The half-space cooling solution for oceanic lithosphere

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch Dating, heat flow and the thermal history of the Earth

Problem

The half-space cooling solution for oceanic lithosphere, with T0=0 ∘CT_0=0\,{}^{\circ}\mathrm{C} at the surface, is T(z,t)=T0+(Tm−T0) erf(η)T(z,t) = T_0 + (T_m-T_0)\,\mathrm{erf}(\eta) with similarity variable η=z/(2κt)\eta = z/(2\sqrt{\kappa t}). ((a)) Derive a general expression for the depth zc(t)z_c(t) of an isotherm of temperature TcT_c, in terms of TcT_c, Tm−T0T_m-T_0, κ\kappa, tt and the inverse error function. ((b)) Take Tm−T0=1345 KT_m - T_0 = 1345\,\mathrm{K}, an isotherm Tc=700 ∘CT_c = 700\,{}^{\circ}\mathrm{C}, and κ=10−6 m2 s−1\kappa = 10^{-6}\,\mathrm{m^2\,s^{-1}}. Using the table value erf(0.5)=0.5205\mathrm{erf}(0.5) = 0.5205, find the depth of this isotherm at an age t=30 Myrt = 30\,\mathrm{Myr}.

Browse the problem library