\[d_c=\frac{\rho_c h}{\rho_m-\rho_c}\]
Variables
dcisostatic compensation depth (m)
rhoccrust density (kg/m³)
rhommantle density (kg/m³)
hcrustal thickness or topographic height (m)
Description
What is this formula?
This formula calculates the depth of isostatic compensation, where the mass excess of topographic features is balanced by lower-density crustal roots within the mantle.
When to use it
Use this equation in geophysics and tectonics when studying mountain roots, crustal balance, and isostatic equilibrium models.
Example
Calculate the compensation depth for a crustal block with a density of 2800 kg/m³, mantle density of 3300 kg/m³, and crustal thickness of 35 km.
Data:
rhoc = 2800 kg/m³
rhom = 3300 kg/m³
h = 35000 m
Formula:
dc = (rhoc*h)/(rhom-rhoc)
Substitution:
dc = (2800*35000)/(3300-2800)
Result:
dc = 1.96 × 10^5 m
Applications
- Mountain root estimation
- Crustal equilibrium studies
- Plate tectonics
- Geodynamic modeling
- Earth structure analysis