Theory of the Earth
Don L. Anderson
Chapter 4. The Lower Mantle and Core
Boston: Blackwell Scientific Publications, c1989
Copyright transferred to the author September 2, 1998.
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Recommended citation:
Anderson, Don L. Theory of the Earth.
Boston: Blackwell Scientific Publications,
1989.
http://resolver.calt
ech.edu/CaltechBOOK:1989.001
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Abstract:
The lower mantle starts just below the major mantle discontinuity near 650 km.
The depth of this discontinuity varies,
perhaps by as much as 100 km and is
variously referred to as the "650-km disco
ntinuity" or "670-km discontinuity." In
recent Earth models there is a region of
high velocity gradient for another 50 to
100 km below the discontinuity. This is pr
obably due to phase changes, but it
could represent a chemical gradient. The "lower mantle proper" therefore does
not start until a depth of about 750 or
800 km. Below this depth the lower mantle
is relatively homogeneous until about 300 km above the core-mantle boundary. If
there is a chemical difference between the upper and lower mantle then, in a
convecting dynamic mantle, the boundary will not be at a fixed depth. This
clarification is needed because of the
controversy about whether slabs penetrate
into the lower mantle or whether they
just push down the discontinuity.
core.
The Lower Mantle
and
Core
I
must
be
getting
somewhere near
the
centre
of
the
earth.
Let me
see:
that would
be
four thousand
miles
down.
I
think-
T
he lower mantle starts
just below
the major mantle dis
-
continuity near
650
km.
The depth
of
this
disconti
-
nuity
varies, perhaps
by
as
much
as 100 km
and
is variously
referred to as the
"
650
-
km discontinuity
"
or
"
670
-
km dis
-
continuity.
"
In recent Earth
models
there is a region
of high
velocity gradient for another
50
to
100 km
below
the dis
-
continuity. This is probably due to phase changes, but it
could represent a chemical gradient.
The
"
lower mantle
proper
"
therefore does
not
start until a depth
of
about
750
or
800
km.
Below this
depth the lower mantle
is relatively
homogeneous until about 300 km
above
the core
-
mantle
boundary.
If
there is a chemical difference
between
the
upper
and
lower mantle then,
in a convecting dynamic man
-
tle,
the boundary will
not be
at a
fixed
depth. This clarifi
-
cation is needed because
of
the controversy
about
whether
slabs penetrate into the lower mantle
or
whether
they
just
push down the discontinuity.
COMPOSITION
OF
THE
LOWER
MANTLE
Several methods can
be used
to estimate the composition
of
the lower mantle
from
seismic data; perhaps the
most
direct
is to compare
shock
-
wave
densities at
high
pressure
of
vari
-
ous silicates
and
oxides
with
seismically determined densi
-
ties. The shock
-
wave Hugoniot data
must
be
corrected
to
adiabats. There
is a trade
-
off between
temperature
and
com
-
position, so this exercise is nonunique. Materials
of
quite
different compositions, say
(Mg,Fe)SiO,
(perovskite)
and
(Mg,Fe)O,
can have identical densities,
and
mixtures
in
-
volving
different proportions
of
MgO,
FeO
and
SiO,
can
satisfy the density constraints.
In
addition, the density
in
the Earth is
not
as
well
determined
as
such
parameters
as
the compressional
and
shear velocities. Nevertheless, many
authors
have used
density alone to argue for
specific
com
-
positional models for the lower mantle or to argue that
the
mantle
is
chemically homogeneous. The density
of
the
lower mantle
and
the density
jump
at 650
km
are very
weak
constraints
on
the chemistry
of
the
lower
mantle or the
change
in
chemistry
between
the upper
and
lower
mantle.
Arguments
based
on
viscosity
and
mean atomic weight
are
even
weaker. The mineralogy
of
the
lower mantle is
even
harder to determine since oxide mixtures, such as
MgO
+
SiO,
(stishovite),
have
densities, at high pressure, similar
to
compounds
such
as
perovskite
having
the same
stoichi-
ometry.
The
bulk
modulus
K,
can
be
determined
by
differenti
-
ating shock
-
wave data,
(paplap),,
but this,
of
course,
is
subject
to
uncertainties. Nevertheless,
using both
p
and
K,
in
comparisons
with
seismic data reduces
the
ambiguities.
A more direct comparison
uses the
seismic parameter
Q,,
which
can
be
determined from
both
seismology
and shock
-
wave
data:
It has been
shown
that a chondritic composition for
the
lower mantle
gives
satisfactory agreement
between shock
-
wave
and
seismic data (Anderson, 1977). Pyrolite,
with
46
percent
SiO,,
can
not
simultaneously satisfy
both
Q,
and
p.
Watt
and
Ahrens
(1982) also concluded
that
the
SiO,
content of
the
lower mantle
is
closer
to
chondritic
than
pyrolitic.
