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