A chain of seamounts loads the ocean floor along a line

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics

Bending, Ringing, Breaking and Flowing, Ch Buckling, plates and elastic foundations

Problem

A chain of seamounts loads the ocean floor along a line. The oceanic lithosphere there has elastic thickness Te=20 kmT_e = 20\,\mathrm{km}, E=70 GPaE = 70\,\mathrm{GPa}, ν=0.25\nu = 0.25, and rests on mantle of density 3300 kg m−33300\,\mathrm{kg\,m^{-3}} below sea water of density 1030 kg m−31030\,\mathrm{kg\,m^{-3}}. Take g=9.8 m s−2g = 9.8\,\mathrm{m\,s^{-2}}. ((a)) Find the flexural rigidity DD and the flexural parameter αf\alpha_f of this lithosphere. ((b)) Find the distance from the seamount chain at which the sea floor first returns to its undisturbed depth (the outer edge of the moat) and the distance at which the surrounding bulge crests. ((c)) Find the distance from the outer edge of the moat to the crest of the bulge.

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