Local isostatic response to an added surface layer ($w=({\rho }_b-{\rho }_f)H/({\rho }_m-{\rho }_f)$)

Let a deposited layer have thickness $H$ and density ${\rho }_b$, replacing a fluid of density ${\rho }_f$, while the original crust translates downward by $w$ above mantle of density ${\rho }_m$. Assume all deposited material stays in the same fluid environment, unchanged pre-existing layer thicknesses, an external material source, and complete local isostatic adjustment without bending resistance.

At a fixed compensation depth, added column mass is $({\rho }_b-{\rho }_f)H$ per unit area, whereas depression replaces a column contrast $({\rho }_m-{\rho }_f)w$. Equal hydrostatic pressure therefore requiresIt follows thatThe pre-existing ground subsides by $w$, while the top of the new layer rises by $\Delta z$ if ${\rho }_b<{\rho }_m$. For a subaerial deposit, air density is negligible. For a fully submerged deposit, use seawater density. A deposit that crosses the fluid surface requires separate treatment of its submerged and emerged portions. Specifying only volume $V$ leaves the answer dependent on loaded area through $H=V/A$.