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The kinematic boundary condition is ${\zeta }_t=w$ at $z=0$. Part c therefore givesand henceIn terms of wavelength $\lambda =2\pi /k$,Without elasticity, $\tau \sim 2\mu k/(\rho g)$: shorter wavelengths penetrate less deeply but relax more slowly because their viscous gradients are larger. At short wavelength, elastic bending dominates andso the strong $B{k}^4$ restoring stress makes very short waves relax rapidly. The graph therefore tends to zero at both wavelength extremes and has one maximum. Differentiating with respect to $k$ places that maximum atThis exponential relaxation is the simplest half-space model of postglacial rebound and glacial isostatic adjustment.

Ice accumulation adds a load that produces an immediate elastic response and slower viscous displacement of the mantle away from the loaded region. The depressed interior may be accompanied by a peripheral forebulge. A long-lived load approaches an approximately compensated state. Melting removes the load, giving rapid elastic recovery followed by mantle return flow and gradual uplift. The forebulge can subside while the formerly loaded centre rises.

Postglacial rebound can continue long after the ice disappears, because mantle relaxation is slow. Raised shorelines, changing relative sea level, vertical geodetic motion and gravity changes record glacial isostatic adjustment. Present motion depends on the whole loading and melting history, mantle rheology and lithospheric stiffness, not only the current absence of ice.