Another approach is to extrapolate seismic data to zero
pressure
with
the
assumption
that
the lower
mantle
is
ho-
mogeneous and
adiabatic (Anderson
and
Jordan, 1970;
An
-
derson
and
others,
1971;
Butler
and
Anderson, 1978). A
variety
of
equations
of
state are available (discussed
in
Chapter
5)
that
can
be
used to
fit
p,
G,
K,,
V,
and
V,
in
the
lower
mantle,
and
the zero
-
pressure
parameters
can
be
com
-
pared with values
inferred or measured for various can
-
didate minerals
and
compositions. Although a large ex
-
trapolation
is
required, there
is
a large range
of
compres
-
sions
available over
the extent
of
the lower mantle,
and
the
parameters
of
the equations
of
state can
be
estimated more
accurately
than they
can
over the
available range
of
com
-
pressions
in
most
static experiments. The temperature cor
-
rections
to be applied
to the extrapolated lower
-
mantle
val
-
ues
are,
of
course, uncertain. Butler
and
Anderson (1978)
concluded that pure
'"erovskite,"
MgSiO,,
was
consistent
with the
seismic data. A range
of
(Mg,Fe)SiO,
composi
-
tions
is also
permitted
because
of
the
uncertainty
in
the
moduli
of
"
perovskite
"
and
lower mantle temperature.
The
next
approach is to use measured or inferred
val
-
ues
of
physical properties
of
various candidate
lower-
pressure
phases (such
as perovskite or magnesiowiistite)
and to
extrapolate
to lower
-
mantle conditions. This
method
suffers
from
an
extensive reliance
on
systematics
involving
analog
compounds.
Gaffney
and
Anderson
(1973)
and
Bur-
dick
and
Anderson
(1975) concluded
that
the lower mantle
was
richer
in
SiO,
than
the upper mantle
or
olivine
-
rich
assemblages.
Bass
and
Anderson
(1984) found that pyrolite
and
(Mg,Fe)SiO,
(perovskite)
gave
similar results at the top
of
the
lower
mantle.
The
relatively homogeneous
part
of
the
lower
mantle,
however,
does
not
set
in
until
about 800
krn
depth.
In
all
of
these
approaches
there
is a trade
-
off between
temperature
and
composition.
If
the
lower mantle falls
on
or
above
the
1400"
adiabat,
then
chondritic or pyroxenitic
compositions
are
preferred.
If
temperatures are
below
the
1200°C adiabat,
then more
olivine (
"
perovskite
"
plus
(MgFe)O)
can
be
accommodated. A
variety
of
evidence
suggests
that the
higher temperatures are
more
appropriate.
Velocity
-
density
systematics can also be applied to
the problem
(Anderson,
1970a).
There are systematic vari
-
ations
between
density,
velocity and mean
atomic
weight
-
M.
The
lower
mantle
has
higher
@
and
p
than
inferred for
the high
-
pressure forms
of
olivine
and
peridotite. This
has
been used
to argue for iron enrichment
in
the lower
mantle.
It was
later
recognized that
these systematics could
not
be
applied
through
a phase
change that involves
an
increase in
coordination.
An
increase
in
coordination involves a large
increase in density
but only
a small
increase, or
even
a de
-
crease,
in
seismic
velocity
(Anderson,
1970b).
This
weak
-
ens
the arguments for
FeO
enrichment
in
the
lower mantle
but
strengthens the arguments for
SiO,
enrichment.
Attempts to
compute
velocity
throughout the mantle,
assuming
chemical
homogeneity but allowing
for phase
changes,
have
not
satisfied
the seismic
data,
at least for
an
olivine
-
rich composition (Lees
and
others, 1983). A differ
-
ence in composition
between
the upper and lower mantle
is
implied.
The
sharpness
of
the
650
-
km
discontinuity implies
either a univariant phase change,
for
which
there is
no
labo
-
ratory evidence, or a compositional
boundary.
The absence
of
earthquakes
below
690
km is
indirect evidence, although
inconclusive, for a chemical boundary that prevents pene
-
trative convection.
The seismic velocities in the upper 150 km
of
the lower
mantle exhibit a high gradient. This is probably
due
to the
continuous transformation
of
garnet solid solution (garnet
plus
majorite)
to
"
perovskite
"
and
y
-
spinel to
"
perovskite
"
plus
(Mg,Fe)O.
Reactions involving the ilmenite structure
may
also
be
involved.
The mantle
between about
800
and
2600
km
depth ap
-
pears to
be
relatively homogeneous, although a slight in
-
crease
with
depth
of
FeO
may
be
permitted (Gaffney
and
Anderson, 1973; Anderson, 1977).
Region
D
"
,
just above
the core
-
mantle boundary,
has
a
different gradient
than
the overlying mantle
and
may
contain
one
or
more
discontinuities.
It is also laterally
inhomoge-
neous, causing scatter
in
the
travel times
and
amplitudes
of
seismic
waves
that traverse
it.
It may
be
a region
of
high
thermal gradient
and
small
-
scale convection, but
its
prop
-
erties cannot be entirely explained
by
thermal boundary
theory. Phase or compositional changes or
both
are prob
-
ably
involved. There is also some evidence that
Q
in
this
region is
lower than
in
the overlying mantle (Anderson
and
Given, 1982).
