Geology Reference
In-Depth Information
If we consider the lithosphere as an elastic
solid layer “floating” over the fluid (in rheo-
logical sense) asthenosphere, we will easily re-
alize that the lateral variability of density in
the oceanic lithosphere must determine a hydro-
static imbalance that can be compensated locally
only by vertical displacements and shear. This
phenomenon is known as
thermal isostasy
and
arises from Archimedes' principle of hydrostatic
equilibrium. To understand the application of this
important principle to the asthenosphere, we re-
call that fluids cannot support static shear stress,
thereby the equation of hydrostatic equilibrium
reads:
Fig. 12.12
Thermal isostasy of the oceanic lithosphere.
Thermal subsidence causes an increase of the ocean floor
depth.
¡
a
,
¡
l
,and
¡
w
, are respectively the densities of
the asthenosphere, the lithosphere, and the sea water.
Columns of material having unit cross-section over the
compensation depth
z
c
(
dark grey rectangle
)musthave
equal weight
@£
ij
@x
j
D
@P
@x
j
D
¡
g
i
(12.60)
where
g
D
g
k
is the gravity field vector. Inte-
grating this equation, we see that the hydrostatic
pressure
P
at any depth
z
does not depend from
x
and
y
and is simply the weight of the column
of rock having height
z
and unit area. In the
asthenosphere, this law must hold even when the
column is formed partly by sea water, partly from
oceanic MORBs, and partly from peridotite.
We h ave :
along the ridge axis and can be ignored. Fur-
thermore, let
h
(
x
)and
w
(
x
) be respectively the
thickness of the lithosphere at offset
x
from the
spreading ridge and the corresponding depth of
the sea floor (Fig.
12.12
). As shown in Fig.
12.9
,
in so far as the age of the ocean floor increases, a
column of height
h
will include a larger fraction
of dense lithosphere and a corresponding smaller
fraction of the less dense asthenosphere. Further-
more, as
x
increases, at any depth below the sea
floor the lithosphere will have increasing density
because of thermal contraction. Consequently,
the increased weight of a column of material with
unit cross-section and height
h
above depth
z
c
must be compensated by a larger amount of water
between the column and the sea surface, that is by
a greater sea floor depth (Fig.
12.12
).
At any time, the depth to the sea floor at dis-
tance
x
from the ridge must ensure the invariance
of
P
(
z
c
). Therefore, isostatic equilibrium requires
subsidence of the oceanic lithosphere in so far
as its age increases. If
e
(
x
) is the elevation of
the ocean floor with respect to the asymptotic
depth
w
1
and
d
(
x
) is the displacement of the
bottom of the lithosphere above the compensation
depth
z
c
, then the pressure
P
(
z
c
)atanyoffset
x
is
given by:
Z
z
P.
z
/
D
g
¡.x;y;
z
/d
z
(12.61)
0
It should be noted that although the density
¡ in (
12.61
) in general depends from
x
and
y
,
by (
12.60
) the pressure will be constant along
any horizontal plane. Now let us consider the
hydrostatic pressure at depth
h
below the sea
floor, where
h
is the maximum thickness of the
lithosphere in the PCM. Assuming that
z
D
0at
the ocean surface and that
w
1
is the sea floor
depth at large distance from the ridge, we can
use the depth
z
c
D
h
C
w
1
as a reference depth,
or
compensation depth
, for applying the isostasy
principle, which then reads:
P
(
z
c
)
D
const
.Letus
assume that the coordinate
x
measures distances
from the spreading ridge, so that direction
y
is
