Theory of the Earth
Don L. Anderson
Chapter 12. The Shape of the Earth, Heat Flow and Convection
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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be found at the following persistent
URL:
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Abstract:
We now come to the more global properti
es of the Earth. The shape of the Earth
and its heat flow are both manifestatio
ns of convection in the interior and
conductive cooling of the outer layers
. The style of convection, however, is
unknown. There are various hypotheses
in this field that parallel those in
petrology and geochemistry. The end-memb
ers are whole-mantle convection in a
chemically uniform mantle and layered co
nvection with little or no interchange
of material between layers. Layered schem
es have several variants involving a
primitive lower mantle or a depleted lower
mantle. In a convecting Earth we lose
all of our reference systems, including the axis of rotation.
hape
of
the
Earth,
Heat
Flow
and
Convection
When
Galileo
let his
balls run down
an
inclined plane with a gravity
which
he
had
chosen
himself.
.
philosophers.
-I.
KANT
W
e now
come
to the more global properties
of
the
Earth. The
shape
of
the Earth and its heat flow are
both manifestations
of
convection
in
the interior and con
-
ductive cooling
of
the outer layers.
The style
of
convection,
however,
is unknown.
There
are various hypotheses
in
this
field
that parallel those
in
petrology and geochemistry.
The
end
-
members are whole
-
mantle convection
in
a
chemically
uniform mantle and layered convection with
little
or
no
interchange
of
material between layers. Layered schemes
have several variants involving a primitive lower mantle
or
a depleted lower mantle.
In
a convecting Earth we
lose
all
of
our reference systems, including the axis
of
rotation.
TOPOGRAPHY
The topography
of
the Earth's surface is
now
generally well
known, though some areas
in
Tibet, central
Africa
and
the
southern oceans remain poorly surveyed.
The
distribution
of
elevations
is distinctly bimodal, with a peak near
0.1
km
representing the mean elevation
of
continents and a peak
near
-
4.7
km corresponding
to
the mean depth
of
the
oceans. This bimodal character contrasts with that
of
the
other terrestrial planets. The spherical harmonic spectrum
of
the Earth's topography shows a strong peak
for
n
=
1,
corresponding to the distribution
of
most continents
in
one hemisphere, and a regular decrease with increasing
ra.
The topography spectrum
is
similar
to
that
of
the other
terrestrial planets. There are small peaks
in
the spectrum
at
n
=
3
and
n
=
9
-
10,
the
latter
apparently corresponding
to the distribution
of
large oceanic islands and hotspots.
In
general,
the most recent orogenic belts such as the
Alpine and Himalaya are associated with high
relief,
up
to
then
a
light
dawned
upon all natural
5
km,
while older orogenic belts such
as
the Appalachian
and
Caledonian,
because of
erosion,
are associated with low
relief,
less than
1
km.
Regional changes
in
the topography
of
the continents are generally accompanied
by
changes
in
mean crustal thickness. Continents stand high because
of
thick,
low density
crust,
compared
to oceans.
The
long
-
wavelength topography
of
the ocean floor ex
-
hibits a simple relationship
to
crustal
age.
The systematic
increase
in
the depth
of
the ocean floor
away
from the
mid-
ocean ridges
can
be
explained
by
simple thermal
models
for
the evolution
of
the oceanic lithosphere. Parsons and
Sclater
(1977)
using
data
from the western North Atlantic and
cen
-
tral
Pacific Oceans showed
that, for
seafloor
ages
from
0
to
70
Ma,
topography is described
by
d(t)
=
2500
+
350t112
where
t
is age
in
Ma
and
d(t)
is
the depth
in
meters.
Older
seafloor
does
not
follow this simple
relationship,
being shallower than predicted.
There are
large portions
of
the
ocean floor whose depth cannot
be
explained
by
simple thermal models; these include oceanic
islands,
hot-
spot swells, aseismic ridges and oceanic plateaus as
well
as
other
areas where the effects
of
surface tectonics and crustal
structure
are
not
readily apparent.
Simple
cooling models
assume that the underlying mantle is uniform and that all
of
the variation
in
bathymetry is due to cooling
of
a thermal
boundary layer.
