Isostatic ridge elevation in a plate model ($h={\rho }_m\alpha \Delta Ta/[2({\rho }_m-{\rho }_w)]$)

A cold linear plate profile has excess column mass ${\rho }_m\alpha \Delta Ta/2$ relative to hot mantle. Equal hydrostatic pressure below the plates is restored by replacing part of the rock column with water. The displayed elevation follows to first order in thermal expansion; its denominator is the rock-minus-water density difference, not the rock density alone.