Chapter
20
Fabric
of
the
mantle
A
nis
o
tr
opy
And
perpendicular
now
and
now
transverse,
Pierce
the
dark
soil
and
as
they
pierce
and
pass
Make
bare
the
secrets
of
the
Earth's
deep
heart.
Shelley,
Prometheus
Unbound
Anisotropy
is
responsible
for
large
variations
in
seismic
velocities;
changes
in
the
orientation
of
mantle
minerals,
or
in
the
direction
of
seismic
waves,
cause
larger
changes
in
velocity
than
can
be
accounted
for
by
changes
in
temperature,
composition
or
mineralogy.
Plate-tectonic
pro-
cesses,
and
gravity,
create
a fabric
in
the
mantle
.
Anisotropy
can
be
microscopic
-
orientation
of
crystals
-
or
macroscopic
-
large-scale
lamina-
tions
or
oriented
slabs
and
dikes.
Discussions
of
velocity
gradients,
both
radial
and
lateral,
and
chemistry
and
mineralogy
of
the
mantle
must
allow
for
the
presence
of
anisotropy.
Anisotropy
is
not
a
second-order
effect.
Seismic
data
that
are
interpreted
in
terms
of
isotropic
theory
can
lead
to
models
that
are
not
even
approximately
cor-
rect.
Slab
anisotropy
can
cause
artifacts
in
tomo-
graphic
models.
A
wealth
of
new
infonnation
regarding
mantle
structure,
history,
mineralogy
and
flow
is
becoming
available
as
the
anisotropy
of
the
mantle
is
becoming
better
understood.
Introduction
In
the
first
edition
of
Th
eory
of
the
Earth
there
were
sections
that
are
largely
missing
in
this
edition.
There
was
a
very
large
section
on
anisotropy
since
it
was
a
relatively
new
concept
to
seismologists
.
There
was
also
a
large
section
devoted
to
the
then-novel
thesis
that
seismic
velocities
were
not
independent
of
frequency,
and
that
anelasticity
had
to
be
allowed
for
in
esti-
mates
of
mantle
temperatures.
Earth
scientists
no
longer
need
to
be
convinced
that
anisotropy
and
anelasticity
are
essential
elements
in
Earth
physics,
but
there
may
still
be
artifacts
in
tomo-
graphic
models
or
in
estimates
of
errors
that
are
caused
by
anisotropy.
At
the
time
of
the
first
edition
of
this
book
-
1989
-
the
Earth
was
usually
assumed
to
be
perfectly
elastic
and
isotropic
to
the
propagation
of
seismic
waves.
These
assumptions
were
made
for
mathemati-
cal
and
operational
convenience.
The
fact
that
a
large
body
of
seismic
data
can
be
satisfacto-
rily
modeled
with
these
assumptions
does
not
prove
that
the
Earth
is
isotropic
or
perfectly
elastic.
There
is
often
a
direct
trade-off
between
anisotropy
and
heterogeneity,
and
between
fre-
quency
dependence
and
depth
dependence
of
seismic
velocities.
An
anisotropic
structure
can
have
characteristics,
such
as
travel
times,
normal-
mode
frequencies
and
dispersion
curves,
that
are
identical,
or
similar,
to
a
different
isotropic
struc-
ture.
A
layered
solid,
for
example,
composed
of
isotropic
layers
that
are
thin
compared
to
a seis-
mic
wavelength
will
behave
as
an
anisotropic
solid
-
the
velocity
of
propagation
depends
on
direction.
The
effective
long-wavelength
elastic
constants
depend
on
the
thicknesses
and
elastic
properties
of
the
individual
layers.
The
reverse
is
also
true;
an
anisotropic
solid
with
these
same
elastic
constants
can
be
modeled
exactly
as
a
stack
of
isotropic
layers.
The
same
holds
true
for
an
isotropic
solid
permeated
by
oriented
cracks
or
aligned
inclusions
.
This
serves
to
illustrate
the
trade-off
between
heterogeneity
and
anisotropy.
Not
all
anisotropic
structures,
however,
can
be
modeled
by
laminated
solids.
The
crystals
of
the
mantle
are
anisotropic
,
and
rocks
from
the
mantle
show
that
these
crys-
tals
exhibit
a
high
degree
of
alignment
.