The
North Atlantic is generally too shallow
for its age,
and
the
Indian Ocean between Australia and
Antarctica is
too deep. The
residual depth anomaly
is
the
departure
of
the
depth
of
the
QCWn
from
the value expected
for
its age and
is given
by
Ad
=
d(t)
+
S(P,
-
PW)
-
(~m
-
~s)
where
d(t)
is the expected depth
based
on age,
S
is the
sediment thickness,
p,,
p,
and
p,
are the densities
of
sedi
-
ments,
water and
mantle, respectively,
and
d is
the
ob
-
served depth.
Residual
depth anomalies observed in the
ocean
have
dimensions
of
order 2000
km
and
amplitudes
greater than
1
km.
Part
of
the residual anomalies are due to
regional changes in crustal thickness. This cannot explain
all
of
the anomalies. Positive depth anomalies are generally
associated
with volcanic
regions
such
as Bermuda, Hawaii,
the Azores
and
the Cape
Verde
Islands. These
might
be
due
to
thinning
of
the lithosphere or the presence
of
abnormally
hot upper mantle.
Hotspot
swells
generally
have
a higher
heat
flow
than
appropriate for
the age
of
the surrounding
oceanic crust.
Menard
and
Dorman
(1977)
noted
that ridge
-
crest
depths, a measure
of
the
depth
of
the ocean
floor
at zero
age,
were
greatest
in
the
equatorial regions. They expanded
the depths in the
Pacific Ocean
as
a function
of
age
and
latitude:
d(t)
=
Kt1/,
+
C,P,
(sin
4)
n=o
and
obtained
Thus,
the
mean
depth
of
the ocean at zero age
is 2.64
km,
and
it deepens at
an average
rate
of
0.313
krn/(million
years)lI2.
In addition to these age
-
and
latitude
-
dependent ef
-
fects,
they
found other depth anomalies
having wavelengths
of
4000
km
and
amplitudes
of
+
0.8
to
-
0.5
km
and
a
crest
-
to
-
trough
relief
of
0.7
to
1
.O
krn.
The anomalies under
the
Pacific
plate trend northwest
-
southeast, subparallel to
the
Hawaiian
hotspot
track,
and
those under the
Nazca
plate
trend east
-
west. A large fraction
of
recent
hotspots
are as
-
sociated with shallow anomalies. The
Nazca
plate is abnor
-
mally shallow.
Although cooling
of
the oceanic upper mantle is
the
first
-
order control
of
oceanic bathymetry,
many
large
bathy-
metric features are
not
related
to
standard cooling
and sub
-
sidence. Crough (1978, 1979) summarized these
"
depth
anomalies
"
and, in particular, oceanic
hotspot
swells.
A
few
places are markedly deep, notably the
seafloor
between
Australia
and
Antarctica
and the
Argentine
Basin
of
the South Atlantic. Other deep
regions
occur in the cen
-
tral
Atlantic and
the eastern
Pacific and
others,
most notably
south
of
India, are
not
so obvious because
of
deep sedimen
-
tary fill.
Most
of
the
negative areas are less than 400 m
below
the expected depth,
and
they
comprise a relatively
small fraction
of
the
seafloor
area.
Shallow areas often exceed 1200
m
in
height
and
oc
-
cupy almost the entire
North
Atlantic and most
of
the west
-
ern
Pacific
that has
been
mapped.
Almost
every
volcanic
island, seamount
or
seamount chain surmounts a
broad
topographic swell. The
swells
generally occur directly
be
-
neath
the
volcanic
centers
and
extend
away
from them
in
tlhe
downstream direction
of
plate
-
hotspot motion. Some
extend a short distance
in
the
upstream
direction. Small re
-
gions
of
anomalously
shallow
depth occur
in
the
northwest
-
ern Indian Ocean
south
of
Pakistan,
in
the western
North
Atlantic near the Caribbean,
in
the Labrador Sea
and
in
the
southernmost South
Pacific. They
are
not
associated
with
volcanism but are
slow
regions
of
the
upper
mantle
as
de
-
termined from seismic
tomography. Shallow regions prob
-
ably
associated
with
plate
flexure
border the Kurile Trench,
the Aleutian
Trench and the
Chile Trench. Major
volcanic
lineaments
without swells
include the northern
end
of
the
Emperor Seamount chain, the Cobb Seamounts
off
the
west
coast
of
North
America
and
the Easter
Island
trace
on
the
East Pacific
Rise. Bermuda
and
Vema, in
the
southeast
At
-
lantic, are isolated
swells
with
no associated
volcanic
trace.
