1. Comparison of Theory and Experimental Results on Seismic Wave Attenuation Ian Jackson a, Ulrich Faul a, John Fitz Gerald a, Stephen Morris b, Yoshitaka Aizawa a,c & Auke Barnhoorn a a Australian National University b University of California, Berkeley c Okayama University, Misasa

2. Fishwick et al., EPSL 2005  frequency  temperature  grain size  melt fraction  chemical composition  dislocation density  water ? How do seismic wave speeds & attenuation vary with Laboratory calibration of the seismological probe Goal: development & application of a lab-based framework for robust interpretation of seismological models of Earth structure

3. Frequency-dependent mechanical behaviour of geological materials @ high temperature Shear modulus decreases & dissipation increases with increasing timescale (decreasing frequency) of stress application

4. Implementation within internally heated gas apparatus: P = 200 MPa T to 1300 C oscill’n periods 1-1000 s shear strains < 10 -5 Specimen & reference assemblies & T profile Specimen encapsulation Experimental method Torsional forced oscillation method

5. Polycrystalline olivines from natural and synthetic precursors ± water, melt & dislocations Dry Fo 90 melt-free sol-gel Dry Fo 90 0.01% melt San Carlos Anita bay dunite d ~ 100  m 0.3 wt% H 2 O welded Pt capsule FTIR determination of [OH] Sol-gel Fo 90 deformed by dislocation creep

6. Melt-free olivine: representative forced-oscillation results Jackson et al., JGR, 2002

7. Melt-bearing olivine: representative forced-oscillation results sol-gel olivine specimen grain size 27.5  m melt fraction 0.037 Jackson et al., JGR, 2004

8. 1/Q peak height vs melt fraction

9. 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.)

10. Parameterisation of viscoelastic rheology

11. Parameterisation of viscoelastic rheology: extended Burgers model

12. Melt-free Fo 90 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

13. Micromechanical interpretation of viscoelastic relaxation

14. Elastically accommodated grain-boundary sliding (Raj & Ashby, Mosher & Raj) Boundary topography x =  h j cos (2  jy/ ) Sliding distanceU = (1- ) 3  a /[2  3 G U  j 3 h j 2 ] Relaxation time  e =  b d/G U  Relaxation strength  = 0.57(1- ) = 0.42 (for = 0.26 & truncation after 100 terms!) Relaxed modulus and height of Debye dissipation peak G R /G U = 1/(1+  )Q -1 D = (  /2)/(1+  ) 1/2 HOWEVER, since h j ~ j -2, the infinite sum  j 3 h j 2 fails to converge implying zero U,  Jackson et al., Mat. Sci. Eng. A, in press

15. Grain-edge morphology & relaxation strength Jackson et al., Mat. Sci. Eng A, in press

16. Transient diffusional creep (Raj) Duration of diffusional transient (following elastically accommodated sliding)  d = (1- )kTd 3 /[40  3 G U  D b  ]. 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  t 1/2 (Gribb and Cooper) yielding a wide absorption band with Q -1 ~ T o 1/2 d -3/2

17. 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 = (T o /d) exp(-E B /RT),  = 1/4*, E B = 400 kJ/mol Melt-bearing olivine (melt fraction  ) Network of triple-junction tubules (dimension ~  ) Dissipation background + broad peak width:  log 10  ~ 2*; height B(  ): 0.01-0.1 location: T o ~ d exp (E P /RT)*, E P ~ 720 kJ/mol Peak inconsistent with melt squirt between tubules * c. f. theory

18. Melt-related viscoelastic relaxation Faul et al., JGR, 2004    constant relaxation time:  (  /   ) Squirt of basaltic melt (  1-100 Pa s @ 1300-1200 C)   << 1 s; also  ~ 0.01 for squirt between tubules Attribution of 1/Q peak to elastically accommodated grain- boundary sliding  g. b. viscosity ~ 10 4 -10 9 Pa s @ 1300-1000 C - intermediate between melt & specimen viscosities p = 2 p = 3 p = 1 after Schmeling (1985)

19. Dislocation relaxation Dislocation motion by formation & migration of kinks in response to shear stress  yz Estimated relaxation times (Karato, PAGEOPH, 1998; Jackson, Treatise on Geophysics, submitted)

20. 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

22. Contrasting microstructures of ‘dry’ & ‘wet’ Anita Bay dunite ‘dry’: patchy distribution of silicate melt & some fluid-filled pores ‘wet’: homogeneously distributed water-rich fluid phase

23. Influence of water II widely dispersed water- rich fluid phase Anita Bay dunite, d ~ 100  m 0.3 wt% H 2 O, welded Pt capsule FTIR determination of [OH] Anita Bay dunite: ‘wet’ vs ‘dry’ Aizawa et al. (in prep.)

24. Melt-bearing olivine: representative microcreep results

25. Melt-bearing olivine: extended Burgers fit