A broad plateau stands at a mean elevation of above the surrounding lowlands

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch The shape and gravity of the Earth: potential, geoid, isostasy and flexure

Problem

A broad plateau stands at a mean elevation of

h = 4.5\,\mathrm{km}

above the surrounding lowlands. Satellite gravity gives a geoid anomaly over the plateau, relative to its surroundings, of

\Delta N_{\rm obs} = +45\,\mathrm m

. A geologist proposes that this geoid high is produced entirely by Airy-compensated topography, with a normal (unloaded) crustal thickness

H = 35\,\mathrm{km}

\rho_c = 2800\,\mathrm{kg\,m^{-3}}

\rho_m = 3300\,\mathrm{kg\,m^{-3}}

and

g = 9.8\,\mathrm{m\,s^{-2}}

. ((a)) Compute the geoid anomaly the Airy-compensated model predicts for this elevation. ((b)) Compare it with

\Delta N_{\rm obs}

, and say whether Airy compensation alone can account for the observed high. ((c)) State, in the chapter's terms, what this comparison can and cannot tell us about the source of any shortfall.

Browse the problem library