D
"
is
a logical
site
for a chemically distinct layer. Light
material from
the
core can
be
plated
to the
base
of
the
man
-
tle,
and
if
denser
than the
mantle, there it
will
remain.
Chemically dense blobs from the mantle
would
also settle
on the core
-
mantle
boundary.
As
the Earth
was
accreting,
the denser silicates,
as well
as iron,
would
probably sink
through
the mantle. A basaltic
layer
at the surface
would
transform
to
eclogite at
high
pressure
and
could sink
to
the
protocore
-
mantle boundary, unimpeded
by
the
spinel-post-
spinel
or
garnet
-
perovskite phase changes
until
the Earth
was
Mars
-
size
or
larger. This assumes that the perovskite
phase change
in
eclogite occurs at a higher pressure
than
in
Al,O,-poor
material
and
the high
-
pressure form
of
eclogite
is less dense
than
Al,O,-poor
assemblages. Subduction to
-
day
probably cannot provide material to the lower mantle.
D
"
may
therefore
be
the site
of
ancient subducted litho
-
sphere.
In the inhomogeneous accretion model the deep inte
-
rior
of
the Earth
would be
initially
rich
in
Fe
and
CaO-
Al,O,-rich
silicates.
D
"
may
therefore
be
more calcium
-
and
aluminum
-
rich
than
the
bulk
of
the mantle.
At
D
pressures
this
may
be
denser
than
"
normal
"
mantle
(Ruff and
Ander
-
son, 1980).
The
seismic parameter
a,
for
the
lower mantle ranges
from about
61
to
63
km
2
/s
2
, depending
on
the temperature
assumed.
For
comparison
MgSiO,
(perovskite),
A120,
and
SiO,
(stishovite) are
63,
63.2
and
73.7
km
2
/s
2
, respectively.
(Mg,Fe)O
ranges
from 40.7 to 47.4
km
2
/s
2
for
reasonable
ranges
in iron
content. Increasing
FeO
decreases
@
unless
Fe
is
in
the low
-
spin
state (see
discussion
below). There
-
fore, it
appears that
MgO
and
Si02
in
approximately
equal
molar
proportions
are implied
for
the lower
mantle.
There
is a slight drop
in Poisson's
ratio across the
650-
krn
discontinuity.
Temperature
and
pressure both increase
Poisson's
ratio
in
a homogeneous
material,
so
this
drop
is
an indication
of
a change in
chemistry or
mineralogy.
In
-
creasing
the
packing efficiency
of
atoms
in
a lattice
and
in
-
creasing
coordination both
serve to decrease
the
Poisson's
ratio
(Anderson and
Julian,
1969).
Spinels
and
garnets,
the
major
minerals
of
the
transition region,
have
zero
-
pressure
Poisson's
ratios
of
about
0.24
to
0.27.
Stishovite
and most
perovskites have values
in
the range
0.22
-
0.23. The
differ
-
ence is
about that observed across the
discontinuity.
MgO
has a
very
low
value,
0.18,
and
is
estimated
to be
about
0.25
at 670 km. The
observed value
at the top
of
the lower
mantle is
about
0.27.
Two
measures
of
homogeneity
are
dKldP
and
the
Bullen
parameter
(B.P.).
These
are
tabulated in
the
Appen
-
dix for
the Preliminary Reference Earth Model (PREM)
of
Dziewonski
and
Anderson. In
homogeneous
self-com-
pressed regions
we
expect
dKldP
to be a
smoothly
decreas
-
ing
function
of
depth
and
B.P.
to
be
close to
unity.
These
conditions are
satisfied approximately between
770
km and
2500
km
depth.
Velocity
gradients are
very
low
in
the lower
200
km
of
the mantle. The
region
at
the top
of
the lower
mantle
has
high
gradients,
possibly
due to the
garnet-
perovskite
or garnet
-
ilmenite transitions.
The partitioning
of
trace
elements
into a
(Mg,Fe)SiO,-
perovskite should
be
evident
in
upper
-
mantle chemistry
if a
deep
(greater
than
700
km)
magma ocean existed
or
if ma
-
terial from the
deep mantle is brought into
the
upper
mantle.
The
trace
-
element
patterns
of
the refractory elements can,
however,
be
explained
by
partitioning between melts
and
the common upper
-
mantle
minerals. This
suggests
a chemi
-
cally zoned
planet, formed
by
a low
-
pressure zone refining
process,
and
a chemically isolated lower
mantle.
CaO
and
AI,O,
According
to
arguments based
on
cosmic
abundance, the
major
components
of
the
lower mantle
are
MgO
and
SiO,.
CaO
and
Al,03
are
likely to
be
the
next
most abundant com
-
ponents,
but
their concentrations are
expected
to
be low,
particularly
if the
material
in the lower mantle
has experi
-
enced low
-
pressure melting
and
removal
of
the
basaltic
components. There
may be
regions,
however, such
as
D
"
,
that
are enriched
in
refractories
such
as
CaO
and
Al,O,.