There
is
also
evidence
that
crystal
alignment
is
uniform
over
large
areas
of
the
upper
mantle
.
At
man-
tle
temperatures,
crystals
tend
to
be
easily
recrys-
tallized
and
aligned
by
the
prevailing
stress
and
flow
fields.
But
there
may
also
be
large-scale
fab-
ric
in
the
upper
mantle,
caused
by
orientation
of
subducted
slabs
or
dikes
,
for
example.
The
effects
of
anisotropy
are
often
subtle
and
,
if
unrecognized
,
are
usually
modeled
as
inhomo-
geneities,
for
example
, as
layering
or
gradients.
The
most
obvious
manifestations
of
anisotropy
are
:
(1)
[s h
ear-wave
splitt
in
g ]
or
birefringence
-
the
two
polarizations
of
S-waves
arrive
at
different
times;
(2)
[
az
imu
t h a l
an
i
so
t
ropy
] -
the
arrival
times,
or
apparent
velocities
of
seismic
waves
at
a
given
distance
from
an
event
,
depend
on
azimuth
;
and
(3)
an
apparent
discrepancy
between
Love
waves
and
Rayleigh
waves
[
Love
Rayleig
h
discrepa
n
cy
].
Even
these
are
not
completely
unambiguous
indi-
cators
of
anisotropy
. Effects
such
as
P
to
S
conver-
sion
,
dipping
interfaces,
attenuation,
and
density
va
riations
must
be
properly
taken
into
account
.
There
is
now
growing
acceptance
that
much
of
the
upper
mantle
may
be
anisotropic
to
the
prop-
ag
ation
of
seismic
waves.
It
has
been
known
for
some
time
that
the
discrepancy
betwee
n m
a n
tle
Ray-
leigh
and
Love
waves
could
be
explain
ed
if
the
vertic
a l
P
and
S
velocities
in
the
upper
man-
tle
were
7-8
%
less
than
the
horizontal
ve
lo
c
i-
ties.
The
Love-Rayleigh
discrepancy
has
survived
to
the
present,
and
average
Earth
models
hav
e
SV
in
the
upper
mantle
less
than
SH
by
about
3%
.
Some
early
models
were
based
on
separat
e
ORIGIN
OF
MANTLE
ANISOTROPY
257
isotropic
inversions
of
Love
and
Rayleigh
waves
(pseudo-isotropic
inversions).
This
is
not
a
valid
procedure.
There
is
a
trade-off
between
anisotropy
and
structure.
In
particular,
the
very
low
upper-mantle
shear
velocities
,
4.0-4.2
km
./s.
found
by
many
isotropic
and
pseudo-isotropic
inversions,
are
not
a
characteristic
of
models
resulting
from
full
anisotropic
inversion.
The
P-
wave
anisotropy
makes
a
significant
contribution
to
Rayleigh
wave
dispersion.
This
must
also
be
allowed
for
in
tomographic
surface
wave
inver-
sions,
but
seldom
is.
Since
intrinsic
anisotropy
requires
both
anisotropic
crystals
and
preferred
orientation.
the
anisotropy
of
the
mantle
contains
informa-
tion
about
the
mineralogy
and
stress
gradients.
For
example,
olivine,
the
most
abundant
upper-
mantle
mineral,
is
extremely
anisotropic
for
both
P-wave
and
S-wave
propagation.
It
is
readily
ori-
ented
by
recrystallization
in
the
ambient
stress
field.
Olivine-rich
outcrops
show
a
consistent
pre-
ferred
orientation
over
large
areas.
In
general,
the
seismically
fast
axes
of
olivine
are
in
the
plane
of
the
flow
,
with
the
a-axis
,
the
fastest
direc-
tion
,
pointing
in
the
direction
of
flow.
The
b-
axis,
the
minimum
velocity
direction,
is
gener-
ally
normal
to
the
flow
plane,
or
vertical.
Pyrox-
enes
are
also
very
anisotropic.
The
magnitude
of
the
anisotropy
in
the
mantle
is
comparable
to
that
found
in
ultramafic
rocks
(Figure
20
.1) .
