The equilibrium flexural response of the lithosphere to loading is independent of the precise mechanical properties of the underlying asthenosphere as long as it facilitates flow. However, the reattainment of equilibrium after removal of the load, a phenomenon known as isostatic rebound, is controlled by the viscosity of the asthenosphere. Measurement of the rates of isostatic rebound provides a means of estimating the viscosity of the upper mantle. Fennoscandia represents an example of this type of study as precise leveling surveys undertaken since the late 19th century have shown that this region is undergoing uplift following the melting of the Pleistocene ice sheet (Fig. 2.32). The maximum uplift rates occur around the Gulf of Bothnia, where the land is rising at a rate of over 10 mm a-1. Twenty thousand years ago the land surface was covered by an ice sheet about 2.5 km thick (Fig. 2.32a). The lithosphere accommodated this load by flexing (Fig. 2.32b), resulting in a subsidence of 600-700 m and a lateral displacement of asthenospheric material. This stage currently pertains in Greenland and Antarctica where, in Greenland, the land surface is depressed by as much as 250 m below sea level by the weight of ice. Melting of the ice was complete about 10,000 years ago (Fig. 2.32c), and since this time the lithosphere has been returning to its original position and the land rising in order to regain isostatic equilibrium. A similar situation pertains in northern Canada where the land surface around Hudson Bay is rising subsequent to the removal of an icecap. The rate of isostatic rebound provides an estimate for the viscosity of the upper mantle of 1021 Pa s (Pascal seconds), and measurements based on world-wide modeling of post-glacial recovery and its associated oceanic loading suggest that this figure generally applies throughout the upper mantle as a whole (Peltier & Andrews, 1976). Compared to the viscosity of water (10—3 Pa s) or a lava flow (4 X 103 Pa s), the viscosity of the sub-lithospheric mantle is extremely high and its fluid behavior is only apparent in processes with a large of such a feature is small in the central part of the plateau so that here the Bouguer anomaly, BA, is related to the free-air anomaly, FAA by the relationship:
where BC is the Bouguer correction, equal to 2nGpch, where pc is the density of the compensated layer. For such an Airy compensation:
IA = BA - Aroot where Aroot is the gravity anomaly of the compensating root. Since the root is broad compared to its thickness, its anomaly may be approximated by that of an infinite slab, that is 2nG(pc - pm)r, where pm is the density of the substrate. Combining the above two equations:
Figure 2.32 Theory of isostatic rebound. (a) The load of an icecap on the lithosphere causes downbending accompanied by the elevation of the peripheral lithosphere and lateral flow in the asthenosphere (b). When the icecap melts (c), isostatic equilibrium is regained by reversed flow in the asthenosphere, sinking of the peripheral bulges and elevation of the central region (d).
time constant. Knowledge of the viscosity of the mantle, however, provides an important control on the nature of mantle convection, as will be discussed in Section 12.5.2.
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