Surface warming over the past century can be modelled as a sinusoidal surface…

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

Surface warming over the past century can be modelled as a sinusoidal surface temperature variation of period P=100 yrP = 100\,\mathrm{yr} propagating into the ground by conduction, with thermal diffusivity κ=10−6 m2 s−1\kappa = 10^{-6}\,\mathrm{m^2\,s^{-1}}. ((a)) Find the thermal skin depth dd for this signal. ((b)) Find the depth at which the amplitude of the signal has fallen to 1%1\% of its surface value.

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