An ice sheet loads the crust like a weight on a floating elastic plate. The lithosphere (elastic thickness Te) bends over the ductile mantle (density ρm), obeying the axisymmetric thin-plate flexure equation:
D·∇⁴w + ρ_m·g·w = q(r)
D = E·Te³ / [12(1-ν²)] (flexural rigidity)
∇²w = w″ + w′/r (axisymmetric Laplacian)
This simulator solves that 4th-order equation numerically on a radial grid (finite differences, ∇⁴ = ∇²∘∇²) for the ice load q(r). The solution isn't a simple bowl: a stiff plate under a central load bends down at the center, flexes back up in a ring beyond the load edge — the forebulge — before settling to zero far away. This is the same mechanism that produces the mid-continent forebulge collapse seen around the former Laurentide and Fennoscandian ice sheets.
The mantle doesn't respond instantly — it flows like a very viscous fluid, so the crust relaxes toward the unloaded (flat) state exponentially once the ice is gone:
w(r,t) = w₀(r) · e^(−t/τ)
where w₀(r) is the glacial-equilibrium deflection and τ is a single effective relaxation time standing in for mantle viscosity (real Earth: τ ≈ 4,000–6,000 yr for Fennoscandia, longer for higher-viscosity mantle). This one-mode approximation is a simplification of full viscoelastic Earth models (which sum many decay modes), but it reproduces the essential observed behavior: the deep basin fills in and the forebulge collapses together, on the timescale that raised the Baltic and Hudson Bay coastlines by hundreds of meters over the last ~10,000 years.
- Ice thickness / radius — set the load magnitude q₀ = ρice·g·H and its footprint.
- Elastic thickness Te — a stiffer plate (larger Te) spreads the depression wider and pushes the forebulge farther out.
- Relaxation time τ — how fast the mantle flows; shorter τ means faster post-glacial rebound.
- Deglaciate Now — removes the load and starts the exponential relaxation clock.