For most
of
the swells
explanations
based
on sediment
or
crustal thickness
and
plate
flexure can be ruled
out.
They
seem
instead to
be
due to variations in lithospheric compo
-
sition or thickness,
or
abnormal upper mantle.
Underplating
the lithosphere
by
basalt or depleted peridotite,
serpentini-
zation
of
the lithosphere, delamination, or reheating
and
thinning the lithosphere are mechanisms that can decrease
the density or thickness
of
the lithosphere
and
cause uplift
of
the seafloor. A higher temperature asthenosphere, greater
amounts
of
partial melt, chemical inhomogeneity
of
the as
-
thenosphere
and upwelling
of
the
asthenosphere are
pos
-
sible sublithospheric mechanisms.
It
would seem
that
the
presence
of
a
hotspot
requires anomalous upper mantle,
and
it is likely that
both
lithospheric
and
asthenospheric
prop
-
erties contribute
to the
swell. Surface
-
wave
tomography, al
-
though
presently having
low
resolving capability,
suggests
that
many swells
do
not have
abnormally
thin
lithosphere
but
are associated
with slower than average
upper
-
mantle
shear
-
wave velocities.
In general, smaller
swells
are located on
younger
sea-
floor, and
the larger ones (Cape
Verde,
Hawaii,
Great
Meteor, Bermuda, Reunion) are on older crust.
Within
the scatter
of
the
data,
the
midplate
swells reach an
ap
-
proximately uniform depth
below
sea level, approximately
4250 m, or the swell height is proportional to
the square
root
of
crustal age (Crough, 1978,
1979;
Menard
and
Mc-
hiutt,
1982).
Swells
on
ridge crests
have
heights that are
inversely proportional
to
the local
spreading
rate; Iceland,
the largest swell,
is
on a slow
-
opening ridge
and
Easter
Island, one
of
the smallest, is on a fast
-
spreading ridge.
Vogt
(1975)
showed that
this is consistent
with
relatively
shallow
flow
along
the ridge axis. The
widths
of
the
sub-
ridge asthenospheric channel is proportional
to the local
spreading
rate,
so that
flow
along
a fast
-
spreading ridge
en-
counters less
viscous
resistance
than
flow
along
a slower
spreading
ridge. The pressure gradient necessary
to
drive
the
lateral
flow
manifests itself
as a topographic gradient.
Slow
-
spreading ridges require a large pressure gradient,
and
they
therefore support
high
swells. The persistence
of
swells
after
they leave the
ridge crest implies
an
anomalous
lithosphere or additional
shallow
flow in
the spreading di
-
rection.
An
alternative explanation for
the
relation
between
swell
height
and
spreading
rate
is constant
flux
of
material
from
the
hotspot.
The
great highlands
of
Africa including the Ethiopian
and
East African plateaus
and
the
Hoggar
and
Tibesti
mas
-
sifs,
the
northern
Rocky
Mountains around
Yellowstone
and
the
Brazilian highlands are examples
of
possible
hotspot-
related continental swells.
In
shape
and
size these
swells
are similar to their oceanic counterparts.
Western North
America
and
northeast Africa are also associated
with slow
upper
-
mantle seismic anomalies.
The departure
of
the bathymetry
-
age relationship from
a simple cooling
law
for Cretaceous lithosphere
may
reflect
the extensive
igneous
activity
that
was
occurring during this
period.
Many
of
the seamounts
and
plateaus in the
westeirn
Pacific were
formed in
the Cretaceous.
THE
GEOID
Although the Earth
is not
flat or egg
-
shaped,
as
previously
believed
at various times, neither is it precisely a sphere or
even
an
ellipsoid
of
revolution. Although mountains, ocean
basins and
variations
in
crustal thickness contribute
to
the
observed
irregular shape
and
gravity
field
of
the
Earth,
they
cannot
explain
the
long
-
wavelength
departures from a
hy
-
drostatic figure.
The centrifugal
effect
of
the
Earth's
rotation causes
an
equatorial bulge, the principal departure
of
the
Earth's
surface from a spherical shape.
If
the Earth
were
covered
by
oceans then, apart from
winds and
internal currents, the
surface
would reflect
the forces due
to
rotation
and
the
gravitational attraction
of
external bodies,
such
as the Sun
and
the Moon,
and
effects
arising from the interior.