Soft
layers
or
oriented
fluid-filled
cracks
also
give
an
apparent
anisotropy.
Much
seismic
data
that
are
used
in
upper-mantle
modeling
are
averages
over
several
tectonic
provinces
or
over
many
azilnuths
.
Az
imu
t h a l a
ni
sotropy
may
therefore
be
aver-
aged
out,
but
differences
between
vertical
and
horizontal
velocities
are
not.
Origin
of
mantle
anisotropy
Nicholas
and
Christensen
(1987)
elucidated
the
reason
for
stron
g
preferred
crystal
orientation
in
d e
formed
rocks
.
First
,
they
noted
that
in
homogenous
deformation
of
a
specimen
com-
posed
of
minerals
with
a
dominant
slip
sy
st
e
m,
the
preferred
orientations
of
slip
planes
and
slip
directions
coincide
respectively
with
the
ori-
entations
of
the
flow
plane
and
the
flow
line
.
258
FABRIC
OF
THE
MANTLE
01.0
0.8
0.6
0.4
0.2
~
0
-"'
>
c.o
-.4
- .6
- .8
- 1 .
0
'---'---'---'---'-----'
-
--'-
-
--'---'--------'
0
40
80
120
160
200
240
280
320
360
Azimuth
Azimuthal
anisotropy
of
Pn
waves
in
the
Pacific
upper
mantle.
The
unique
anisotropy
of
the
Pacific
upper
mantle
has
also
been
mapped
with
surface
waves
(after
Morris
et
a/.
,
1969).
Simple
shear
in
a
crystal
rotates
all
the
lines
attached
to
the
crystal
except
those
in
the
slip
plane.
This
results
in
a
bulk
rotation
of
crystals
so
that
the
slip
planes
are
aligned,
as
required
to
maintain
contact
between
crystals
.
The
crys-
tal
reorientations
are
not
a
direct
result
of
the
applied
stress
but
are
a
geometrical
requirement.
Bulk
anisotropy
due
to
crystal
orientation
is
therefore
induced
by
plastic
strain
and
is
only
indirectly
related
to
stress.
The
result,
of
course,
is
also
a
strong
anisotropy
of
the
viscosity
of
the
rock,
and
presumably
attenuation,
as
well
as
elastic
properties.
This
means
that
seismic
tech-
niques
can
be
used
to
infer
flow
in
the
mantle.
It
also
means
that
mantle
viscosity
inferred
from
postglacial
rebound
is
not
necessarily
the
same
as
that
involved
in
plate
tectonics
and
mantle
convection.
Peridotites
from
the
upper
mantle
display
a
strong
preferred
orientation
of
the
domi-
nant
minerals
,
olivine
and
orthopyroxene.
They
exhibit
a
pronounced
acoustic-wave
anisotropy
that
is
consistent
with
the
anisotropy
of
the
constituent
minerals
and
their
orientation.
In
igneous
rocks
preferred
orientation
can
be
caused
by
grain
rotation,
recrystallization
in
a
nonhydrostatic
stress
field
or
in
the
presence
of
a
thermal
gradient,
crystal
setting
in
magma
chambers,
flow
orientation
and
dislocation-
controlled
slip
.
Macroscopic
fabrics
caused
by
banding,
cracking,
sill
and
dike
injection
can
also
cause
anisotropy.
Eclogites
and
basalts
are
much
less
anisotropic;
anisotropy
can
therefore
be
used
as
a
petrological
tool.
Plastic
flow
induces
preferred
orientations
in
rock-forming
minerals.
The
relative
roles
of
deviatoric
stresses
and
plastic
strain
have
been
long
debated.
In
order
to
assure
continuity
of
a
deforming
crystal
with
its
neighbors,
five
inde-
pendent
degrees
of
motion
are
required
(the
Von
Mises
criterion).
This
can
be
achieved
in
a crys-
tal
with
the
activation
of
five
independent
slip
systems
or
with
a
combination
of
fewer
slip
sys-
tems
and
other
modes
of
deformation.
In
silicates
only
one
or
two
slip
systems
are
activated
under
a
given
set
of
conditions
involving
a
given
tem-
perature,
pressure
and
deviatoric
stresses
.
