Geoscience Reference
In-Depth Information
''water'') have been proposed as two factors other
than partial melting that have the potential to
explain seismic low velocities and low-Q regions
in the upper mantle. In order to evaluate the
relative contributions of these multiple factors
to the geophysical observations and dynamics,
a quantitative assessment of the effects of
melt, temperature, and water on seismic wave
velocities, seismic Q, and rheology is important.
Ultrasonic and seismic waves have the frequen-
cies of 10
6
The purpose of this chapter is to review the
effects of a partial melt on elasticity, anelastic-
ity, and viscosity, with a special emphasis on
''quantification.'' Hence, a major focus will be
on elasticity and viscosity, for which quantita-
tive assessments can be undertaken (Table 3.1).
For anelasticity, the general and phenomeno-
logical framework is presented as a basis for
future progress. Until quite recently, a quanti-
tative assessment of the effects of melting has
been difficult, even for elasticity and viscosity,
because of the strong sensitivity to microstruc-
tures. Even when the mechanical properties of
each solid and liquid phase are known, the bulk
mechanical properties of the composites are not
uniquely determined by the volume fraction of
melt, but strongly depend on the detailed geome-
try of melt-filled pores. Therefore, to understand
the bulk mechanical properties, it is necessary
to understand both pore geometry and the effect
of pore geometry on the mechanical properties.
Both these matters are reviewed below in sepa-
rate sections, and there is no doubt that signifi-
cant progress in these areas has been made over
the past decade. One matter of note is the de-
velopment of a realistic microstructural model
(contiguity model) that can be applied commonly
to elasticity, anelasticity, and viscosity. Histor-
ically, completely different types of microstruc-
tural models were used in studying these various
10
−
3
Hz, respectively,
whereas melt segregation and mantle convection
have frequencies of
10
9
Hz and 1
−
−
10
−
9
Hz. Over such a broad
frequency range, the mechanical response of a
rock at high homologous temperatures changes
from elastic to viscous, where the transitional
property is called anelasticity. Anelasticity causes
dispersion (frequency dependence of elastic mod-
uli) and attenuation. Seismic wave velocities
are determined by elasticity and anelasticity,
while the seismic attenuation Q
−
1
is determined
by anelasticity alone. Table 3.1 summarizes an
overview of the present state of knowledge on
the effects of melt, temperature, and water on
elasticity, anelasticity, and viscosity. Also shown
in Table 3.1 are the effects of grain size on anelas-
ticity and viscosity. Compared with elasticity and
viscosity, anelasticity is still poorly understood,
making it difficult to quantitatively predict veloc-
ity change and attenuation at seismic frequencies.
<
Table 3.1
Present state of knowledge concerning the effects of various factors on
the mechanical properties of rock.
Elasticity
Anelasticity
Viscosity
GB
disl.
diff.
disl.
a
Melt
?
?
Temperature
b
?
?
Water
?
?
Grain size
-
?
-
-
Quantitative assessment can be performed. Underlying mechanism is established.
Quantitative assessment can be performed. Underlying mechanism is not established.
? Potentially important, but quantitative assessment is still difficult.
- No effect.
a: Poroelasticity
b: Anharmonicity
