6.1 Earth's heat budget and heat flow

Heat Distribution within Earth's Interior

Earth's heat budget describes where the planet's internal thermal energy comes from and how it moves from the deep interior toward the surface. This topic matters because heat flow is the engine behind plate tectonics, volcanism, and the geodynamo that generates Earth's magnetic field. Understanding it connects nearly every other concept in geophysics.

Sources of Earth's Internal Heat

Earth's internal heat comes from two main sources: radioactive decay and primordial heat.

Radioactive decay is the dominant source, accounting for roughly 80% of the total internal heat budget. Unstable isotopes of uranium ($^{238}U$, $^{235}U$), thorium ($^{232}Th$), and potassium ($^{40}K$) undergo spontaneous nuclear breakdown, releasing energy as heat. These isotopes are concentrated in the crust and upper mantle because they are incompatible elements that preferentially partition into silicate melts during differentiation.

Primordial heat makes up the remaining ~20%. This is leftover thermal energy from:

• The accretion of planetesimals during Earth's formation
• Gravitational energy released during core-mantle differentiation
• Giant impacts (most notably the Moon-forming impact)

Primordial heat has been slowly dissipating over 4.5 billion years, but Earth is large enough that significant amounts remain stored in the deep interior.

Uneven Distribution of Heat

Heat production and temperature are distributed unevenly through Earth's layers, and it's worth keeping the distinction between the two clear.

Heat production (the rate at which new thermal energy is generated) is highest in the crust and upper mantle, where radioactive elements are most concentrated. The lower mantle and core contain far fewer radioactive isotopes, so they produce less heat per unit volume.

Temperature, on the other hand, increases with depth. Earth's core reaches an estimated 5,000–6,000°C. Those extreme temperatures reflect:

• Residual primordial heat trapped at depth
• The release of latent heat as the liquid outer core gradually crystallizes onto the solid inner core
• The insulating effect of the overlying mantle, which slows heat loss

So the crust produces more heat per kilogram, but the core is far hotter. This distinction trips people up on exams.

Heat Transfer Mechanisms in Earth

Three mechanisms move heat through the planet: conduction, convection, and radiation. Each dominates in different regions.

Conduction in the Lithosphere

Conduction is the transfer of thermal energy through direct atomic or molecular contact, with no bulk movement of material. One atom vibrates, transfers kinetic energy to its neighbor, and so on. This is the primary way heat moves through the rigid lithosphere (crust and uppermost mantle).

The rate of conductive heat transfer depends on thermal conductivity ($k$), which varies by rock type and mineral composition:

• Quartz-rich rocks (e.g., quartzite) conduct heat relatively well
• Feldspar-rich rocks conduct heat more slowly
• Olivine has higher thermal conductivity than pyroxene

Because conduction is slow compared to convection, the lithosphere acts as a thermal lid on the planet, controlling how efficiently Earth loses heat to the surface.

Convection in the Mantle

Convection is the dominant heat transfer mechanism in the mantle and is the process most directly responsible for plate tectonics. It involves the bulk movement of material driven by density differences: hotter, less dense rock rises while cooler, denser rock sinks.

How mantle convection works, step by step:

1. Heat from the core and from radioactive decay warms the lower mantle
2. The heated rock becomes less dense and rises buoyantly
3. As it approaches the upper mantle and lithosphere, it spreads laterally and loses heat
4. The cooled rock becomes denser and eventually sinks back down
5. This cycle forms large-scale convection cells spanning thousands of kilometers

These convection cells interact with the lithosphere at plate boundaries:

• Divergent boundaries (mid-ocean ridges): Rising limbs of convection push plates apart
• Convergent boundaries (subduction zones): Sinking limbs pull cold lithosphere back into the mantle

The relationship between convection and plate motion is more complex than a simple conveyor belt, but at this level, the connection between rising/sinking mantle flow and plate movement is the key takeaway.

Radiation in the Deep Interior

Radiative heat transfer involves the emission and absorption of electromagnetic energy (primarily infrared). In most of Earth's interior, radiation is a minor contributor compared to conduction and convection. However, it becomes more significant at extreme temperatures because radiative output scales with $T^4$.

