| The continental geotherm through time... | |||||||||
| Exercise 4: Radiogenic isotopes decay through time with a constant time scale λ called the decay constant. Therefore in the past, continental geotherms were warmer as continental crusts were enriched in radiogenic isotopes. . 40K, 238U and 235U, and 232Th are the main heat producing radiogenic isotopes. Their concentrations vary through time according to the following relationships where t, the time, is in years, and K0, Th0 and U0 are present day concentrations: |
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| • K(t)=K0.Exp[-λK.t]: With λK=5.543 10-10 • Th(t)=Th0.Exp[-λTh.t]: With λTh=4.9475 10-11 • U(t)=U0.(0.992849.Exp[-λ238U.t] + 0.00725.Exp[-λ235U.t]): With λ238U=1.55125 10-10 and λ235U=9.8485 10-10 |
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| The rate of heat release varies from isotopes to the next. For K, Th and U the rate of heat release is (in W.kg-1): |
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| • HK=3.48 10-9 • HTh=2.64 10-5 • H238U=9.46 10-5 • H235U=5.69 10-4 |
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| The average content in K, Th and U (in part per million) of present-day Archaean crust is: | |||||||||
| • K0=7500 ppm; • Th0=2.9 ppm; • U0= 0.75 ppm |
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| 1/ Assuming depth-independent radiogenic heat production in the crust and no radiogenic heat production in the mantle, construct the continental geotherm for a 40 km thick crust with a density of 2700 kg.m-3, a basal mantle heat flow of 15.10-3 W.m-2 (we assume that the basal heat flow remains constant through time), and a constant temperature at the surface of 20 ºC. The thermal conductivity of the continental crust and the mantle is: k=2.5 W.m-1C-1.
2/ Determine the temperature at the base of the crust and the thickness of the continental lithosphere at 4, 3, 2, 1 Ga and present. |
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