Untitled Document
Viscoelasticity, poroelasticity and seismic properties
Ian Jackson, John Fitz Gerald, Robert Farla, Harri Kokkonen,
Hayden Miller
Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
Figure 1
At sufficiently high temperatures in the Earth’s interior, the mechanical
behaviour changes from elastic to viscoelastic with profound implications
for mantle rheology and also seismic wave speeds and attenuation. Such
viscoelastic behaviour results from the stress-induced migration of vacancies
and dislocations (extended defects reflecting prior or current deformation:
see also Farla et al.). Equally, the stress-induced flow of fluids
within cracked/porous media results in departures from elastic behaviour,
termed poroelasticity. The following are highlights for 2008 of our ongoing
study of rheology and seismic properties:
Hot-pressing and high-temperature deformation of titaniferous olivines
(with U.H. Faul of Boston University): Work has continued this
year towards an understanding of the influence of trace impurities on
the rheology of fine-grained polycrystalline olivine. Specimens have
been hot-pressed at 1300°C from sol-gel-derived Fo90 olivine precursors
containing 0.1 wt % each CaO and TiO2, and deformed at 1200-1300°C in
compressive creep tests at progressively higher stress reaching ~300
MPa. Preliminary indications are that these materials (Fig. 1) undergo
much more rapid grain growth than their Ti-free counterparts and are
significantly weaker.
Seismic-wave dispersion and attenuation (with U.H. Faul, S.J.S. Morris
of UC Berkeley, and D.R. Schmitt of the Univ. of Alberta): Our
torsional forced-oscillation method for the study of high-temperature
viscoelastic relaxation has recently been refined to take account of
(i) compliance associated with frictional coupling between the specimen
and neighbouring torsion rods, and (ii) significantly viscoelastic behaviour
of the alumina control specimen [1].
Our published data concerning
the shear modulus G and dissipation 1/Q for fine-grained melt-free and
melt-bearing olivine have been re-processed with this improved strategy. Allowance
for the compliant frictional coupling results in systematically higher
G and lower 1/Q - especially for relatively coarse-grained (low-loss)
materials tested at the highest temperatures (31200°C)
and longest periods (>100 s). These effects are offset to some
degree by allowance for the appreciably viscoelastic behaviour of the
high-grade polycrystalline alumina control specimen. The interim result
is an enhanced grain-size sensitivity of the viscoelastic relaxation
(Fig. 2) meaning higher wavespeeds and lower attenuation on extrapolation
to upper-mantle grain sizes. Additional experimental data for medium-coarse-grained
materials are needed to underpin more robust extrapolation. Planned changes
to the experimental procedure involving more active gripping of the cylindrical
specimen and use of a single-crystal alumina control specimen may increase
the signal/noise ratio for such low-loss materials. In a new initiative,
our 'attenuation apparatus' is currently being modified to allow forced-oscillation
measurements in extension/flexure, as well as torsion. Such measurements
will allow the probing of poroelastic effects in cracked and fluid-saturated
media that are analogues for upper-crustal rocks.
Modelling of elastic properties and equation of state
(with B.L.N. Kennett): The
thermodynamically consistent finite-strain model of Stixrude and Lithgow-Bertelloni
(GJI, 2005) provides an attractive framework for the assessment and assimilation
of experimental data concerning elastic properties and equation of state.
The model requires the specification of 9 parameters: molar volume, (isotropic)
bulk and shear moduli and their pressure derivatives, the effective Debye
temperature, and the Grüneisen parameter and its volume and shear
strain derivatives. We have explored the feasibility of using Sambridge's
Neighbourhood Algorithm strategy (GJI, 1999) to undertake a guided search
of the model space that is constrained simultaneously by diverse experimental
datasets as an alternative to iterative least-squares fitting. This approach
has been tested on data for MgO including measurements of specific heat
and thermal expansion, static and shock compression, and the pressure
and temperature dependence of elastic wavespeeds. The search converged
on a unique model that adequately represents most of the experimental
data, but not before revealing tensions between marginally incompatible
datasets.
[1] Jackson, I, A. Barnhoorn, Y. Aizawa and C. Saint. Improved
experimental procedures for the study of high-temperature viscoelastic
relaxation, Phys. Earth Planet. Interiors (in press).