Metamorphism is change without melting: rock buried deep enough is heated and squeezed until its minerals rebuild themselves. To understand it we need numbers for how hot and how squeezed rock gets with depth. Temperature comes from the geothermal gradient; pressure comes from the weight of the rock above, the same idea as water pressure in a pool, using a formula we can rearrange.
Why it works
Picture a column of rock 1 m² across and $h$ meters tall. Its mass is $\rho \times h$ (density times volume), its weight is $\rho g h$, and that weight spreads over 1 m², so the pressure at the bottom is $P = \rho g h$. For crust of $2,700\,\text{kg/m}^3$: $2,700 \times 9.8 \times 1,000 \approx 26,000,000\,\text{Pa}$ per kilometer, about 26 MPa per km. Geologists also use kilobars: $1\,\text{kbar} = 100\,\text{MPa}$, so the pressure grows about 1 kbar every 3.8 km.
- Confining pressure comes from the rock above and pushes equally from all sides. It squeezes rock smaller and denser but has no direction.
- Differential (directed) stress pushes harder one way than another, as when plates collide. It flattens grains and makes platy minerals such as mica grow at right angles to the push, lining them up into foliation.
Key idea
Pressure from overlying rock is $P = \rho g h$, about 26 MPa per kilometer in the crust; temperature rises along the geotherm. Equal pressure only compresses rock; foliation needs stronger squeezing in one direction.
Worked examples
Worked example: Pressure at 10 km
Rock averages $2,700\,\text{kg/m}^3$. What is the pressure 10 km down?
- $P = 2,700 \times 9.8 \times 10,000 = 2.65 \times 10^{8}\,\text{Pa}$.
- That is 265 MPa, or 2.65 kbar: about 2,600 times the air pressure at sea level.
Answer: About $265\,\text{MPa}$.
Worked example: How deep was this schist?
Minerals in a schist show it formed at 6 kbar. The rock above averaged $2,800\,\text{kg/m}^3$. How deep was it?
- $6\,\text{kbar} = 600\,\text{MPa} = 6 \times 10^{8}\,\text{Pa}$.
- $h = \dfrac{P}{\rho g} = \dfrac{6 \times 10^{8}}{2,800 \times 9.8} \approx 21,900\,\text{m}$.
- About 22 km. The schist now at the surface was once buried that deep, under mountains long since worn away.
Answer: About $22\,\text{km}$.
Common mistake
Many people think pressure alone lines minerals up into layers. Pressure that is equal on all sides, like water pressure on a diver, shrinks a rock but has no direction to line anything up along. Foliation needs directed stress, which is why foliated rocks mark old mountain belts where plates collided. Check: a deep pluton that cooled under huge but even pressure, like most granite, has no foliation.