Geoscience Reference
In-Depth Information
3
Figure 8.21.
The total
driving force available
from the subducting slab,
F
SP
(0) as a function of
subduction velocity
v
. The
horizontal dashed line
shows the asymptotic
limit as
v
increases to
infinity. (After Richter and
McKenzie (1978).)
2
1
0
0
5
10
v (cm yr
--1
)
where
c
P
is the specific heat and
v
is the rate at which the slab sinks. The total force
available is
F
SP
evaluated at
z
=
0,
F
SP
(0).
F
SP
(
z
) decreases with depth into the
mantle, until, by
z
0. Figure 8.21 shows the dependence of
this total force on the consumption velocity
v
.Anadditional driving force in the
sinking slab would arise if the olivine-spinel phase change within the slab were
elevated compared with the mantle (Fig. 9.44). However, if there is a metastable
olivine wedge in the slab, then this would be a resistive force rather than a driving
force. The magnitude of this force is about half that caused by the difference in
temperature between the slab and the mantle. The total slab-pull force is estimated
to be 10
13
Nm
−
1
in magnitude, which is greater than the 10
12
Nm
−
1
of the
ridge-push force. Both slab-pull and ridge-push are caused by the difference in
density between hot and cold mantle; hot mantle can rise only because cold mantle
sinks.
=
d
,itiszero,
F
SP
(
d
)
=
Resistive forces
Resistive forces occur locally at the ridge axis (occurrence of shallow earth-
quakes), along the bases of the plates as
mantle-drag
(assuming that the mantle
flow is less than the plate velocity; if the reverse is true, then this would be a
driving force), along transform faults (earthquakes) and on the descending slab.
Estimates of these forces suggest that the resistive force acting on the top of the
sinking slab is greater than the shear force acting on its sides. The resistive force
acting on the base of the plate is proportional to the area of the plate but is of
the same magnitude as the resistive forces acting on the descending slab. These
resistive forces cannot easily be estimated analytically and must be calculated
numerically from the differential equations for flow in a fluid. The forces are pro-
portional to the product of mantle viscosity
and plate velocity
v
and are about
10
13
Nm
−
1
in magnitude (depending on the value of mantle viscosity assumed).
Fora6000-10 000-km-long plate, they would total (80-100)
η
v
.
It is difficult to estimate the resistive forces acting on faults. However, the stress
drop for large earthquakes is
η
10
6
Nm
−
2
in magnitude. Earthquakes at ridge axes
are shallow and small, and their contribution to the resistive forces can be ignored
in comparison with the fluid-dynamic drag forces. The resistive forces acting
∼
