Pressure, Temperature, and Density Variations in the Earth

The Earth’s internal structure is defined by systematic variations in pressure, temperature, and density. These parameters not only describe the physical conditions at different depths but also control processes such as mantle convection, volcanism, plate tectonics, and the geodynamo. A key concept in understanding Earth’s thermal structure is the geothermal gradient, which explains how temperature changes with depth.

Temperature Variations

1. Geothermal Gradient
   • Defined as the rate of increase of temperature with depth in Earth’s crust.
   • Average continental gradient: 25–30 °C/km.
   • Oceanic crust gradient: higher (~50–100 °C/km) near ridges, but decreases with age.
   • Influenced by heat flow, rock conductivity, and tectonic setting.
2. Heat Sources Inside Earth
   • Primordial Heat — leftover from Earth’s accretion and differentiation.
   • Radiogenic Heat — decay of isotopes (U, Th, K) in crust and mantle.
   • Core Heat Flow — thermal exchange at core–mantle boundary.
3. Adiabatic Gradient
   • Deeper in mantle and core, heat transfer is dominated by convection.
   • The adiabatic gradient (~0.3 °C/km) describes temperature increase without heat loss, much smaller than the surface geothermal gradient.
4. Approximate Temperature Estimates
   • Crust–mantle boundary (Moho): ~1000 °C
   • Upper Mantle: 1200–1500 °C
   • Lower Mantle: ~2500–3000 °C
   • Outer Core: ~4000–5000 °C
   • Inner Core: ~5200–6000 °C

Pressure Variations

• Surface Pressure: At sea level, pressure is ~0.1 MPa (1 bar).
• Increase with Depth: Pressure rises nearly linearly with depth due to overlying rock load.
  • P=ρgh, where ρ = density of overlying material, g = gravity, h = depth.
• Examples:
  • Base of continental crust (~35 km): ~1 GPa
  • 670 km depth (mantle transition zone): ~24 GPa
  • Core-Mantle Boundary (CMB): ~135 GPa
  • Inner Core Center: ~360 GPa

Density Variations

• Crust: 2.7–3.0 g/cm³ (granite and basalt dominated).
• Mantle: 3.3–5.6 g/cm³ (olivine, pyroxene, garnet, high-pressure phases).
• Outer Core: 9.9–12.2 g/cm³ (liquid Fe-Ni alloy).
• Inner Core: 12.6–13.0 g/cm³ (solid Fe-Ni, compressed by high pressure).

Mineral Phase Changes: Density increases are also caused by mineral transformations, e.g.,

• Olivine → Wadsleyite (~410 km)
• Wadsleyite → Ringwoodite (~520 km)
• Ringwoodite → Bridgmanite + Ferropericlase (~660 km)

These transitions correspond to seismic discontinuities.

Interrelations

• Pressure vs. Temperature: Despite high temperatures, extreme pressure in the inner core keeps iron solid.
• Temperature vs. Density: Heat causes buoyancy contrasts, driving mantle convection.
• Geothermal vs. Adiabatic Gradient: Explains the difference between conduction-dominated crust and convection-dominated mantle.
• Impact on Seismic Waves: Density and elastic moduli variations influence seismic velocities, allowing mapping of Earth’s interior.