3. Continental Heat Flow

Ge 163 4/3/15

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

Fourier’s Law

�

q = −kT,xq = heat flux

(units: W m-2 k = thermal conductivity

(units: W m-1 K-1 T temperature x spatial coordinate

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

Smoothed Heat Flow from borehole measurements

SMU web site 25 65 100 mW/m^2

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= 2500 - 542 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, 269-311, 1980.

Position of heat flow measurements of Sclater et al. [1980] on ages of continental crust. 1. >1700 Ma; 2. 1700-800 Ma; 3. 800-250 Ma; 4. < 250 Ma

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

1. >1700 Ma; 2. 1700-800 Ma; 3. 800-250 Ma; 4. < 250 Ma

Sclater et al. [1980]

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 42-50 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

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

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 10-11 to 1.8 x 10-10 W kg-1

This compares to ~9.6 x 10-10 W kg-1 for granite

Birch, Roy & Decker [1968] showed (empirically) that

�

qs = qr + das

Where qs is the surface heat flow, qr is the ‘reduced’ heat flow, d is a length scale, and as is the surface heat production as units: mW m-3 qs & qr units: mW m-2

In 1970, Lachenbruch showed that this linear qs-as relation could be satitsfied with an exponentially decreasing heat production with depth

Sclater et al.[19080]

Maybe heat production decays with depth, let us assume that it follows an exponential

�

T,t = κT,zz + FT,t = 0�

H = Hse−z / hr

Units: Hs= [W kg-1] F = [H c-1]

Steady-state

becomes

�

0 = k d2Tdz2

+ ρHse−z / hr

qs

z �

H = Hse−z / hr

H

�

q = −qm

z→∞

Solution

�

qs = qm + hrρHs

qs = qr + hrasFrom the eastern US (crystalline rocks) qm=30 mW m-2 hr=7.5 km

qm = reduced heat flow Note how hr 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 qs-as relation is maintained [This is not the case for linear or constant distributions]

Potential Scenario for concentration of heat producing elements

Jaupart et al. [1981]

The steady-state assumption

Sclater et al. [1980]

Thermal time-constant 200-300 Myr L~(κτ)1/2 L~80-100 km

Continental geotherm consistent with qs and as-as (decay of with depth)

Assuming:

�

T,t = κT,zz + F

�

H = Hse−z / hr

�

T,t = 0Using solution of with

�

T = Ts + qmzk

+ ρHshr2

k(1− e−z / hr )

T = Ts + qmzk

+ (qs − qm )hrk

(1− e−z / hr )

Ts=10ºC qs=56.5 mW m-2 qm=30 mW m-2 hr=10 km k=3.35 W m-1 K-1

Sclater et al. [1980]

Geobarometry and geothermometry from Xenoliths in Kimberlite pipes

More on geographic variability

Sclater et al. [1980]

Smoothed Heat Flow from borehole measurements

SMU web site 25 65 100 mW/m^2