The
homogenous
deformation
of
a
dominant
slip
sys-
tem
and
the
orientation
of
slip
planes
and
slip
directions
tend
to
coincide
with
the
flow
plane
and
the
flow
direction.
Mantle
peridotites
typically
contain
more
than
65
%
olivine
and
20%
orthopyToxene
.
The
high-P
wave
direction
in
olivine
(Figure
20.2)
is
along
the
a-axis
[1001],
which
is
also
the
domi-
nant
slip
direction
at
high
temperature
.
The
low-
est
velocity
crystallographic
direction
is
[0101],
the
b-direction.
which
is
normal
to
a
common
slip
plane
.
Thus
,
the
pattern
in
olivine
aggregates
is
related
to
slip
orientations.
There
is
no
such
simple
relationship
with
shear
waves
and
,
in
fact,
the
S-wave
anisotropy
of
peridotites
is
small
.
Orthopyroxenes
also
have
large
P-wave
aniso-
tropies
and
relatively
small
S-wave
anisotropies.
The
high-Vp
direction
coincides
with
the
[1001]
pole
of
the
unique
slip
plane
and
the
inter-
mediate
Vp
crystallographic
direction
coincides
with
the
unique
[0011]
slip
line
(Figure
20.2).
In
natural
peridotites
the
preferred
orientation
of
olivine
is
more
pronounced
than
the
other
minerals
. Olivine
is
apparently
the
most
ductile
and
easily
oriented
upper-mantle
mineral,
and
therefore
controls
the
seismic
anisotropy
of
the
9 .
89
km
/ s
7.92
km
/ s
a
c
a
8.25
km
/ s
ORIGIN
OF
MANTLE
ANISOTROP
Y
259
Possible
olivine
and
orthopyroxene
orientations
within
the
upper
mantle
showing
compressional
velocities
for
the
three
crystallographic
axes
, and
compressional
and
shear
velocities
in
the
olivine
a- c
plane
and
orthopyroxene
b-e
pl
ane
(after
Christensen
and
Lundquist
,
1982)
.
OLIVINE
ORTHOPYROXENE
10
10
a
c
OLIVINE
ORTHOPYROXENE
upper
mantle
.
The
anisotropy
of
.B-spinel,
a high-
pressure
form
of
olivine
that
is
expected
to
be
a
major
mantle
component
below
400
km.
is
also
high.
TI1e
y-spinel
form
of
olivine
,
stable
below
about
500
km,
is
much
less
anisotropic.
Recrystallization
of
olivine
to
spinel
forms
can
be
expected
to
yield
aggregates
with
preferred
orientation
but
with
perhaps
less
pronounced
P-wave
anisotropy
. .B-spinel
has
a
strong
S-wave
anisotropy
(24
%
variation
with
direction
,
16
%
maximum
difference
between
polarizations).
The
fast
shear
directions
are
parallel
to
the
slow
P-wave
directions
,
whereas
in
olivine
the
fast
S-directions
correspond
to
intermediate
P-wave
velocity
directions.
Orthopyroxene
transforms
to
a
cubic
garnet-like
structure
that
is
stable
over
much
of
the
transition
region
part
of
the
upper
mantle
.
TI1is
mineral,
majorite,
is
expected
to
be
relatively
i
sotropic.
Therefore,
most
of
the
mantle
between
400
and
650
km
depth
is
expected
to
have
relatively
low
anisotropy
,
with
the
anisotropy
decreasing
as
olivine
transforms
to
the
spinel
structures
.
At
low
temperatures,
as
in
subduction
zones,
the
stable
form
of
pyroxene
is
an
ilmenite-type
structure
that
is
extremely
anisotropic
.
Thus
,
the
deep
part
of
slabs
may
exhibit
pronounced
anisotropy
, a
property
that
could
be
mistaken
for
deep
slab
penetration
in
certain
seismic
experiments
.
Petrofabric
studies
combined
with
field
stud-
ies
on
ophiolite
harzburgites
give
the
following
relationships.
(1)
Olivine
c axes
and
orthopymxene
b
axes
lie
approximately
parallel
to
the
inferred
ridge
axis
in
a
plane
parallel
to
the
Moho
disconti-
nuity.
