Questions: Heat Flow Measurement and Geothermal Gradient

Question 1

Borehole A passes through granite (thermal conductivity κ = 3.0 W/m·K) and shows a temperature gradient of 30°C/km. Borehole B passes through shale (κ = 1.5 W/m·K) and also shows a gradient of 30°C/km. What can you conclude about the surface heat flow at each location?

• A. Both locations have identical heat flow because they have the same temperature gradient
• B. Location A has twice the heat flow of location B because its rock conducts heat more efficiently at the same gradient
• C. Location B has higher heat flow because shale is a better insulator and retains more geothermal energy
• D. You cannot determine relative heat flow without knowing the absolute temperatures at each borehole

Answer: (B)

Heat flow is q = κ × dT/dz. With the same gradient (dT/dz = 30°C/km = 0.03°C/m), heat flow is simply proportional to thermal conductivity. Location A: q = 3.0 × 0.03 = 0.090 W/m². Location B: q = 1.5 × 0.03 = 0.045 W/m². Location A has exactly twice the heat flow. This is the key insight: the temperature gradient alone is not heat flow — you must multiply by conductivity. A steep gradient in low-conductivity rock can yield lower heat flow than a shallow gradient in high-conductivity rock.

Question 2

What two independent measurements must be combined to calculate surface heat flow at a borehole site?

• A. Surface temperature and depth of the borehole
• B. Temperature at the surface and temperature at the bottom of the borehole
• C. The temperature gradient (dT/dz) from the borehole temperature profile and the thermal conductivity (κ) from laboratory analysis of core samples
• D. Crustal thickness and the mantle temperature below the lithosphere

Answer: (C)

Heat flow q = κ × dT/dz requires both components. The temperature gradient is obtained by lowering a temperature probe through the borehole and fitting a slope to the linear portion of the temperature-depth profile. Thermal conductivity is measured separately on rock cores in the laboratory (using a divided-bar apparatus or needle probe). Neither measurement alone gives heat flow — a steep gradient in insulating rock may carry the same heat flux as a gentle gradient in conducting rock.

Question 3

The temperature gradient measured in the upper 10–20 meters of a borehole reliably reflects the steady-state geothermal heat flow from Earth's interior.

• T. True
• F. False

Answer: False

False. The shallow subsurface is contaminated by surface temperature fluctuations — seasonal cycles, multi-decadal climate variability, and even the annual temperature wave — which penetrate tens of meters into the crust. These signals superimpose a non-geothermal component on the temperature profile, making shallow gradients unreliable indicators of deep heat flow. Geothermal measurements use deeper portions of the borehole, where surface temperature signals have attenuated and the profile reflects only the steady conduction of internal heat.

Question 4

Mid-ocean ridges generally have higher surface heat flow than stable continental cratons because hot asthenospheric material rises close to the surface at ridges.

• T. True
• F. False

Answer: True

True. At mid-ocean ridges, upwelling mantle material reaches within a few kilometers of the seafloor, driving heat flow well above 150 mW/m² (though much is carried by hydrothermal circulation rather than pure conduction). Stable cratons like the Canadian Shield have thick, cold lithospheric roots that insulate the surface from deep heat, giving values of only 30–50 mW/m². This dramatic range reflects the fundamental difference in lithospheric thermal structure between tectonically active and ancient stable regions.

Question 5

Explain why two boreholes with identical temperature gradients can have very different surface heat flow values, and what additional measurement is required to resolve the difference.

Model answer: The temperature gradient (dT/dz) is only one factor in the heat flow equation q = κ × dT/dz. The other factor is thermal conductivity (κ), which varies substantially among rock types — granite has much higher conductivity than shale or mudstone. Two sites with the same gradient but different rock types will have different heat flows. To resolve the difference, rock cores from each borehole must be analyzed in the laboratory to measure thermal conductivity. Heat flow is then computed as the product of the measured gradient and the measured conductivity.

This is the central practical challenge of heat flow measurement and why it requires both a borehole temperature survey and a separate petrophysical measurement. High-conductivity rocks like quartzite transmit heat efficiently even at low gradients; low-conductivity rocks like organic shale retain more heat and steepen the gradient at the same flux. Geothermal surveys that neglect conductivity variation systematically misinterpret temperature gradients as heat flow.