When
tidal
effects
are removed, the shape
of
the
surface is due to
density variations
in
the interior.
Mean
sea level is
an
equi-
potential surface called the
geoid
or
Jigure
of
the Earth.
Crustal features, continents, mountain ranges
and
mid-
oceanic ridges represent departures
of
the actual surface
from the geoid,
but mass
compensation at depth,
isostasy,
minimizes the
influence
of
surface features on the geoid.
To
first
order,
near
-
surface mass
anomalies that are compen
-
sated at
shallow
depth
have
no
effect on the geoid.
The shape
of
the
geoid
is now
known
fairly well, par
-
ticularly
in
oceanic regions, because
of
the contributions
from satellite
geodesy.
Apart from the
geoid
highs associ
-
ated
with
subduction zones, there is little correlation
of
th~e
long
-
wavelength geoid with such
features as continents
and
PACIFIC
PLATE
Geoid
High
FIGURE
12
-
1
Geoid
lows
are
concentrated in
a narrow
polar
band passing
through Antarctica, the Canadian Shield
and Siberia.
Most
of
the continents
and
smaller tectonic plates
are
in this band.
Long-
wavelength geoid highs and the larger plates
(Africa,
Pacific)
are
antipodal and
are
centered
on
the equator.
The
geoid highs con
-
trol the location
of
the
axis
of
rotation.
midocean
ridges. The
geoid reflects
temperature
and
den
-
sity variations
in
the interior, but these are
not
simply
re
-
lated to the surface expressions
of
plate tectonics.
The largest departures
of
the geoid from a radially
symmetric rotating spheroid are the equatorial
and
anti
-
podal
geoid highs centered on the central
Pacific and
Africa
(Figure
12
-
1).
The complementary pattern
of
geoid lows lie
in a polar
band that
contains
most
of
the large
shield
re
-
gions
of
the world. The largest geoid highs
of
intermediate
scale are associated
with
subduction zones. The
most no
-
table geoid high is centered
on
the subduction zones
of
the
southwest
Pacific
near
New
Guinea, again near the equator.
The equatorial location
of
geoid highs
is
not
accidental;
mass
anomalies
in the mantle control the moments
of
inertia
of
the Earth and, therefore,
the
location
of
the
spin
axis
and
the equator. The largest intermediate
-
wavelength geoid
lows
are found south
of
India, near Antarctica (south
of
New
Zealand)
and
south
of
Australia. The locations
of
the
mass
anomalies responsible for these lows are probably in
the
lower
mantle.
Many shield
areas are
in
or near
geoid
lows, some
of
which
are the result
of
deglaciation
and
in
-
complete rebound. The thick continental crust would,
by
itself, raise the center
of
gravity
of
continents relative to
oceans
and
cause slight
geoid
highs.
The
thick lithosphere
(
-
150
km) under continental shields is cold, but the seis
-
mic
velocities
and
xenoliths from kimberlite pipes suggest
that
it is olivine
-
rich
and
garnet
-
poor; the temperature
and
petrology
have
compensating
effects
on density. The long
-
term stability
of
shields indicates that, on average, the crust
plus its underlying lithosphere is buoyant.
Midocean
ridges
show mild
intermediate
-
wavelength
geoid
highs,
but they
occur
on
the edges
of
long
-
wavelength
highs. Hotspots,
too,
are associated
with
geoid highs. The
long
-
wavelength
fea
-
tures
of
the
geoid
are probably due to density variations
in
the lower mantle
and
the resulting deformations
of
the
core-
FIGURE
12
-
2
Geoid undulations (to degree
180)
referred
to
a hydrostatic flattening of
%99
638.
Contour
interval
is
5m
(after Rapp,
1981).
mantle boundary
and
other boundaries
in
the mantle (Rich
-
ards
and
Hager,
1984).
Geoid anomalies are expressed
as
the difference
in ele
-
vation
between
the
measured
geoid
and
some
reference
shape. The reference shape
is usually
either a spheroid
with
the observed flattening or the theoretical hydrostatic flatten
-
ing associated with
the Earth's
rotation. The latter,
used
in
Figure 12
-
2, is
the
appropriate geoid for geophysical pur
-
poses
and
is known as the nonhydrostatic geoid.
