A newly mapped seamount chain sits on oceanic lithosphere of elastic thickness

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 newly mapped seamount chain sits on oceanic lithosphere of elastic thickness Te=35 kmT_e = 35\,\mathrm{km}, with E=70 GPaE = 70\,\mathrm{GPa}, ν=0.25\nu = 0.25, ρm=3300 kg m−3\rho_m = 3300\,\mathrm{kg\,m^{-3}}, water infill ρfill=1000 kg m−3\rho_{\rm fill} = 1000\,\mathrm{kg\,m^{-3}} and g=9.81 m s−2g = 9.81\,\mathrm{m\,s^{-2}}. The chain's load repeats with a dominant wavelength λ=350 km\lambda = 350\,\mathrm{km}, and its topography stands h=1.2 kmh = 1.2\,\mathrm{km} above the surrounding sea floor, built of rock of density ρc=2800 kg m−3\rho_c = 2800\,\mathrm{kg\,m^{-3}}. ((a)) Find the flexural rigidity DD and the flexural parameter αf\alpha_f. ((b)) Find the degree of compensation C(k)C(k) at the chain's dominant wavelength, and say whether the load is closer to fully plate-supported or fully Airy-balanced. ((c)) Model the chain's load as q(x)=q0cos⁡kxq(x)=q_0\cos kx with q0=(ρc−ρfill)ghq_0=(\rho_c-\rho_{\rm fill})gh, the rock's weight less that of the sea water it replaces. Find the actual deflection amplitude at the load's centre, and compare it with the deflection a fully Airy-balanced column under the same load would show.

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