Forces and dynamics - Physical Processes in Earth and Environmental Sciences - page 55

h mr

Ocean

Nivel del Mar

h c

Crust

Midocean ridge or rift uplift

D

r c

r 1 r 2 r c

r 0

Moho

2,900 kg m -3

3,000 kg m -3
Partial melt

Mantle

r m

3,350 kg m -3

r m > r 0 > r c > r 1 > r 2

Fig. 3.29 Sketches to illustrate the Pratt hypothesis for isostasy. Here topography is supported by lateral density contrasts in the upper mantle
(left) and crust (right).

crust either “floating” on the denser mantle or supported
by a mantle of lower density. This equilibrium state is
termed isostasy ; it implies that below a certain depth the
mean lithostatic pressure at any given depth is equal.
As already noted (Section 3.5.3), above this depth a
lateral gradient may exist in this pressure. In the Airy
hypothesis, any substantial crustal topography is balanced
by the presence of a corresponding crustal root of the
same density; this is the floating iceberg scenario
(Fig. 3.28). In the Pratt hypothesis, the crustal topography
is due to lateral density contrasts in the upper mantle (at
the ocean ridges) or in separate floating crustal blocks
(Fig. 3.29). Sometimes the isostatic compensation due to
an imposed load like an ice sheet takes the form of a down-
ward flexure of the lithosphere, accompanied by radial
outflow of viscous asthenosphere (Fig. 3.30). The reverse
process occurs when the load is removed, as in the isostatic
rebound that accompanies ice sheet melting.
An important exception to isostatic equilibrium occurs
when we consider the whole denser lithosphere resting on
the slightly less dense asthenosphere, a situation forced by
the nature of the thermal boundary layer and the creation

Ice sheet
or
structural load

h 0

Lithosphere

r 1

l

w 0

Asthenosphere

r m

Fig. 3.30 Sketch to illustrate the Vening-Meinesz hypothesis for
isostatic compensation by lithospheric bending and outward flow
due to surface loading.

of lithospheric plate at the mid-ocean ridges (Sections 5.1
and 5.2). Lithospheric plates are denser than the astheno-
sphere and hence at the site of a subduction zone, a low-
angle shear fracture is formed and the plate sinks due to
negative buoyancy (Fig. 3.27).

3.7 Inward acceleration

In our previous treatment of acceleration (Section 3.2),
we examined it as if it resulted solely from a change in
the magnitude of velocity. In our discussion of speed and
velocity (Section 2.4), we have seen that fluid travels at a
certain speed or velocity in straight lines or in curved
paths. We have introduced these approaches as relevant
to linear or angular speed, velocity, or acceleration.
Many physical environments on land, in the ocean, and

atmosphere allow motion in curved space, with substance
moving from point to point along circular arcs, like the
river bend illustrated in Fig. 3.31. In many cases, where
the radius of the arc of curvature is very large relative to
the path traveled, it is possible to ignore the effects of cur-
vature and to still assume linear velocity. But in many
flows the angular velocity of slow-moving flows gives rise
to major effects which cannot be ignored.