method is used for comparison
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Some details on code “development”
Citcom and CitcomS modifications: (thanks to Allen, Eh, and Jeroen)
surface velocities and T from GMT grd filesregional model sidevelocities from recoded, modular spectral method (not quite done...)multigrid and CG solver issuespowerlaw implemented with new, damped iteration scheme, clipped viscosities (104 range)VTK output conversiontested double/single precision
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Resolution and accuracy
global CitcomS:12 CPU x 64 x 64 x 64 (~ 3,100,000) elements, ~50km resolutionthis is probably not enough, but fast
can easily improve resolution for instantaneous computations, long simulations problematicsome benchmarking done, more to dopowerlaw rheology work in progress
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Choices and input models
presentday plate velocities prescribed on topseismic tomography for density structureneed viscosity profile, and R = dln T / dln vtypically: smean or ngrand, constant Ras in Becker & O'Connell (2001), Becker & Boschi (2002), and Becker et al. (2003)
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Presentday surface velocities in nonetrotation reference frame
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Viscosity profiles
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Input structure at 290 km(ngrand tomography)
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Viscosity at 290 km for η = f(r, T)
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Viscosity at 290 km for η = f(r, T, σ),powerlaw oceanic asthenosphere
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Effect of rheology: Newtonian, η = f(r)
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Effect of rheology: Newtonian, η = f(r, T)
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Effect of rheology: powerlaw, η = f(r, T, σ)
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Nested circulation models
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Previous work on nested flow models: some examples
Tan, Gurnis, et al. on plumes: coupled Citcom and CitcomSMihalffy, Marquart, & Schmeling on plumes: side flow boundary conditions from Hager & O'Connell code PYREzed CitcomS
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Nested models, η = f(r, T), only density driven
using large scale, S wave tomography
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Nested models, η = f(r, T), density and top plate flow
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Nested models, η = f(r, T), density and large scale flow
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Puttin' it all together
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SKS splitting in trenches2.5D flow, FSE, and seismic synthetics: Hall et al. (2000)poster by Lassak et al. (here)work by Liverpool group
Hall et al. (2000)
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California splitting
Mantle flow and FSE:Becker (2002)
GPS and rigid plate flow:Silver & Holt (2002)
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African splitting
Behn et al. (2004)
mantle flow,instantaneous strainrates
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Pacific surface wave anisotropy
Gaboret et al. (2003)
mantle flow,instantaneous strainrates
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Phase velocity maps explored
Becker et al. (2003)T = 50 s Rayleigh waves, FSE, smean tomography model
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Phase velocity maps explored
Becker et al. (2003)
FSE better than APMactive upwellings better than slabsNR degrades fitchanges in plate motions improve fitLPO ~same as FSE
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Some loose ends
LPO means dislocation (powerlaw) creep, yet all models use diffusion (Newtonian) creepFSE is not the whole story, should use LPOlateral viscosity variations important (cratons, asthenosphere, η(T ),...)timedependence of mantle flow
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Surface wave anisotropy revisited: radial η(z), low strain, FSE
ngrand tomography, plate motions, Ekstrom (2001) tomography
Rayleigh waveat 100 s (~150 km depth)
∆αocean
= 37.7
(best models in
Becker et al., 2003, have ∆α
ocean ~ 24
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Surface wave anisotropy revisited: powerlaw η(z, T, σ), low strain, FSE
ngrand tomography, plate motions, Ekstrom (2001) tomography
Rayleigh waveat 100 s (~150 km depth)
∆αocean
= 41.9
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Surface wave anisotropy revisited: radial η(z), low strain, KR LPO
ngrand tomography, plate motions, Ekstrom (2001) tomography
Rayleigh waveat 100 s (~150 km depth)
∆αocean
= 38.7
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Surface wave anisotropy revisited: radial η(z), high strain, KR LPO
ngrand tomography, plate motions, Ekstrom (2001) tomography
Rayleigh waveat 100 s (~150 km depth)
∆αocean
= 37.8
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Radial η(z), high strain, KR LPO,different anisotropic model
ngrand tomography, plate motions, Trampert & Woodhouse (2003)
Rayleigh waveat 100 s (~150 km depth)
∆αocean
= 31.9
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Surface wave findings
effect of LPO vs. FSE moderate, but LPO allows for amplitude predictionslateral viscosity variations less important than radial structurestrong effect of input density (bad & good)surface wave models have global coverage, but patterns are of uneven robustness
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Westcoast: different ξlow strain high strain
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Westcoast: density modelsslabs only tomography
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Regional anisotropy conclusions
can explain observed variety in splittingcan use variation in fast axes and delay time to constrain depth dependence of anisotropycan explain amplitudes of splitting (kindof)there's a hint of a crustal deformation signal (to be explored with better models)slab models (with induced return flow) lead to better model fits
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Open questions for seismic anisotropy modeling
What are the length scales of heterogeneity, and how are they imaged?What is the best theoretical description of LPO formation?How important is the crust for shear wave splitting (S and SKS)?How do we constrain H20, so that we can comprehensively model alternative slip systems?
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General conclusions
need to evaluate the robustness of mantle flow estimates with respect to rheologyfurther exploration of convection, and tectonophysics, reconstructions is cruciala lot of progress will come from joint (seismology and geodynamics) modelsdata quality (coverage) is a problemand...
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Some suggestions for CIG(mostly harmless)
keep it simple (in the beginning)modularize and document existing codes, at a low level, without framework commitmentcreate a repository of cleanedup subroutinesfacilitate utilization of CS developmentsassist in I/O handling and interpolation
long term goalscoupled lithospheric/mantle codesnested models