3. Continental Heat Flow. Ge 163 4/3/15

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1 3. Continental Heat Flow Ge 163 4/3/15

2 Outline 1. Measurement of heat flow and Fourier s law 2. Overview of major variations 3. Sclater Histograms 4. Heat-flow - heat-production relationship 5. Continental geotherm

3 Fourier s Law q = kt,x q = heat flux (units: W m -2 k = thermal conductivity (units: W m -1 K -1 T temperature x spatial coordinate

4 Variations of heat flow on continents Major geological factors * orogeny arc-arc amalgamation continental collision *rifting and continental stretching *amount of radioactive elements in crust *erosion *sedimentation Environmental factors *Large-scale water circulation *Past climatic changes

5 Smoothed Heat Flow from borehole measurements mw/m^2 SMU web site

6 Heat flow is generally high and very scattered in young regions and decays to a value of around 42 mw m -2 in early Proterozoic terrains [Proterozoic= Ma] Some authors have suggested that in North America the effect of the last glaciation was to reduce the near surface temperature gradient by as much as 20% Sclater et al. [1980] suggest that the combined Effect of both slow circulation of water and glaciation could have a combined effect of 30%. Sclater, J. G., Jaupart, C., and Galson, D., The heat flow through oceanic and continental crust and the heat loss of the Earth, Rev. of Geophys. Space Phys., 18, , 1980.

7 Position of heat flow measurements of Sclater et al. [1980] on ages of continental crust. 1. >1700 Ma; Ma; Ma; 4. < 250 Ma

8 Note on the construction of the histograms: In order to reduce bias, values which differed by 10% or less & lay within a radius of 30 km were averaged For groups with large deviations, all values were considered

9 1. >1700 Ma; Ma; Ma; 4. < 250 Ma

10 Sclater et al. [1980]

11 General Conclusions from the Histograms Eurasia and N. American values have almost identical distributions. Youngest province mean is high, ~80 mw m -2, and is associated with large scatter For all continents older than 800 Ma, the heat flow tends to a constant value lying in the range mw m -2. Both the mean and scatter decrease with age; evidence that the heat flow is approaching an equilibirum value Except for two older provinces outside of Africa, almost no value below 25 mw m -2. This cut-off is observed for the younger provinces owing to the flatness of the distributions

12 Heat Flow and Surface Heat Production A general decrease in depth in the concentration in U, Th, & K has been noted, although there is high variability laterally on both a large-scale and small scale. Ageneral decrease with depth has been noted in a series of plutons in Idaho, in a vertical section in the Alps, and in several deep boreholes

13 Metamorphic rocks High grade metamorphic rocks are significantly Lower in Th & U than their counterparts in lower metamorphic grades. Typically lower crustal rocks have low heat production 2.4 x to 1.8 x W kg -1 This compares to ~9.6 x W kg -1 for granite

14 Birch, Roy & Decker [1968] showed (empirically) that q s = q r + da s Where q s is the surface heat flow, q r is the reduced heat flow, d is a length scale, and a s is the surface heat production a s units: mw m -3 q s & q r units: mw m -2 In 1970, Lachenbruch showed that this linear q s -a s relation could be satitsfied with an exponentially decreasing heat production with depth

15 Sclater et al.[19080]

16 Maybe heat production decays with depth, let us assume that it follows an exponential H = H s e z / h r T,t = κt,zz + F T,t = 0 becomes Steady-state 0 = k d 2 T dz 2 + ρh s e z / h r Units: H s = [W kg -1 ] F = [H c -1 ] q s H = H s e z / h r H q = q m z z

17 Solution q s = q m + h r ρh s q s = q r + h r a s From the eastern US (crystalline rocks) q m =30 mw m -2 h r =7.5 km q m = reduced heat flow Note how h r is significantly less than the 35 km usual crustal depth Lachenbruch also showed that the exponential distribution is self-perserving on uplift and that the linear q s -a s relation is maintained [This is not the case for linear or constant distributions]

18 Potential Scenario for concentration of heat producing elements Jaupart et al. [1981]

19 The steady-state assumption Sclater et al. [1980] Thermal time-constant Myr L~(κτ) 1/2 L~ km

20 Continental geotherm consistent with q s and a s -a s (decay of with depth) Assuming: Using solution of H = H s e z / h r T,t = κt,zz + F T = T s + q mz k + ρh 2 sh r (1 e z / h r k ) T = T s + q z m k + (q q )h s m r (1 e z / h r k ) with T,t = 0 T s =10ºC q s =56.5 mw m -2 q m =30 mw m -2 h r =10 km k=3.35 W m -1 K -1

21 Geobarometry and geothermometry from Xenoliths in Kimberlite pipes Sclater et al. [1980]

22 More on geographic variability Sclater et al. [1980]

23 Smoothed Heat Flow from borehole measurements mw/m^2 SMU web site

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