CaO
and
A120,
have
densities
and
elastic properties similar
to
those
inferred for
the lower
mantle,
and
therefore appre
-
ciable
amounts
may
be
accommodated without affecting the
seismic properties. Thus
they
are essentially invisible
and
arbitrary
amounts can
be
accommodated.
Ca
-
rich
perov-
skites,
however,
may
have
lower
cP
than
(MgFe)SiO,-per-
ovskite
(Ruff and
Anderson, 1980)
and this
may
contribute
to
the low
seismic gradients
observed
in
D
"
.
The
low den
-
sity
of
CaSi0,-perovskite,
compared
to
(Mg,Fe)SiO,-per-
ovskite,
may
prevent Ca
-
rich material such
as eclogite
from
sinking
into
the lower
mantle. The
CaO
content
of
planets
constructed
from
new
solar
abundances
of
the
refractories
(see Chapter
1)
is higher than
chondritic
and
the
CaO/A120,
ratio is higher.
CaSiO,
transforms
to
a perovskite
structure
with
a
density
about
the
same
or slightly greater
than
MgSi0,-
perovskite
(Ringwood, 1975, 1982).
At
lower pressures
CaSiO,
combines
with
MgSiO,
to
form
diopside
and
Ca-
garnets.
CaO
also
combines
with
A1203
to form compounds
at
low
pressure,
but
Ringwood
(1975)
argued that
A1203
will
not be
accommodated in
CaSi0,-perovskite
related
compounds.
CaSiO,
xA1203
(garnet)
will
therefore dispro
-
portionate to
CaSiO,(perovskite)
+
xA1203
at
high pres
-
sure. This
transformation
occurs
at a much
higher pressure
than
the
CaSi0,-perovskite
transformation. In spite
of
the
above
comments,
Liu
(1977) apparently synthesized
a phase
Ca,A12Si0,
related
to
perovskite with
a density
of
4.43
g/
cm
3
. Weng
and
others
(1983),
on the basis
of
high
-
pressure
measurements on the system
MgSiO,
CaSiO,
.
Al,O,,
con
-
cluded that
CaSiO,
forms
a separate phase. Shock
-
wave
measurements (Svendsen, 1987)
on
CaSiO, and
CaMgSi,O,
give high
-
pressure phases
with
densities consistent
with
ei
-
ther
mixed
oxides
or
perovskite that have
zero
-
pressure den
-
sities
of
4.0
to
4.13 g/cm
3
. At
high
pressure the measured
densities
are considerably less
than the
lower
mantle. There
was
no
evidence for a
superdense
phase.
In
fact,
CaO
-
rich
material
approaches the density
of
the
lower mantle only
for
high
iron
contents
(about
18
mole
percent
FeSiO,)
(Svend-
sen,
1987). The
disproportionation products
of
CaSiO,
.
xA1203
will
be
even
less dense because
of
the
low
density
of
A1203.
The
low
inferred zero
-
pressure density
for
CaSiO,
from
high
-
pressure shock
-
wave
experiments
suggests that
CaSiO, has
not
completely transformed even
at pressures
as
high
as
1.8
megabars.
On balance, it
appears that
CaSi0,-perovskite
exists
as a separate
phase
in
the lower mantle.
At
lower
pressure
CaSiO,
forms garnet
solid solutions
with
(Mg,Fe)SiO,
.
xA1203
and
therefore
disproportionation
reactions are in
-
volved in
the formation
of
CaSi0,-perovskite.
Because
of
the broad
stability
interval
of
garnet,
the
transformation
pressure is
much
higher than
for
pure
CaSiO,.
CaSi03-
perovskite,
because
of
its
low
density relative
to
(Mg,Fe)SiO,-perovskite
and
apparently
high
transforma
-
tion
pressure, does
not
contribute
much
to
the
negative
buoyancy
of
eclogite
in subducted slabs.
Stishovite
has
a
p,
of
4.29
g/cm
3
and
will
serve to
substantially increase the
density
of
subducted quartz
-
bearing
eclogite,
but not
SO2-
poor
basaltleclogite.
Ringwood
assumed that the
grossularite
portion
of
gar-
net
disproportionates to
CaSiO,
(perovskite) plus
Al2O3
at
depths
above
670
km.
However, this
assemblage is less
dense
than
the
lower
mantle or
(Mg,Fe)SiO,(perovskite).
This
suggests that
the
basaltic
and
pyroxenitic portions
of
subducted lithosphere,
and
the eclogite cumulates formed
in
early
Earth history are trapped in the upper mantle. De
-
pleted
peridotite
is also trapped
in
the upper mantle because
of
its
low
density.
Subducted slabs will
tend
to depress a
chemical interface at 650 km,
and
convection will also de
-
form
this boundary. In
fact, the
"
650
-
km
"
discontinuity
may
vary
in
depth
by
more than
80
km.
Depths reported
in seismological studies range from 640 to 720
km.
The
sharpness
of
the discontinuity is consistent
with
a chemical
discontinuity.
