A granite in an actively eroding range has the same heat-production and conductivity…

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

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

Problem

A granite in an actively eroding range has the same heat-production and conductivity structure as the province of section 3.4: surface heat production

A_0 = 2.5\,\mathrm{\mu W\,m^{-3}}

falling off with depth scale

h_r = 10\,\mathrm{km}

, reduced heat flow

q_r = 30\,\mathrm{mW\,m^{-2}}

, conductivity

k = 2.5\,\mathrm{W\,m^{-1}\,K^{-1}}

and surface temperature

T_0 = 10\,{}^\circ\mathrm{C}

, so its present geotherm is

T(z) = T_0 + q_rz/k + (A_0h_r^2/k)(1-e^{-z/h_r})

. Biotite in a sample closes (

T_c \approx 300\,{}^\circ\mathrm{C}

) at

12\,\mathrm{Myr}

ago, and apatite fission tracks in the same sample close (

T_c \approx 110\,{}^\circ\mathrm{C}

) at

4\,\mathrm{Myr}

ago. ((a)) Taking today's geotherm as a stand-in for the rock's thermal surroundings over the last

12\,\mathrm{Myr}

, find the two depths at which it now reaches

300\,{}^\circ\mathrm{C}

and

110\,{}^\circ\mathrm{C}

. ((b)) Hence find the average exhumation rate between the two closures. ((c)) Apply the provisional constant gradient of

25\,\mathrm{K\,km^{-1}}

from section 3.2, used there to turn a cooling rate into an exhumation rate, to this sample's two closures, and say which of the two exhumation-rate estimates is more trustworthy and why.

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