Gravity - The Solid Earth - page 223

which indicate that an elastic and perfectly plastic lithosphere is the more appro-
priate model there.
The values for the elastic thickness of the oceanic plates determined in this
section are considerably less than the values determined from seismic and thermal
data (Sections 4.1.3 and 7.5). A 100-km-thick elastic plate could not deform
as the oceanic lithosphere is observed to bend, bending would be much more
gradual. These apparent contradictions are a consequence of the thermal structure
of the lithosphere (discussed in Section 7.5). Figure 5.17 shows that the long-
term elastic thickness of the Pacific plate apparently increases with age and
approximately corresponds to the 450- ◦ C isotherm. The elastic thickness of the
continental lithosphere is frequently considerably greater than that of the oceanic
lithosphere; however, there is a wide range of values and there is no simple
relationship between elastic thickness and age of the lithosphere.

5.7.2 Isostatic rebound
The examples just discussed assume an equilibrium situation in which the load
has been in place for a long time and deformation has occurred. A study of the rate
of deformation after the application or removal of a load, however, shows that the
rate of deformation is dependent both on the flexural rigidity of the lithosphere
and on the viscosity 5 of the mantle. Mountain building and subsequent erosion
can be so slow that the viscosity of the underlying mantle is not important;
the mantle can be assumed to be in equilibrium at all times. However, the ice
caps - which during the late Pleistocene covered much of Greenland, northern
North America and Scandinavia - provide loads of both the right magnitude and
the right age to enable the viscosity of the mantle to be estimated. Figure 5.18
illustrates the deformation and rebound which occur as the lithosphere is first
loaded and then unloaded.

Start of
glaciation

LOAD

ELASTIC LITHOSPHERE

VISCOUS MANTLE

Load causes
subsidence

Ice melts at end
of glaciation

To determine the viscosity of the uppermost mantle, one must find a narrow
load. An example of such a load was the water of Lake Bonneville in Utah, U.S.A.,
the ancestor of the present Great Salt Lake. The old lake, which existed during
the Pleistocene and had a radius of about 100 km and a central depth of about

Subsequent slow rebound
of lithosphere

5

Newtonian viscosity is defined as the ratio of shear stress to strain rate and is therefore essentially
a measure of the internal friction of a fluid. The viscosity of many fluids is Newtonian, that
is independent of the strain rate (e.g. water, most gases, oils, glycerine). Fluids for which the
viscosity varies with the strain rate are termed non-Newtonian (e.g. paints, egg white, play putty,
cornflour/starch in water). There is debate about the exact properties of the mantle. However, here
we simply assume it to be a Newtonian fluid. The unit of viscosity is the pascal second (Pa s),
1Pas ≡ 1Nm − 2 s. The viscosity of water at 20 ◦ Cis10 − 3 Pa s; at 100 ◦ C, it is 0.3 × 10 − 3 Pa s.
Castor oil at 0 ◦ C has a viscosity of 5.3 Pa s; at 20 ◦ C its viscosity is 1 Pa s; and at 100 ◦ C its
viscosity is 2 × 10 − 2 Pa s. The viscosity of most fluids and of rock decreases rapidly with increasing
temperature. However, within the Earth, pressure tends to counteract the effects of temperature.

Figure 5.18. The
deformation and uplift
which occur as a result of
loading and unloading of
an elastic lithospheric
plate overlying a viscous
mantle.