Garnet
has
an
extensive stability
field
in
a silicate
of
eclogite composition; the transformation from garnet to
perovslute is
probably not
complete until about 750
km.
This
is much
deeper
than
the transformation
in
olivine
and
A120,-poor
pyroxene. Grossularite plus
CaSiO,
forms a
garnet solid solution
that
is probably stable to 900
km
(Liu,
1979)
and
is considerably less dense
than
(Mg,Fe)SiO,
(perovskite),
which
is stable at shallower depths. The bulk
density
of
eclogite at 650
km
is therefore less than
the den
-
sity
of
the
lower
mantle.
An
eclogite
layer
is gravitationally
stable at
midmantle
depths. Transformations
in
CaO
and
Al,O,-rich
silicates probably contribute
to
the
high velocity
gradient
found between the
400
-
and
650
-
km disconti
-
nuities.
It is often
assumed
that overridden oceanic lithosphere
disappears out
of
the bottom
of
the
Wadati
-
Benioff
zone.
Some aspects
of
continental
geology,
Gowever,
invoke the
presence
of
subducted
lithosphere 1000
-
3000
km
into the
continental interior (Dickinson
and
Snyder, 1978). The
thermal lifetime
of
overridden oceanic lithosphere is
very
long. It heats
up with time but
cools the adjacent mantle,
so
that
if the slab
remains
in
the
upper
mantle it should
show
up
as
a high
-
velocity anomaly.
If
subducted material is
trapped in the upper mantle, the
western Atlantic and
the
Brazilian and Canadian
shields will
be
underlain by
oceanic
lithosphere
that
represents Jurassic
Pacific
Ocean.
In
fact,
these
parts
of
the
world
are
in
geoid lows
and
have high
upper
-
mantle velocities. The fate
of
subducted oceanic
lithosphere is
intimately
related to the problems
of
whole-
mantle versus layered mantle
convection
and
chemical
in-
homogeneity
of
the mantle. There is,
as
yet,
no
convincing
evidence that slabs
sink
into the lower mantle.
Low
-
Spin
Fez+
Two
alternate electronic configurations, high
-
spin
and
low
-
spin, are possible for
Fez+.
The high
-
spin
(H.
S
.)
state is
usually
stable
in
silicates
and
oxides at normal pressures.
The ionic radius
of
the low
-
spin
(L.S.)
state is
much
smaller
than
the high
-
spin state,
and
a spin
-
pairing transition
is in
-
duced
by
increased
pressure. A large increase in density
accompanies this phase transformation.
For
example, the
volume
change accompanying a phase change in
Fe,O,
at
500 kbar, attributed to the
high
-
spin
-
low
-
spin
transition, is
1 1
-
15
percent.
GaEney
and Anderson
(1973) proposed that
spin-
pairing is likely
in
the
mantle
at depths
below
1700
km
and
perhaps at higher levels
as
well. The small ionic radius
of
Fe
2
+(L.S.)
probably means that
Fe
2
+ will not
readily sub
-
stitute for
Mg
2
+ under lower
-
mantle conditions. Additional
Fe2+
(L.S.)O-bearing
phases
will
form
with
high densities
and bulk
modulus.
Assuming
that
Fe
2
+ spin
-
pairing occurs
below
670
km,
Gaffney and
Anderson (1973)
showed
that
the lower mantle could
be
enriched in
FeO
and
SiO,
relative
to the upper mantle. The magnesium
-
rich phases
of
the
lower
mantle
may
be
relatively iron free:
MgFeSiO,
-,
MgSiO,
(perovskite)
+
FeO(L.S.)
which would
facilitate the entry
of
FeO
into molten iron
and
removal
to the core.
The possible presence
of
low
-
spin
Fe
2
+ in the lower
mantle complicates the interpretation
of
seismic data in
terms
of
chemistry
and mineralogy.
The lower mantle
may
be
chondritic or
"
solar
"
in major elements or
it may
be
residual refractory material remaining after extraction
of
the
basaltic elements, calcium, aluminum
and
sodium. In the
latter case
it would be
expected to
be
depleted
in
the radio
-
active elements, uranium, thorium
and
potassium.
At
very
high pressure
FeO
may
become
metallic and, therefore,
readily enter the core.
REGION
D
"
The lowermost 200 km
of
the mantle, region
D
"
, has long
been known
to
be
a region
of
generally
low
seismic gradient
and
increased scatter
in
travel times and amplitudes.
Lay
and
Helmberger (1983) found a shear
-
velocity jump
of
2.8
percent
in
this region that
may
vary in depth
by up
to 40
km.
They
concluded that a large shear
-
velocity disconti
-
nuity
exists about 280 km above the
core,
in
a region
of
otherwise
low velocity
gradient. The basic feature
of
a 2.75
k
0.25
percent
velocity
discontinuity is present for each
of
several distinct paths. There appears
to be
a lateral variation
in
the
velocity
increase and
sharpness
of
the structure,
but
the basic character
of
the discontinuity seems to
be
well
established. Wright
and
Lyons (1981) found a rapid in
-
crease
in
compressional
wave
velocity
of
2.5
to
3.0
percent
about 200 km
above
the core
-
mantle
boundary.
