A submarine ridge loads an elastic plate of flexural rigidity

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · 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 submarine ridge loads an elastic plate of flexural rigidity D=5.0×1022 N mD = 5.0\times10^{22}\,\mathrm{N\,m}. The load has a dominant wavelength λ=300 km\lambda = 300\,\mathrm{km}, and the mantle beneath is displaced against a crustal infill so that the effective density contrast is ρm−ρfill=500 kg m−3\rho_m - \rho_{\rm fill} = 500\,\mathrm{kg\,m^{-3}}. Take g=9.8 m s−2g = 9.8\,\mathrm{m\,s^{-2}}. ((a)) Compute the wavenumber k=2π/λk = 2\pi/\lambda. ((b)) Compute the degree of compensation C(k)=[1+Dk4(ρm−ρfill)g]−1C(k) = \left[1 + \dfrac{Dk^4}{(\rho_m-\rho_{\rm fill})g}\right]^{-1}. ((c)) State in words whether this load is mostly carried by the plate or mostly in Airy balance.

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