Download The stability of the continents and the tendency for old oceanic


Geodynamics
456‐556
Problem
set
#3.
Isostasy
and
Ridge
Push
(Due in class on May 6)
A.
Why
do
only
oceans
get
subducted?
The
stability
of
the
continents
and
the
tendency
for
old
oceanic
plates
to
subduct
back
into
the
mantle
can
be
explained
by
calculating
the
average
density
of
each
plate.
The
density,
ρ,
of
rock
is
related
to
temperature,
T
,
according
to
ρ
=ρ0(1
−
αT
)
(1)
where
ρo
is
the
rock
density
at
surface
temperature
and
pressure
(S.T.P.)
and
α
is
the
thermal
expansion
coefficient
of
the
rock.
Equation
1
says
that
rocks
become
less
dense
as
they
are
heated
because
they
expand.
In
the
following
questions,
refer
to
the
template
sketched
in
Figure
1
and
use
the
values
listed
in
Table
1.
1.
Determine
the
average
density
of
an
old
oceanic
plate
using
the
following
procedure.
(a)
First,
calculate
the
average
temperatures
of
the
crust
and
the
average
temperature
of
the
sub‐
crustal
upper
mantle
(i.e.
the
lithospheric
mantle).
Assume
a
linear
geothermal
gradient
from
◦
0 C
at
the
surface
to
temperature
TB
at
the
base
of
the
plate.
(b)
Use
equation
1
to
calculate
the
average
densities
of
the
crust
and
the
lithospheric
mantle
from
their
temperatures.
(c)
Calculate
the
average
density
of
the
oceanic
plate
from
the
two
densities
you
determined
in
part
(b),
bearing
in
mind
the
relative
thicknesses
of
the
crust
and
lithospheric
mantle.
2.
Now
calculate
the
average
density
of
a
continental
plate
by
repeating
the
procedure
in
part
(1).
3.
Thirdly,
calculate
the
density
of
the
convecting
mantle
immediately
below
the
plate
(i.e.
the
asthenosphere)
using
equation
1.
4.
Compare
the
average
densities
you
have
just
calculated
for
an
oceanic
plate,
a
continental
plate
and
the
asthenosphere.
You
should
find
that
the
old
oceanic
plate
is
denser
than
the
convecting
mantle
beneath,
whilst
continental
plates
are
less
dense
than
the
convecting
mantle
beneath.
Thus
oceanic
plates
are
unstable
and
will
sink
back
down
into
the
mantle,
given
a
chance.
Continental
plates
float
stably
on
top
of
the
convecting
mantle.
B.
Why
are
oceans
deep?
The
difference
in
elevation
between
continents
and
oceans
can
be
explained
using
the
principle
of
isostasy.
Isostasy
says
that
if
we
consider
two
blocks
of
different
density
and
thickness
floating
in
a
fluid,
the
pressure
at
some
reference
depth
below
both
blocks
must
be
equal.
The
pressure,
P
,
at
the
base
of
a
unit
column
of
rock
is
given
by
P
=
ρgh
(2)
where
ρ
is
the
density
and
h
is
the
column
thickness.
The
aim
of
the
following
calculations
is
to
find
the
difference
in
height
between
continents
and
oceans,
termed
ΔH
in
Figure
2.
1.
Using
equation
2,
write
down
an
expression
for
the
pressure
at
the
reference
depth
beneath
an
oceanic
plate.
The
pressures
generated
by
the
water
column
and
the
rock
column
can
be
added.
Use
the
average
density
for
the
oceanic
plate
you
calculated
in
part
A(1).
2.
Similarly,
write
down
an
expression
for
the
pressure
at
the
reference
depth
beneath
the
continental
plate
illustrated
in
Figure
2.
3.
Set
the
two
expressions
for
pressure
at
the
reference
depth
equal.
You
should
find
that
ΔH
is
the
only
unknown
in
the
resulting
equation.
Rearrange
your
equation
and
calculate
ΔH.
4.
You
should
find
that
the
difference
in
height
between
continents
and
oceans
is
just
over
6
km.
In
fact,
oceanic
abyssal
plains
lie
at
a
depth
of
between
5
and
6
km
and
the
average
height
of
the
continents
above
sea‐level
is
0.8
km.
C. Isostasy and ice sheets
1.
Consider
the
Laurentide
ice
sheet
that
was,
at
the
last
glacial
maximum
(LGM,
about
20
Ka),
3
km
thick
in
its
center.
Calculate
the
expected
subsidence
of
the
crust
if
this
ice
sheet
was
in
place
long
enough
for
isostatic
equilibrium
to
have
been
achieved.
Assume
densities
of
ice
and
mantle
to
be
910
and
3300
kg/m ,
respectively.
Note
that
the
answer
is
independent
of
what
you
assume
for
the
density
of
the
crust.
3
D. Average Continental crustal thickness
1.
If
the
mean
altitude
of
continents
is
0.8
km,
and
the
mean
oceanic
depth
is
3.5
km,
and
the
mean
oceanic
crustal
thickness
is
6
km,
how
thick
is
the
mean
continental
crust?
Assume
that
the
densities
involved
are:
seawater
(1000
kg/m ),
continental
and
oceanic
crust
(2700
and
3000
kg/m ,
respectively)
and
upper
mantle
(3300
kg/m ).
3
3
3
E.
Isostasy,
potential
energy,
and
the
forces
of
ridge‐push
For
part
b/
of
the
following
problem:
If
you
can
not
integrate,
then
assume
a
constant
density
for
the
complete
lithosphere
(similar
to
the
sketches
above)
to
estimate
the
Gravitational
Potential
Energy
for
each
column
(the
area
in
the
triangle).
d/
Assuming
that
lithospheric
rocks
have
a
strength
of
70
MPa,
would
the
gravitational
forces
determined
in
b/
produce
lithospheric
deformation?