D
"
may
represent a chemically distinct region
of
the
mantle.
If
so it
may
vary
laterally,
and
the discontinuity in
D
"
would
vary considerably in radius, the hot regions
being
elevated
with
respect
to
the cold regions. A chemically dis
-
tinct
layer at
the
base of
the mantle that is only marginally
denser
than
the overlying mantle
would be
able to rise into
the lower mantle
when
it is hot
and
sink
back when
it cools
off. The mantle
-
core boundary,
being
a chemical interface,
is a
region
of
high
thermal gradient, at least in the colder
parts
of
the
lower
mantle.
I argued earlier that neither the peridotitic
nor
the
eclo-
gitic
portions of subducted oceanic lithosphere
can
sink
into
the lower mantle.
However,
while the Earth
was
accreting,
conditions
would have been more
favorable for deep
snb-
duction
of
eclogite.
D
"
may
therefore
be
the repository
for ancient subducted lithosphere. Likewise, light material
from the core
may
have
underplated
the
mantle.
In
either
case
D
"
would be more
refractory (Ca
-
, Al
-
, Ti
-
rich) than
the
average mantle.
Because the core is a
good
conductor
and has
low
vis
-
cosity, it is
nearly
isothermal. Lateral temperature varia
-
tions can
be
maintained
in
the mantle, but they
converge at
the base
of
D
"
.
This
means
that temperature gradients are
variable
in
D.
In some
places,
in
hotter mantle, the gradi
-
ent
may
even be negative
in D
"
. Regions
of
negative shear
velocity gradient
in
D
"
are probably regions
of
high tem
-
perature gradient
and high heat
loss from
the
core.
THE
CORE
The core
is approximately
half
the radius
of
the Earth
and
is about
twice
as
dense as the mantle.
It represents
32
per
-
cent
of
the mass
of
the
Earth.
A large dense core can
be
inferred from the
mean
density
and
moment of inertia of
the
Earth,
and
this calculation
was
performed
by
Emil Wiechert
in
1891. The existence
of
stony meteorites
and
iron
mete
-
orites
had
earlier led
to
the suggestion that the Earth
may
have
an
iron core surrounded
by
a silicate mantle. The
first
seismic evidence for the existence
of
a core
was
presented
in
1906
by
Oldham,
although it
was
some time before it
was
realized that the core does
not
transmit shear
waves
and
is therefore probably a fluid. It
was
recognized that the
ve
-
locity
of
compressional
waves
dropped considerably at the
core
-
mantle
boundary.
Beno
Gutenberg
made
the
first
ac
-
curate determination
of
the depth of the
core,
2900
km,
in
1912,
and
this
is
remarkably close to current values. The
mantle
-
core boundary is sometimes referred to as the
Gu-
tenberg
discontinuity
and
sometimes as the
CMB.
Although the idea that the
westward
drift
of
the mag
-
netic
field
might be due to a liquid core goes
back
300
years, the
fluidity
of
the core was
not
established until 1926
when Jeffreys
pointed out that tidal
yielding
required a
smaller rigidity for the Earth
as
a whole than
indicated
by
seismic
waves
for
the
mantle.
It was
soon
agreed
by
most
that the transition from mantle to core
involves both
a
change
in
composition
and
a change in state. Subsequent
work
has
shown that the boundary
is extremely sharp. There
is some evidence for variability
in
depth,
in
addition
to
hy
-
drostatic ellipticity.
Variations
in
lower
-
mantle density
and
convection in the lower mantle can cause at least
several
kilometers
of
relief
on the core
-
mantle boundary.
The
outer
core has extremely
high
Q
and
transmits P
-
waves
with very
low
attenuation. Evidence
that
the outer core
is
mainly
an
iron
-
rich
fluid
also comes from
the
magnetohydrodynamic
requirement
that
the core
be
a good
electrical conductor.
Although the outer core
behaves
as
a fluid, it does
not
necessarily follow
that
temperatures are above
the
liquidus.
It would behave as
a fluid even
if it contained 30
percent or
more
of
suspended particles.
All
we
know
for sure
is that
at least part
of
the outer core is
above
the
solidus
or
eutectic
temperature
and
that
the
outer core, on average,
has
a very
low
rigidity
and low
viscosity. Because
of
the
effect
of
pres
-
sure on the
liquidus
temperature, a homogeneous core
can
only
be
adiabatic
if it is above
the
liquidus
throughout.
An
initially homogeneous core
with
an
adiabatic temperature
profile
that lies
between
the
solidus
and
liquidus
will
con
-
tain suspended particles that
will
tend
to rise or sink, de
-
pending
on
their
density.
The resulting core
will be
on
the
liquidus
throughout
and will have
a radial gradient in
iron
content. The core will
be
stably
stratified
if the
iron
content
increases
with
depth.
Inge Lehmann (1936)
used
seismic data from the
"
core
shadow
"
to
infer the presence
of
a higher
velocity
inner
core. Although no
waves
have
yet
been identified that have
traversed the inner core
unarnbiguously
as
shear
waves,
in
-
direct evidence indicates that
the
inner core is solid (Birch,
1952).
