Isostatic Equilibrium Simulator

simulator intermediate ~10 min
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Root depth: 3.6 km — 35 km crust at 0.8 km elevation. Compensation depth: 38.6 km. Airy isostasy.

Continental crust 35 km thick with density 2700 kg/m3 at 0.8 km elevation develops a compensating root 3.6 km deep into the 3300 kg/m3 mantle.

Formula

h = T(ρ_m − ρ_c)/ρ_m − T_ref(ρ_m − ρ_c)/ρ_m (Airy elevation)
d_root = h · ρ_c / (ρ_m − ρ_c) (root depth)
ρ_Pratt = ρ_m · D / (D + h) (Pratt density)

Floating Continents

Just as an iceberg floats with most of its mass below water, Earth's crust floats on the denser underlying mantle. This principle of isostasy, recognized by Airy and Pratt in the 1850s, explains why mountains have deep roots, why removing ice sheets causes land to rise, and why the ocean floor sits several kilometers below the continents.

Airy Isostasy

In Airy's model, the crust has uniform density but varies in thickness. Mountains are supported by deep crustal roots displacing dense mantle material, much like a tall wooden block floating deeper in water. Seismic surveys confirm this: the Moho beneath the Himalayas reaches 70 km depth compared to 35 km beneath stable platforms, and 6-7 km beneath ocean basins.

Pratt Isostasy

Pratt's alternative model proposes that all crustal columns extend to the same compensation depth but differ in density. Higher topography has lower density. This model applies well to mid-ocean ridges, where thermal expansion reduces density and elevates the seafloor, and to some continental regions where lateral density variations dominate over thickness changes.

Isostatic Adjustment

When the load on the lithosphere changes — through ice sheet growth or melting, erosion, or sedimentation — the crust adjusts toward a new equilibrium. This glacial isostatic adjustment occurs over thousands of years, limited by the viscous flow rate of the mantle asthenosphere. Current uplift rates in Scandinavia and Canada, measured by GPS and tide gauges, constrain mantle viscosity to approximately 10^21 Pa·s.

FAQ

What is isostasy?

Isostasy is the gravitational equilibrium between Earth's crust and mantle, analogous to blocks of wood floating in water. Higher-standing topography is compensated by deeper crustal roots (Airy model) or lower crustal density (Pratt model). The lithosphere 'floats' on the denser asthenosphere, and any load change triggers slow adjustment toward equilibrium.

What is the difference between Airy and Pratt isostasy?

In Airy isostasy, all crustal blocks have the same density but different thicknesses — mountains have deep roots. In Pratt isostasy, all blocks extend to the same depth but have different densities — higher topography has lower density. Real Earth combines both mechanisms, with Airy dominant for continents.

What is glacial isostatic adjustment?

When ice sheets form, their weight depresses the crust. When ice melts, the land slowly rebounds toward isostatic equilibrium at rates of ~1 cm/year. Scandinavia and Hudson Bay are still rising from the last glaciation 10,000 years ago, and will continue for thousands of years until equilibrium is reached.

How is isostasy verified?

Isostasy is verified by comparing observed gravity anomalies with those predicted by topographic loading models. Well-compensated regions show small isostatic residual anomalies, while recent loads (young mountains, ice sheets) show larger residuals indicating incomplete adjustment. Seismic measurements of Moho depth confirm predicted crustal roots.

Sources

Embed

<iframe src="https://homo-deus.com/lab/geophysics/isostasy/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub