A bathymetric survey across an old oceanic trench

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 bathymetric survey across an old oceanic trench, flanked by sea water, shows the sea floor crossing back up through its undisturbed depth (the edge of the moat) at a horizontal distance of 195 km195\,\mathrm{km} from the trench axis, and the outer-rise arch peaking at 260 km260\,\mathrm{km}. Treat the trench flank as the same line-load flexure solution used for an island chain, with ρm=3300 kg m−3\rho_m = 3300\,\mathrm{kg\,m^{-3}}, ρfill=1000 kg m−3\rho_{\rm fill} = 1000\,\mathrm{kg\,m^{-3}} (water), g=9.81 m s−2g = 9.81\,\mathrm{m\,s^{-2}}, E=70 GPaE = 70\,\mathrm{GPa} and ν=0.25\nu = 0.25. ((a)) Check that the two distances are consistent with a single flexural parameter αf\alpha_f, and find αf\alpha_f from each. ((b)) Find the flexural rigidity DD. ((c)) Find the elastic thickness TeT_e, and compare it with the range the chapter quotes for old Pacific lithosphere.

Browse the problem library