(2)
The
olivine
a
axes
and
the
orthopYToxene
c
axes
align
s
ubp
arallel
to
the
inferred
speading
direction.
(3)
TI1e
olivine
b
axes
and
the
orthopYToxene
a
axes
are
approximately
perpendicular
to
the
Moho.
These
results
indicate
that
the
compressional
velocity
in
the
vertical
direction
increases
with
the
orthopyroxene
content,
whereas
horizontal
velocities
and
anisotropy
decrease
with
increas-
ing
orthopyroxerie
content.
260
FABRIC
0
F T H E
MANTLE
The
maximum
compressional
wave
velocity
in
orthopyroxene
(along
the
a
axis)
parallels
the
minimum
(b
axis)
velocity
of
olivine.
For
olivine
b
axis
vertical
regions
of
the
mantle,
as
in
ophi-
olite
peridotites,
the
vertical
P-velocity
increases
with
orthopyroxene
content.
The
reverse
is
true
for
other
directions
and
for
average
properties.
Appreciable
shear-wave
birefringence
is
expected
in
all
directions
even
if
the
individual
shear
velocities
do
not
depend
much
on
azimuth.
The
total
P-wave
variation
with
azimuth
in
olivine-
and
orthopyroxene-rich
aggregates
is
about
4-6%,
while
the
S-waves
only
vary
by
1
to
2%
(Figure
20
.3)
.
The
difference
between
the
two
shear-wave
polarizations,
however
, is
4-6%.
The
azimuthal
variation
of
S-waves
can
be
expected
to
be
hard
to
measure
because
the
maximum
velocity
differ-
ence
occurs
over
a
small
angular
difference
and
N
VP
N
N
E
E
N
E
because
of
the
long-wavelength
nature
of
shear
VS
max
waves.
The
shear-wave
anisotropy
in
the
ilmenite
structure
of
pyroxene
,
expected
to
be
important
in
the
deeper
parts
of
subducted
slabs,
is
quite
pronounced
and
bears
a
different
relationship
to
the
P-wave
anisotropy
than
that
in
peridotites.
On
e
possible
manifestation
of
slab
anisotropy
is
the
variation
of
travel
times
with
take-off
angle
from
intermediate-
and
deep-focus
earthquakes.
Fast
in-plane
velocities,
as
expected
for
oriented
olivine,
and
probably
spinel
and
ilmenite,
may
easily
be
misinterpreted
as
evidence
for
deep
slab
penetration.
The
mineral
assemblages
in
cold
slabs
are
also
different
from
the
stable
phases
in
normal
and
hot
mantle.
The
colder
phases
are
generally
denser
and
seismically
fast.
An
isotro
py
and
isobaric
phase
changes
in
the
source
region
have
been
ignored
in
most
studies
purporting
to
show
deep
slab
penetration
into
the
lower
mantle.
There
is
a
trade-off
between
the
length
of
a high-velocity
slab
and
its
veloc-
ity
contrast
and
anisotropy
and
structure
at
the
source
.
Anisotropy
of
crystals
Because
of
the
simplicity
an
d
availability
of
the
mi
c
roscope
,
the
optical
properties
of
minerals
N
N
E
Equal
area
projection
of
the
acoustic
velocities
measured
on
samples
of
peridotite
. Dashed
line
is
vertical
direction
, solid
great
circle
is
the
horizontal
(after
Chri
s
tensen
and
Salisbury
, 1979).
E
receive
more
attention
than
the
acoustic
prop-
erties
.
It
is
the
acoustic
or
ultrasonic
properties
,
however
,
that
are
most
relevant
to
the
inter-
pretation
of
seismic
data
. Being
crystals,
miner-
als
exhibit
both
optical
and
acoustic
anisotropy.
Aggregates
of
crystals,
rocks
,
are
also
anisotropic
and
display
fabrics
that
can
be
analyzed
in
the
same
terms
used
to
describe
crystal
symmetry.
Tables
20.1,
20.2
and
20.3
summarize
the
acous-
tic
anisotropy
of
some
important
rock-forming
minerals.
Pyroxenes
and
olivine
are
unique
in
havin
g
a
greater
P-wave
anisotropy
than
S-wav
e
anisotropy.
Spinel
and
garnet,
cubic
crystals
,