The average heat flux at the Earth’s surface provides important information on the amount of heat being produced in the Earth and the temperature distribution in its interior. In the 1800s it was recognized that the temperature in caves and mines increases with depth. Typical values for this increase are dT/dy = 20 to 30 K km−1. Since the thermal conductivities of near-surface rocks are usually in the range 2 to 3 W m−1 K−1, the heat flow to the surface of the Earth implied by these temperature gradients is, according to Equation (4–1), 40 to 90 mW m−2. It is standard practice to take the upward surface heat flow to be a positive quantity, even though from Equation (4–1), with y measured positive downward, it has a negative value.
Although temperature measurements in caves and mines give approximate values for the near-surface thermal gradient, accurate measurements of the thermal gradient in continental areas require deep drill holes. Deep measurements are necessary because climatic variations in the Earth’s surface temperature, particularly those due to ice ages, influence the temperatures in the near-surface rocks. These effects are considered quantitatively in Section 4–14. In order to reach the steady-state thermal structure, holes must be drilled deeper than about 300 m.
The thermal gradient is measured by lowering a thermistor (an accurate electronic thermometer) down the drill hole. Care must be exercised to prevent the circulation of drilling fluid during drilling from affecting the measured gradient. This can be done in either of two ways. Measurements can be made at the bottom of the drill hole during drilling. The drilling fluid does not have time to change the temperature at the bottom of the hole. Alternatively, the temperature log of the hole (the measurement of the temperature as a function of depth) can be carried out some time after drilling has ceased. It usually takes 1 to 2 years for a drill hole to equilibrate to the ambient geothermal gradient. Drill holes are invariably filled with groundwater. It is the temperature of this water that is measured by the thermistor. As long as the water is not flowing, its temperature equilibrates with that of the surrounding rock. However, many drill holes cross aquifers (underground channels of porous rock in which water flows), with the result that water will flow up or down the drill hole if it is not lined and will affect the temperature distribution. From Fourier’s law it is clear that the determination of the heat flux requires a measurement of both the temperature gradient and the thermal conductivity of the rock. The thermal conductivity of rocks can be deter4.3 Measuring the Earth’s Surface Heat Flux 241
Laboratory device for measuring the thermal conductivity of a rock sample mined in the laboratory by subjecting samples cut from drill holes to known heat fluxes and measuring the temperature drops across them. Figure 4–3 is a schematic of one way in which this can be done.
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