• In the lower mantle, radiative transfer may contribute up to ~30% of the total heat flux
• In the outer core, radiative transfer likely plays a supporting role alongside convection, which generates Earth's magnetic field through the geodynamo

The exact contribution of radiation in the deep Earth remains an active area of research, partly because measuring the radiative properties of minerals at extreme pressures and temperatures is experimentally difficult.

Heat Flow and Tectonic Settings

Surface heat flow, measured in $\text{mW/m}^2$, varies systematically with tectonic setting. These patterns are some of the strongest evidence linking mantle convection to surface geology.

High Heat Flow: Active Tectonic Regions

Regions with active tectonics show elevated heat flow because hot mantle material sits at shallow depths.

• Mid-ocean ridges have the highest heat flow values, typically exceeding $100 \text{ mW/m}^2$. Hot asthenospheric material upwells directly beneath a very thin lithosphere. Heat flow decreases systematically with distance from the ridge axis as the new oceanic crust cools and the lithosphere thickens. This cooling pattern follows a predictable square-root-of-age relationship.
• Continental rift valleys also show elevated heat flow. The East African Rift System, for example, records values of $60\text{–}110 \text{ mW/m}^2$, well above the continental average, because the lithosphere is being stretched and thinned, allowing hot mantle to rise closer to the surface.
• Volcanic arcs above subduction zones display locally high heat flow due to magma generation in the mantle wedge.

Lower Heat Flow: Stable and Subduction Regions

• Subduction zones generally show lower heat flow on the trench side, because cold oceanic lithosphere descends into the mantle, depressing temperatures. The back-arc region behind the trench, however, can show elevated heat flow where the mantle wedge is heated by fluids released from the subducting slab.
• Cratons (old, stable continental interiors like the Canadian Shield or West African Craton) typically have heat flow below $60 \text{ mW/m}^2$. Their thick, cold lithospheric roots extend deep into the mantle, and much of the original radioactive heat production in their crust has decayed over billions of years.
• Old oceanic crust far from ridges also shows low heat flow, reflecting the progressive cooling of the lithosphere with age.

Inferring Subsurface Thermal Conditions

Measuring Heat Flow

Heat flow ($Q$) is determined from two quantities using Fourier's law of heat conduction:

$Q = k \cdot \frac{dT}{dz}$

where:

• $Q$ = heat flow ($\text{mW/m}^2$)
• $k$ = thermal conductivity of the rock ($\text{W/m·K}$)
• $\frac{dT}{dz}$ = geothermal gradient, the rate of temperature increase with depth ($\text{°C/km}$)

To measure heat flow in practice:

1. Drill a borehole (on land) or deploy a marine heat flow probe (on the seafloor)
2. Measure the temperature at multiple depths to determine the geothermal gradient
3. Collect rock or sediment samples and measure their thermal conductivity in the lab
4. Multiply the gradient by the conductivity to get heat flow

The global average surface heat flow is approximately $87 \text{ mW/m}^2$, but values range from below $40 \text{ mW/m}^2$ in old cratons to over $200 \text{ mW/m}^2$ at mid-ocean ridges.

Interpreting Heat Flow Patterns

Heat flow values tell you about what's happening beneath the surface:

• High values indicate thin lithosphere and/or hot material at shallow depth. Think magma chambers, young oceanic crust, hydrothermal systems, and active volcanic regions.
• Low values indicate thick, cold lithosphere. Think old continental shields and aged oceanic plates.
• Localized anomalies can reveal buried features. A patch of unusually high heat flow in an otherwise stable continental region might indicate a shallow intrusion, an active geothermal system, or elevated crustal radioactivity.

Integrating Heat Flow with Other Geophysical Data

Heat flow measurements become much more powerful when combined with other geophysical observations:

• Seismic data: Seismic wave velocities decrease in hotter, partially molten rock. Combining seismic tomography with heat flow data helps map thermal structure at depth.
• Gravity data: Density variations caused by temperature differences produce gravity anomalies. A region with high heat flow and a negative gravity anomaly likely has hot, low-density material at depth.
• Together, these datasets allow construction of 3D thermal models of the lithosphere and upper mantle, which are essential for understanding mantle dynamics, assessing geothermal energy potential, and interpreting tectonic processes.