By
refer
-
encing the shape
of
the Earth's equipotential to the observed
flattening
by
subtracting
the
C,
terms
from
the
observed
shape, one is
throwing
away
some potentially important
geophysical data. The observed
C20
is
not
in
fact the same
as
one
obtains for
an
Earth
in
hydrostatic equilibrium,
and
this fact is
telling us
about the mass distribution
in
the
man
-
tle.
By
convention the origin
is taken as the center
of
mass,
so there is
no
C,,
term.
The
geometric flattening
of
the
Earth is
?h8
26.
The hydrostatic
flattening
is
9599
64.
The
C,
terms are spherical harmonic coefficients.
C,,
are
zonal
harmonics,
with
boundaries
between
positive
and
negative features
being
small circles parallel to the equato
-
rial plane.
For
a rotating homogeneous sphere the
C,,
term
is
the major term in
a
spherical harmonic expansion
of
the
shape. This is sometimes referred to as the equatorial bulge.
The
C,,
are
sectoral
harmonics,
and
the general case
C,,,
0
<
m
<
I,
are known
as
tesseral harmonics.
If the origin
of
the coordinate
system
is not
at the center
of
the
Earth,
then
there
will
be
a C,,
term.
North
-
south
-
running bands
of
high
or
low
geoid
anomalies
will
show
up
as
strong
sectoral
com
-
ponents
in
a spherical harmonic expansion.
The
maximum geoid
anomalies are
of
the order
of
100
m. This can
be compared
with
the
21
-
km difference
be
-
tween the
equatorial
and
polar radii.
To
a good
approxima
-
tion
the
net
mass
of
all
columns
of
the crust
and
mantle
are
equal
when averaged over
dimensions
of
a few hundred
kilometers. This is one definition
of
isostasy.
Smaller
-
scale
anomalies can
be
supported
by
the strength
of
the crust
and
lithosphere. The
geoid anomaly
is
nonzero
in
such
cases
and
depends on the distribution
of
mass. It depends on the
dipole
moment
of
the density distribution
where
z
is the radial direction,
h
is the depth
of
the anoma
-
lous density distribution
and
Ap(z)
is the density
anomaly.
Clearly,
if the
depth
extent
of
the anomalous
mass
is shal
-
low,
the geoid
anomaly
is small. This
is why
continents
do
not show up
well
in
the geoid.
The
geoid anomaly
due to
a
long
-
wavelength
isostatic
density distribution is
Tihe
dipole
moment
Ap(z)
is nonzero,
and
the
first moment
of
the
density
anomaly, that
is the
net
mass
anomaly,
is zero
for
isostatic density distributions.
The elevation
anomaly,
Ah,
associated
with
the den
-
sity
anomaly
is
A negative
Ap,
caused for example
by
thermal ex
-
pansion,
will
cause the elevation
of
the surface to increase
(Ah
=
positive)
and
gives
a positive
geoid
anomaly
be
-
cause the center
of
mass is closer
to the
Earth's
surface. The
mass deficiency
of
the anomalous material is
more than
can
-
celed out
by
the excess elevation.
All
major subduction zones are characterized either
by
geoid highs
(Tonga
and Java
through
Japan, Central
and
South America)
or
by
local
maxima
(Kuriles through Aleu
-
tians). The
long
-
wavelength
part
of
the
geoid is about that
expected for the excess
mass
of
the cold slab.
The
shorter-
wavelength
geoid anomalies,
however,
are less, indicating
that the excess
mass
is not
simply rigidly supported. Hager
(1984)
showed
that there is
an
excellent correlation
between
the
1
=
4
-
9 geoid and
the theoretical slab geoid
and
showed
that this
could be
explained
if the viscosity
of
the
mantle increased
with
depth
by
about a factor
of
30.
'The
high viscosity
of
the mantle at the lower
end
of
the slab
partially supports the excess load. A chemical boundary
near 650
krn
depth
could
also support the slab. The thick
crust
of
island arcs
and
the
high
temperatures
and
partial
melting
of
the
"
mantle wedge
7
' above the slab
may
also
contribute to the
geoid
highs
at subduction zones. The deep
trenches represent a
mass deficiency, and this
effect
alone
would
give a
geoid low.
