Geoscience Reference
In-Depth Information
3
Elasticity, Anelasticity, and Viscosity
of a Partially Molten Rock
YASUKO TAKEI
Earthquake Research Institute, University of Tokyo, Tokyo, Japan
Summary
and electromagnetic observations in the Earth.
Various theoretical and experimental studies
have confirmed that partial melting decreases
elastic moduli, the quality factor (Q), and the
creep strength of rocks (e.g., O'Connell & Budi-
ansky, 1974; Mavko, 1980; Murase & Fukuyama,
1980; Cooper
et al
., 1989; Hirth & Kohlstedt,
1995; Jackson
et al
., 2004). Compared with the
melt effect, the effect of temperature on the elastic
moduli of mantle minerals, measured at ultra-
sonic frequencies
This chapter reviews the mechanical properties of
partially molten rocks as structure-sensitive, vis-
coelastic, multi-phase systems. On the one hand,
recent progress in theoretical modeling has shown
that the effects of microstructures on elasticity,
anelasticity, and viscosity can be treated quan-
titatively using a single microstructural model
(contiguity model), and this model enables us
to integrate the results of seismology, laboratory
studies, and mantle dynamics. On the other hand,
the many unknown variables in rock anelastic-
ity make it difficult to use seismological data
to derive quantitative information about melt
fractions and pore geometry. Because such quan-
titative information about the melt phase would
provide valuable constraints on the dynamics of
melt segregation in the Earth, the uncertainties
in rock anelasticity need to be clarified.
MHz, is much smaller (Isaak,
1992). As a consequence, low-velocity regions
observed seismologically in the upper mantle
have mainly been interpreted as indicating partial
melting, rather than a high-temperature anomaly.
However, recent experimental studies performed
at seismic frequencies (1
>
10
−
3
Hz) have shown
that the temperature effect on the elastic moduli
can be much larger at seismic frequencies than
at ultrasonic frequencies, for the reason that
temperature activates the anelastic relaxation of
olivine aggregates (Jackson
et al
., 2002). Because
hydrogen-related defects are also expected to
chemically activate the anelastic relaxation (e.g.,
Karato & Jung, 1998), larger effects are expected
at seismic frequencies than those measured
at high frequencies (
−
3.1 Introduction
Partial melting and melt segregation play key
roles in the dynamics and chemical evolution
of the Earth. Therefore, intensive and extensive
work has been done to simulate these processes
numerically and experimentally, and to detect
the presence of a melt phase from seismological
>
lnV
S
=−
0.2% for
0.9wt% H
2
O at 12GPa; Jacobsen
et al
., 2008).
As a result, a high-temperature anomaly and
hydrogen-related defects (hereafter referred to as
GHz,
