Pratt's hypothesis assumes a constant depth to the base of the outermost shell of the Earth, whose density varies according to the surface topography. Thus, mountain ranges would be underlain by relatively low density material and ocean basins by relatively high density material (Fig. 2.29b). Equating the weights of columns of unit cross-section beneath a mountain range and a region of zero elevation gives:
If one substitutes appropriate densities for the crust, mantle, and sea water in these equations they predict that the relief on the Moho should be approximately seven times the relief at the Earth's surface.
g(Tv + h)Ph = gTrPc which on rearrangement provides the condition for isostatic equilibrium of the mountain range:
A similar computation for an ocean basin gives:
In these early models of isostasy it was assumed that the outer shell of the Earth, whose topography is compensated, corresponded to the crust. Certainly the large density contrast existing across the Moho plays a major part in the compensation. It is now believed, however, that the compensated layer is rather thicker and includes part of the upper mantle. This strong outer layer of the Earth is known as the lithosphere (Section 2.12). The lithosphere is underlain by a much weaker layer known as the asthenosphere which deforms by flow, and which can thus be displaced by vertical movements of the lithosphere. The density contrast across the lithosphere-asthenosphere boundary is, however, very small.
Both the Airy and Pratt hypotheses are essentially applications of Archimedes' Principle whereby adjacent blocks attain isostatic equilibrium through their buoyancy in the fluid substratum. They assume that adjacent blocks are decoupled by fault planes and achieve equilibrium by rising or subsiding independently. However, these models of local compensation imply unreasonable mechanical properties for the crust and upper mantle (Banks et al., 1977), because they predict that independent movement would take place even for very small loads. The lithosphere is demon-strably not as weak as this implies, as large gravity anomalies exist over igneous intrusions with ages in excess of 100 Ma. The lithosphere must therefore be able to support stress differences of up to 20-30 MPa for considerable periods of time without the necessity of local compensation.
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