Other
geoid
highs, unrelated
to
slabs, appear to
be
associated
with
hotter
than
normal
mantle,
such
as
hotspot
volcanism
and low
seismic veloci
-
ties
in the upper mantle.
The ocean
floor
in
back
-
arc
basins
is often lower
than
equivalent age normal ocean, suggesting that the mass
erc-
cess associated
with
the slab is pulling
down
the surface.
This is
not
the only possibility. A thinner
-
than
-
average
crust
or
a colder or denser
shallow
mantle could also depress
the seafloor.
Cooling
and
thermal contraction
of
the oceanic litho
-
sphere causes a depression
of
the
seafloor
with
age
and
a
decrease in the
geoid
height.
Cooling of
the lithosphere
causes the geoid
height
to decrease uniformly
with
increas
-
ing
age,
symmetrically
away
from the ridge crest. The
change is typically
5
-
10 m
over
distances
of
1000
to
2008
krn.
The elevation
and
geoid
offset
across fracture zones is
due
to
the age differences
of
the crust
and
lithosphere. As
-
suming a plate model
with
a fixed
thickness
and
lower
boundary temperature, a plate thickness
of
66
km has
been
estimated for plates less
than
30 Ma
in
age
and
92 km for
older plates (Cazenave, 1984; Cazenave
and
others, 1986).
This implies a
broad upwarping
of
geotherms
in the
younger
parts
of
the Pacific
Ocean.
The variation
of
geoid height
with
age
is
for a cooling half
-
space
model and
at
young
ages
in
the
plate
model
(where
G
is gravitational constant,
g
is surface
gravity,
p,
is upper
-
mantle density,
Ah
is change
in
geoid
height,
At
is difference
in age
and
T
is boundary tempera
-
ture). Observations are
more
consistent
with
a plate
model
in
which
lithospheric evolution
slows down
with
time
and
plate buoyancy approaches
an
asymptotic value.
However,
it is also likely
that
lateral heterogeneity
in
the mantle
beneath the plates,
and
extensive
volcanism
at certain pe
-
riods
of
time,
notably
the Cretaceous,
affect the
geoid
-
age
relation.
The
long
-
wavelength
topographic
highs
in
the
oceans
generally correlate
with
positive
geoid
anomalies, giving
6
-
8 meters
of
geoid per
kilometer
of
relief
(Cazenave,
1984; Cazenave
and
others, 1986).
Tanimoto
and
Anderson
(1985)
showed
that there
was
good
correlation
between
intermediate
-
wavelength
geoid
anomalies
and
seismic velocities
in
the
upper mantle; slow
regions
were geoid
highs
arid
vice versa. Subduction
zones
are
slow
in
the
shallow
mantle,
presumably
due to
the
hot,
partially
molten
mantle
wedge
under back
-
arc basins.
In
the subduction
regions
the total geoid
anomaly
is
the
sum
of
the
positive
effect
of
the
dense
sinker
and
the
negative
effects
caused
by
boundary deformations (Hager,
1984).
For
a layer
of
uniform
viscosity,
the
net
dynamic
geoid
anomaly
caused
by
a dense sinker
is
negative;
the
effects
from the deformed boundaries
overwhelm
the
effect
from the sinker itself.
For an
increase is viscosity
with
depth, the deformation
of
the upper boundary is less
and
the
net
geoid
anomaly
is positive.
For
a given density contrast, the magnitude
and sign
of
the resulting
geoid anomaly
in a dynamic
Earth
depends on
the viscosity structure
and
the chemical stratification.
Ob
-
servation
of
the gravitational
fieId
of the Earth
thus provides
a null experiment,
where
the
net
result
is a small
number
determined
by
the difference
of
large effects (Richards
and
Hager, 1984). The
sign
of
the result depends
on
which
of
the
effects
is dominant. The
anomaly
also depends on
the
depth
of
the convecting system,
with
deep systems leading
to
larger
geoid
anomalies for a given density
anomaly.
Observations
of
the
geoid
in
conjunction
with
observations
of
seismic
velocity
heterogeneities place constraints
upon
the variation
of
mantle viscosity
and
the depth
of
mantle
convection.
Interpreting the
Geoid
The geoid
bears
little relation to present tectonic features
of
the Earth other
than
trenches. The Mesozoic supercontinent
of
Pangaea,
however,
apparently
occupied
a central position