Geoscience Reference
In-Depth Information
Attenuation mechanisms
The actual physical mechanism of attenuation
in the mantle is uncertain, but it is likely to
be a relaxation process involving a distribu-
tion of relaxation times, or a scattering pro-
cess involving a distribution of scatterers. Many
of the attenuation mechanisms that have been
identified in solids occur at relatively low tem-
peratures and high frequencies and can there-
fore be eliminated from consideration. These
include point-defect and dislocation resonance
mechanisms, which typically give absorption
peaks at kilohertz and megahertz frequencies
at temperatures below about half the melt-
ing point. The so-called grain-boundary and
cold-work peak and the 'high-temperature back-
ground' occur at lower frequencies and higher
temperatures. These mechanisms involve the
stress-induced diffusion of dislocations. The Bor-
doni peak occurs at relatively low temperature
in cold-worked metals but may be a higher-
temperature peak in silicates. It is apparently
due to the motion of dislocations since it disap-
pears upon annealing. Because of the large wave-
lengths of seismic waves, it is not required that
the dissipation mechanism be microscopic, or
grain-scale.
correction
. For simple dislocation and grain
boundary networks the difference between the
relaxed and unrelaxed moduli is about 8%.
Anharmonic and anelastic corrections
to seismic velocities are now routinely applied
in comparisons with laboratory values. These are
more complex, but more physically based, than
the simple linear scalings between velocity and
temperature or density that were used in the
past.
The relationship between retardation spectra
and transient creep and the
Jeffreys-
Lomnitz creep law
are given in
Theory of
the Earth, Chapter
14. Jeffreys used this law
as an argument against continental drift.
Partial melting
Seismic studies indicate that increased absorp-
tion, particularly of S-waves, occurs below vol-
canic zones and is therefore presumably related
to partial melting. Regional variations in seis-
mic absorption are a powerful tool in map-
ping the thermal state of the crust and upper
mantle. It has also been suggested that partial
melting is the most probable cause of the low-
velocity layer in the upper mantle of the Earth.
Thus the role of partial melting in the atten-
uation of seismic waves may be a critical one,
at least in certain regions of the Earth. Stud-
ies of the melting of polycrystalline solids have
shown that melting begins at grain boundaries,
often at temperatures far below the melting
point of the main constituents of the grains.
This effect is caused by impurities that have col-
lected at the grain boundaries during the initial
solidification.
In principle, a large anelastic contribution
can cause a large decrease in seismic velocity
without partial melting but many of the low-
Q
regions are volcanic. In high heat-flow areas it
is difficult to design a geotherm that does not
imply upper mantle melting. Partial melting is
a possible cause of seismic attenuation, and low
velocity, particularly at very low frequencies.
Figure 19.3 shows the
Q
in an ice--brine--NaCl
system
Spectrum of relaxation times
Relaxation mechanisms lead to an internal fric-
tion peak of the form
∞
Q
−
1
(
ω
)
=
2
2
)] d
τ
D
(
τ
) [
ωτ/
(1
+
ω
τ
−∞
where
D
(
τ
) is called the retardation spectrum
and
is the modulus defect, the relative differe-
nce between the high-frequency, unrelaxed shear
modulus and the low-frequency, relaxed mod-
ulus. The modulus defect is also a measure
of the total reduction in modulus that is
obtained in going from low temperature to high
temperature.
Convenient forms of the retardation spec-
trum are given in Minster and Anderson (1981)
and discussed at greater length in Theory of
the Earth. These equations are now widely
used in
correcting seismic velocities
in the mantle to standard temperatures
and frequencies
, the so-called
anelastic
for
a
concentration
of
2%
NaCl.
Note
theabruptdropin
Q
as
partial
melting
is