Julian
and
others
(1
972)
reported evidence for
PKJKP,
a compressional
wave
in
the mantle and
outer core
that traverses the inner core
as
a shear
wave,
but this
has
yet to
be
confirmed. Early free
-
oscillation
models
(Jordan
and
Anderson, 1973)
gave
very
low
shear velocities for
the
inner
core,
2 to 3
kmls,
and some models
(Backus
and
Gil
-
bert, 1970)
had
entirely
fluid
cores. More recent
models
give shear velocities
in
the inner core
ranging
from
3.46
to
3.7
km/s
(Anderson
and
Hart, 1976;
Dziewonski
and
An
-
derson, 1981).
Gutenberg (1957) suggested
that
the
boundary
of
the
inner core
is frequency dependent
and,
therefore, that the
inner core
might be
a highly
viscous
fluid
rather than
a
crys
-
talline solid. The boundary
of
the inner core is also ex
-
tremely sharp
(Engdahl
and
others, 1970).
The
Q
of
the
inner core is relatively
low,
and
appears
to
increase
with
depth.
The
high
Poisson's
ratio
of
the
inner core,
0.44,
has
been
used
to
argue that it
is not
a crystalline solid, or
that
it
is
near
the
melting
point or partially
molten or
that
it in
-
volves
an electronic phase change.
However, Poisson's
ratio
increases
with
both
temperature
and
pressure
and is
ex
-
pected
to
be
high at inner core pressures, particularly
if it is
metallic (Anderson,
1977; Brown
and
McQueen,
1982).
Some metals
have
Poisson's
ratios
of
0.43
to
0.46
even un
-
der laboratory conditions.
Table
4
-
1 presents numerous properties
of
the
core.
Composition
of
the
Core
Butler
and
Anderson
(1978)
fit
a variety
of
equations
of
state to the seismic data for the outer core. Third
-
order
finite
strain theory
was
shown
to
be
inadequate,
and
the
best
fits
TABLE
4
-
1
Properties
of
Core
Symbol
Property
Outer
Inner
Uncertainty
Core
Core
R
Radius (km)
3480
1221
P
Pressure (Mbar)
1.36
3.29
-
3.64
p
Density
(g/cm
3
)
9.90
-
12.17
12.76
-
13.09
Po
6.6
-
6.73
7.6
k0.2
K,
Bulk modulus (Mbar)
6.4
-
13.0
13.4
-
14.3
KO
1.2
-
1.4
G
Shear modulus (Mbar)
c0.02
1.57
-
1.76
k0.2
K:
4.3
-
4.8
1.76
k0.2
Vp
Compressional velocity
(kmls)
8.06
-
10.36
11.03
-
11.26
V,
Shear velocity
(kmls)
-
0
3.50
-
3.67
V,
Bulk velocity
(kmls)
8.06
-
10.36
10.26
-
10.44
v4.,
4.3
-
4.6
50.35
y
Griineisen
ratio
1.7
1.6
20
pct.
cp
Specific heat
(erg1g.K)
5
x
lo6
10
pct.
a
Expansivity
(K-I)
10
-5
30
pct.
k
Thermal conductivity
(erg1cm.K.s)
4
X
lo6
X
2
a
Electrical resistivity
(pflcm)
100
-
160
x2
v
Shear viscosity
(cm
2
/s)
8
x
lo-3
x
lo2
T,
Melting temperature (K)
2600
-
5000
6150
-
7000
R,
Magnetic Reynolds number
200
-
600
x
lo2
Decay time (years)
15,000
Ohmic dissipation
(W)
Poloidal
lo8
Toroidal
1010-1012
10"
Heat loss (W)
10~~-10~~
Rotation rate (rad
S-l)
7.29
x
lo-5
Westward
drift
0.2"Iyr
Dipole
in
core
(Wb
m-2)
3.8
x
lo4
H,
Poloidal
field
(gauss)
6
H,
Toroidal
field
(gauss)
50
-
2400
<lo6
p
Permeativity
1
Heat
of
fusion
(erglg)
4
x
lo9
Ekman number
10-l5
Reynolds number
3
X
lo8
Rossby number
4
x
lo-7
Magnetic Rossby number
2
x
lo-9
Verhoogen
(1973),
Ruff
and
Anderson
(l980),
Stevenson
(1981),
Jacobs
(1975),
Dziewonski and Ander
-
son
(1981),
Melchior
(1986),
Gubbins (1977).
were
obtained
for fourth
-
order
finite
strain,
Bardeen's
equa
-
tion
of
state
and
an
equation
of
state
involving
an
exponen
-
tial repulsive
potential.
