Comparison of Theory and Experimental Results on Seismic Wave Attenuation
Ian Jacksona, Ulrich Faula, John Fitz Geralda, Stephen Morrisb,
Yoshitaka Aizawaa,c & Auke Barnhoorna
a Australian National University b University of California, Berkeleyc Okayama University, Misasa
Fishwick et al., EPSL 2005
frequencytemperaturegrain sizemelt fractionchemical compositiondislocation densitywater ?
How do seismic wave speeds & attenuation vary with
Laboratory calibration ofthe seismological probe
Goal: development & application of a lab-based framework for robust interpretation of seismological models of Earth structure
Frequency-dependent mechanical behaviour of geological materials @ high temperature
Shear modulus decreases& dissipation increases
with increasing timescale(decreasing frequency)
of stress application
Implementation withininternally heated gas
apparatus: P = 200 MPaT to 1300 C
oscill’n periods 1-1000 sshear strains < 10-5
Specimen& referenceassemblies& T profile
Specimenencapsulation
Experimental method
Torsional forced oscillation method
Polycrystalline olivines from natural and synthetic precursors ± water, melt & dislocations
Dry Fo90
melt-freesol-gel
Dry Fo90
0.01% meltSan Carlos
Anita bay dunite
d ~ 100 m0.3 wt% H2O
welded Ptcapsule
FTIR determination of [OH]
Sol-gel Fo90 deformed by
dislocation creep
Melt-free olivine: representative forced-oscillation results
Jackson et al., JGR, 2002
Melt-bearing olivine: representative forced-oscillation results
sol-gel olivine specimengrain size 27.5 mmelt fraction 0.037
Jackson et al., JGR, 2004
1/Q peak height vs melt fraction
Influence of water: preliminary results
Anita Bay dunite: d ~ 100 m, 0.3 wt% water, Aizawa et al. (in prep.)
Aizawa et al. (in prep.)
Parameterisation of viscoelastic rheology
Parameterisation of viscoelastic rheology: extended Burgers model
Melt-free Fo90 olivine:extended Burgers model
temperature: 1000-1300 C, period: 1-1000 s,grain size: 3-165 micron
N = 206, chisquared = 213
Faul & Jackson, EPSL, 2005
Micromechanical interpretation of viscoelastic relaxation
Elastically accommodated grain-boundary sliding (Raj & Ashby, Mosher & Raj)
Boundary topography x = hj cos (2jy/)
Sliding distance U = (1-)3a/[23GUj3hj2]
Relaxation time e = bd/GURelaxation strength = 0.57(1-) = 0.42 (for = 0.26 & truncation after 100 terms!)Relaxed modulus and height of Debye dissipation peak
GR/GU = 1/(1+) Q-1D = (/2)/(1+)1/2
HOWEVER, since hj ~ j-2 , the infinite sum j3hj2 fails to
converge implying zero U,
Jackson et al., Mat. Sci. Eng. A, in press
Grain-edge morphology& relaxation strength
Jackson et al., Mat. Sci. Eng A, in press
Transient diffusional creep (Raj)
Duration of diffusional transient (following elastically accommodated sliding)
d = (1-)kTd3/[403GUDb].
Transient creep rate is enhanced relative to steady-state diffusional creep rate by factor (t/d)-1/2
which integrates to a creep function of Andrade form t1/2 (Gribb and Cooper) yielding a wide absorption band with Q-1 ~ To
1/2d-3/2
Viscoelastic behaviour of olivine ± melt: observations vs theory
Melt-free olivine Tightly interlocking grains (triple junctions ~ 2 nm) Dissipation background only*: 1/Q ~ X; with
X = (To/d) exp(-EB/RT),= 1/4*, EB = 400 kJ/mol
Melt-bearing olivine (melt fraction ) Network of triple-junction tubules (dimension ~ ) Dissipation background + broad peak
width: log10 ~ 2*; height B(): 0.01-0.1
location: To ~ d exp (EP/RT)*, EP ~ 720 kJ/mol Peak inconsistent with melt squirt between tubules
* c. f. theory
Melt-related viscoelastic relaxation
Faul et al., JGR, 2004
constantrelaxation time: (/)
Squirt of basaltic melt ( 1-100Pa s @ 1300-1200 C) << 1 s; also ~ 0.01 for squirtbetween tubules
Attribution of 1/Q peak to elastically accommodated grain-boundary sliding g. b. viscosity ~ 104-109 Pa s @ 1300-1000 C -intermediate between melt& specimen viscosities
p = 2
p = 3
p = 1
after Schmeling (1985)
Dislocation relaxation
Dislocation motionby formation
& migration of kinksin response to shear
stress yz
Estimated relaxation times(Karato, PAGEOPH, 1998;
Jackson, Treatise on Geophysics,submitted)
Conclusions
Mildly frequency- and grain-size-sensitive background-only behaviour of fine-grained melt-free olivine (c. f. silicon nitride, carbide and alumina) suggests diffusionally accommodated grain-boundary sliding (gbs)
Prior elastically accommodated gbs inhibited by tight grain-edge intersections in melt-free materials?
1/Q peak + background for melt-bearing materials with grain edges rounded at triple-junction melt tubules suggests gbs with mix of elastic & diffusional accommodation
Need improved micromechanical model incorporating compliant grain-edge tubules & allowing possibility of sliding with concurrent elastic & diffusional accommodation
Dislocation relaxation & role of water remain to be systematically addressed
Contrasting microstructures of ‘dry’ &
‘wet’ Anita Bay dunite
‘dry’: patchy distributionof silicate melt & some
fluid-filled pores
‘wet’: homogeneously
distributed water-rich fluid phase
Influence of water II
widely dispersed water-rich fluid phase
Anita Bay dunite, d ~ 100m0.3 wt% H2O, welded Pt capsule
FTIR determination of [OH]
Anita Bay dunite:‘wet’ vs ‘dry’
Aizawa et al. (in prep.)
Melt-bearing olivine: representative microcreep
results
Melt-bearing olivine:extended Burgers fit
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