Geoscience Reference
In-Depth Information
Table 20.1
Anisotropic properties of rock forming minerals
Anisotropy
†
Max S
P direction
(percent)
Direction1
Mineral
Symmetry
Max.
Min.
Polarization
P
S
Olivine
Orthorhombic
[100]
[010]
45
◦
/135
◦∗
25
22
Garnet
Cubic
[001]
∼
50
◦∗
[110] / [110]
0.6
1
Orthopyroxene
Orthorhombic
[100]
[010]
[010] / [001]
16
16
[011] / [011]
Clinopyroxene
Monoclinic
[001]
[101]
21
20
Muscovite
Monoclinic
[110]
[001]
[010] / [100]
58
85
[011] / [011]
Orthoclase
Monoclinic
[010]
[101]
46
63
[011] / [011]
Anorthite
Triclinic
[010]
[101]
36
52
Rutile
Tetragonal
[001]
[100]
[100] / [010]
28
68
[011] / [011]
Nepheline
Hexagonal
[001]
[100]
24
32
Spinel
Cubic
[101]
[001]
[100] / [010]
12
68
β
-Mg
2
SiO
4
Orthorhombic
[010]
[001]
—
16
14
Babuska (1981), Sawamoto and others (1984).
∗
Relative to [001].
†
[(
V
max
−
V
min
)/
V
mean
]
×
100.
have low P-wave anisotropy. Hexagonal crystals,
and the closely related class of trigonal crys-
tals, have high shear-wave anisotropies. This is
pertinent to the deeper part of cold subducted
slabs in which the trigonal ilmenite form of
pyroxene may be stable. Deep-focus earthquakes
exhibit a pronounced angular variation in both
S- and P-wave velocities and strong shear-wave
birefringence. Cubic crystals do not necessarily
have low shear-wave anisotropy. The major min-
erals of the shallow mantle are all extremely
anisotropic.
The elastic properties of simple oxides and sil-
icates are predominantly controlled by the oxy-
gen anion framework, especially for hexagonally
close-packed and cubic close-packed structures,
but also by the nature of the cations occur-
ring within the oxygen interstices. Corundum
(Al
2
O
3
) consists of a hexagonal close-packed array
of large oxygen ions into which the smaller
aluminum ions are inserted in interstitial posi-
tions. Forsterite (Mg
2
SiO
4
) consists of a frame-
work of approximately hexagonal close-packed
oxygen ions with the Mg
2
∼
cations occupying
one-half of the available octahedral sites (sites
surrounded by six oxygen ions) and the Si
4
∼
cations occupying one-eighth of the available
tetrahedral sites (sites surrounded by four oxy-
gens). The packing of the oxygens depends on the
nature of the cations.
-spinel and clinopyroxene are sta-
ble below 400 km, and these are also fairly
anisotropic. Below 400 km the major mantle min-
erals at high temperature,
β
-spinel and garnet-
majorite are less anisotropic. At the temperatures
prevailing in subduction zones, the cold high-
pressure forms of orthopyroxene, clinopyroxene
and garnet are expected to give high velocities
and anisotropies. If these are lined up, by stress
or flow or recrystallization, then the slab itself
will be anisotropic. This effect will be hard to
distinguish from a long isotropic slab, if only
sources in the slab are used. The mantle minerals
outsideofasinkingslabarealsolikelytobe
aligned.
γ
Theory of anisotropy
In a transversely isotropic solid with a verti-
cal axis of symmetry, we can define four elastic
constants in terms of P- and S-waves propagat-
ing perpendicular and parallel to the axis of
