Geology Reference
In-Depth Information
2
4
¡
w
w
.x/
C
¡
a
d.x/
C
3
5
For large offsets
x
, the depth to the sea floor
assumes values close to following asymptotic
value:
h.x/
Z
P.
z
c
/
D
g
¡
l
.x;/d
0
2
'¡
a
.T
a
T
0
/h
2.¡
a
¡
w
/
w
1
D
w
0
C
(12.66)
4
¡
w
.
w
1
e.x//
C
¡
a
d.x/
D
g
where
w
0
is the depth to the ridge crest. This
expression gives the equilibrium depth of old
oceanic basins. Assuming
w
0
D
2.6 km,˛
D
3.1
10
-5
K
-1
, ¡
a
D
3, 300 kg kgm
-3
,
T
a
-
T
0
D
1,270
ı
C,
h
D
100 km, and ¡
w
D
1,000 kg m
-3
,
we obtain from (
12.66
) an asymptotic depth
w
1
D
5.4 km. In the case of young crust, the
elevation above the asymptotic depth has the
approximate expression:
3
h.x/
Z
5
C
¡
l0
.1
'T .x;//d
0
(12.62)
where ¡
l
0
is the lithosphere density at room tem-
perature (
T
0
) and the integral is performed over
the lithosphere thickness at offset
x
. The con-
dition of isostatic equilibrium can be expressed
equating the
P
(
z
c
)atoffset
x
to the asymptotic
value:
'¡
l0
.T
a
T
0
/h
2.¡
l0
¡
w
/
e.x/
Š
r
2›x
v
I
r
2›x
v
2'¡
l0
.T
a
T
0
/
.¡
l0
¡
w
/
¡
w
.
w
1
e.x//
C
¡
a
d.x/
<< h
Z
h.x/
(12.67)
C
¡
l0
.1
'T .x;//d
Therefore, the depth to the ocean floor will
increase with the square root of the distance from
the ridge or, equivalently, with the square root
of the age. These results have been confirmed
with high accuracy by the observed ocean floor
bathymetry. A good fit was obtained by Stein
and Stein (
1992
), who proposed the following
reference model, based on the PCM, for the
young and old ocean floor depths:
0
Z
h
D
¡
w
w
1
C
¡
l0
.1
'T .
1
;//d
0
(12.63)
Parsons and Sclater (
1977
) used this condition
to determine the depth to the ocean floor. They
obtained the following expression for the eleva-
tion
e
(
x
) above the asymptotic depth:
2600
C
365
p
t
I
t<20Ma
5651
2473e
0:0278t
X
1
4'¡
l0
.T
a
T
0
/h
.¡
l0
¡
w
/
2
1
.2n
C
1/
2
w
.t/
D
I
t
20 Ma
(12.68)
e.x/
D
nD0
exp
R
C
.2n
C
1/
2
2
x
q
R
2
(12.64)
12.5 Driving Mechanism of Plate
Tectonics: Slab Pull
and Ridge Push
where
R
is the Peclet number of the oceanic litho-
sphere and represents the ratio of heat advection
full
spreading rate, this dimensionless quantity is
given by:
In the previous section, we have seen that the
thermodynamics of the oceanic lithosphere,
which includes both vertical diffusion and
horizontal advection of heat, determines lateral
variations of density and thickness. Although
v
h
2›
R
D
(12.65)
