Geoscience Reference
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throughout most of the upper mantle, but these
effects are overridden below 400 km where most
mantle minerals are in the cubic structure. A
phase change, along with high pressure and low
stress, may contribute to the lengthening of the
relaxation times. Relaxation times change only
slightly through most of the lower mantle.
Most of the lower mantle therefore has high
Q, for body waves and low Q, for free oscillations
(Tables 19.2 and 19.3). The relationship between
the P, S and Rayleigh wave Q is;
100,000
10,000
1000
200
1
10
100
1000
Q
−
1
p
LQ
−
1
s
L
)
Q
−
1
K
=
+
(1
−
Period (s)
Fig. 19.8
Q
K
as a function of frequency for various regions
in the Earth (Anderson and Given, 1982).
)
2
where L
=
(4
/
3)(
β/α
and
β
and
α
are the shear
and compressional velocities.
For a Poisson solid with Q
−
1
K
=
0,
temperature gradient and high tectonic stresses
can keep the absorption band at high frequencies
Q
P
=
(9
/
4)
Q
s
