Geology Reference
In-Depth Information
Fig. 12.13 Major stresses and forces exerted on tectonic
plates. Black arrows slab pull ( f SP ); violet arrows viscous
drag ( £ D ); red arrows ridge push ( £ RP ); blue arrows
friction stress ( £ F ); brown arrows lift ( £ L ) and suction
( £ S ). Velocities v A and v B are relative to the top transition
zone ( O ). It is assumed that the ridge R is at rest with
respect to the transition zone frame
considered the slab pull as a hydrostatic body
force having magnitude f sp ( z ) D [ ¡ l ( z )- ¡ m ( z )] g
(by Archimedes' principle), ¡ m and g being
the mantle density and the gravity acceleration,
respectively.
An inventory of stresses and forces exerted
on tectonic plates is illustrated in Fig. 12.13 .
According to Forsyth and Uyeda ( 1975 ), they can
be divided in driving forces determining plate
motions and resistive forces that oppose them.
The most important elements of the former class
are the slab pull, f sp , exerted by downgoing slabs
and the torque about the centre of the Earth aris-
ing from the lateral variations of thickness of the
oceanic lithosphere, which have been discussed
in the previous section and are associated with its
progressive cooling. The latter is often referred
to as ridge push , N RP , although the key factor
determining this torque is lithospheric thicken-
ing, not ridge elevation (Lister 1975 ; Hager and
O'Connell 1981 ;Harper 1984 ). According to
Harper ( 1984 ), the basal traction generated by
ridge push at a location r is given by:
where r t is the spatial gradient of ocean floor age
at r . Therefore, the traction associated with plate
thickening is higher in the case of slow-spreading
ridges. This expression allows to calculate the
total torque exerted on an oceanic plate as a con-
sequence of cooling. Integrating over the surface
S of the plate and applying Stokes's theorem (see
Appendix 1 ) , we obtain a total torque:
Z
r T RP dS D pR Z
S
N RP D
r t dS
S
D pR I
tdr
(12.70)
C.S/
where R is the Earth's radius, C ( S ) is the bound-
ary of S , and the integral path is clockwise. The
last integral in ( 12.70 ) shows that although ridge
push is ultimately the result of hydrostatic forces,
it can be calculated as if it were a boundary
force, and this is effectively the way in which
it is usually considered. The term “ridge push”
comes from its appearance as a force exerted by
ridges, because clearly the youngest ocean floor
age always occurs at spreading centres.
T RP .r/ D a '.T a T 0 /› r t p r t.r/
(12.69)
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