Their best
fits
for
the region
be
-
tween 2200
and
3200 km radius gave
the
following values
for zero
-
pressure quantities:
po
=
6.60
-
6.71
g/cm
3
KO
=
1.22
-
1.40
Mbar
V,
=
4.30
-
4.57
krnls
=
18.5
-
20.9
km
2
/s
2
K:
=
4.5
-
4.8
These are uncorrected
for temperature
and
therefore
represent
high
-
temperature
values. Butler
and
Anderson
concluded that
a pure
iron
-
nickel core
has
too
high
a density
and
too
low
a bulk sound velocity
to be
compatible
with
the
seismic
data. A lighter
alloying element that
increases the
bulk sound speed seems
to
be
required. The
pressure
de
-
rivative at
KO
at
P
=
0
is
KA
and
this appears
to
have
nor
-
mal
values.
If
the
ratios
of
nonvolatile elements
in
the Earth
are
similar to
those
in
the
Sun
and
chondritic meteorites,
then
an
iron
-
rich core
is required. Some
early workers proposed
that
silicates
may
undergo
metallic phase
changes
and
that
material
of
high density,
high
electrical conductivity
and
TABLE
4-2
Properties
of
Iron
Property
Units
Value
Po
g/cm
3
7.02
(liq.
at
1810
K)
8.35
(F)
a
K-I
11.9
X
(liq.)
KO
Mbar
1.40
0.85
(liq.)
1.95
(€1
"$a
kml
s
3.80
Y
-
2.2
-
2.4
Electrical resistivity
pncm
140
Thermal conductivity
erglcm
K
s
3.22
X
lo6
Shear
viscosity
poises
3
X
(liq. at MP)
Ahrens
(1979),
Jeanloz
and
Knittle
(1986),
Stevenson
(1981).
low
melting point
might be'
formed from silicates at high
pressure.
However,
material
of
sufficiently
high density
has
not been
observed
in
any shock
-
wave
or static
-
compression
experiment on silicates or oxides,
and
the iron hypothesis
is the
most
reasonable one. Properties
of
pure iron are listed
in
Table
4
-
2.
Figures 4
-
1
and
4
-
2 show
that the properties
of
the core
closely parallel the properties
of
iron but that a light
alloy
-
ing element is required
that
also serves
to increase the
com
-
pressional
wave
velocity. This
alloying element should also
serve
to
decrease the melting point, since the melting point
of
pure
iron is
probably
higher
than
temperatures in the
outer core. Elements such
as
nickel and
cobalt are likely to
be in the
core,
but if they
occur
in
cosmic ratios
with
iron
Pressure
(M
bar)
FIGURE
4
-
1
Estimated densities
of
iron,
nickel and some iron
-
rich
alloys,
compared with core densities (heavy line).
The
estimated reduc
-
tion
in
density
due
to melting
is shown (dashed line)
for one
of
the alloys (after Anderson, 1977).
Pressure
(M
bar)
FIGURE
4
-
2
Compressional velocities
(V,)
in
the outer core and compres
-
sional
(6)
and
bulk sound speeds
(V,)
in
the
inner
core (heavy
lines) compared
to
estimates
for
iron and nickel.
Values
are
shown
for
two
Poisson's
ratios
r~
in the inner core (after Ander
-
son,
1977).
they will
not
affect the seismic properties
and
melting
tem
-
perature
very
much. Candidate elements
should
dissolve
in
iron
in
order to affect the
melting point
and
to avoid sepa
-
rating out
of
the core. Material
held
in
suspension
could
reduce the
velocity,
but
unless the
core is turbulent,
or the
particles are
very
small,
such
material
would
rapidly settle
out because
of
the presumed
low
viscosity
of
the
core. This
mechanism cannot
be
ruled
out completely, because
new
suspended material
may
be
constantly replenished
by
con
-
vection
across the
liquidus
or
by
erosion
of the
lower
mantle
and
inner core.
Candidate materials,
based
on
cosmic abundances
alone, are hydrogen, helium, carbon, nitrogen, silicon,
magnesium, oxygen
and
sulfur. The volatiles hydrogen,
helium
and
possibly carbon, nitrogen
and sulfur,
which
form volatile
compounds under
appropriate conditions, are
depleted
in
the Earth
relative even to
the amount in the
in-
falling planetesimals because
of
devolatilization during
the
accretional process. Silicon
and magnesium
are likely to
partition strongly into the silicate phase, in preference
to
iron,
at core pressure just
as
they
do
at low pressure. Some
carbon, nitrogen, silicon
and
sulfur
may
enter the core
since
they
form iron alloys. Sulfur
and
oxygen (perhaps
as
FeO
or some other oxide) appear
to
be
the strongest candi
-
dates
for
large concentrations
in
the core.
Sulfur depresses the melting point substantially
(
-
1000°C)
at
low pressure.
Shock
-
wave
results indicate
that
6
to
12
percent
of
sulfur
can
explain the density
in
the
core (Anderson, 1977; Ahrens, 1979).
This
range
has
been
confirmed
by
more recent
data (Brown
and
McQueen,
1982). The density
of
a
-
iron
(7.87
g/cm
3
) is much
greater
than the
sulfides
of
iron; compare, for instance,
FeS
(troil-
ite),
4.83
g/cm
3
;
FeS
(sphalerite structure),
3.60
g/cm
3
;
FeS