Airy's hypothesis assumes that the outermost shell of the Earth is of a constant density and overlies a higher density layer. Surface topography is compensated by varying the thickness of the outer shell in such a way that its buoyancy balances the surface load. A simple analogy would be blocks of ice of varying thickness floating in water, with the thickest showing the greatest elevation above the surface. Thus mountain ranges would be underlain by a thick root, and ocean basins by a thinned outer layer or antiroot (Fig. 2.29a). The base of the outer shell is consequently an exaggerated mirror image of the surface topography. Consider the columns of unit cross-section beneath a mountain range and a region of zero elevation shown in Fig. 2.29a. Equating their weights gives:
where g is the acceleration due to gravity.
Rearranging this equation gives the condition for isostatic equilibrium:
Mountain range hpc
A similar computation provides the condition for compensation of an ocean basin:
Anti' root mm
Figure 2.29 (a) Airy mechanism of isostatic compensation. h, height of mountain above sea level; z, depth of water of density pw ; TA, normal thickness of crust of density pc ; r, thickness of root; a, thickness of antiroot; DA, depth of compensation below root; pm, density of mantle. (b) The Pratt mechanism of isostatic compensation. Legend as for (a) except Tp, normal thickness of crust; ph, density of crust beneath mountain; pz, density of crust beneath ocean; Dp, depth of compensation below Tp .
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