Category: Deep Time & Stratigraphy
At the Last Glacial Maximum (LGM, approximately 21,000 years ago), colossal continental ice sheets—the Laurentide in North America and the Fennoscandian in northern Europe—covered millions of square kilometers, reaching thicknesses exceeding three to four kilometers. The colossal mass of this ice flexed the underlying elastic lithosphere downward by hundreds of meters, displacing viscous mantle asthenosphere outward. Following rapid deglaciation, the solid Earth began an ongoing, time-dependent viscoelastic recovery: Glacial Isostatic Adjustment (GIA). Analyzing this rebound provides our premier empirical method for measuring mantle viscosity.
1. The Physics of Glacial Isostatic Adjustment (GIA)
Archimedes’ principle dictates that an elastic plate floating on a fluid substrate depresses until the displaced fluid mass matches the applied load. The vertical deflection w of an elastic lithosphere of flexural rigidity D under an ice load σ_ice is governed by the biharmonic plate equation:
D ∇⁴w + (ρ_mantle − ρ_water) g w = σ_ice
Because the ice load was applied over tens of thousands of years, the mantle beneath relaxed viscously, flowing outward to form an elevated peripheral bulge (forebulge) around the margins of the ice sheets.
Deglaciation and Viscous Inflow
Between 19,000 and 8,000 years ago, rapid warming melted the continental ice sheets, transferring over 50 million cubic kilometers of water into the global ocean. Relieved of its load, the depressed crust began rebounding vertically, while the displaced mantle asthenosphere flowed back toward the center of the depression.
2. Maxwell Viscoelastic Relaxation and Mantle Viscosity Inversion
The rate of rebound is dictated by the viscoelastic properties of the mantle. In a Maxwell viscoelastic body, the total strain rate is the sum of instantaneous elastic strain and time-dependent viscous flow:
dε / dt = (1 / μ) · (dσ / dt) + σ / η
The characteristic Maxwell relaxation time τ_M represents the timescale required for viscous flow to relieve elastic shear stress:
τ_M = η_mantle / μ_elastic
Measuring Mantle Viscosity
By measuring raised post-glacial shorelines, radiocarbon-dated sea-level curves, and continuous geodetic GPS vertical velocities, geophysicists determine the relaxation time τ_M (~4,000–8,000 years). Inverting these rebound curves provides the definitive calibration of Earth’s internal viscosity profile:
- Upper Mantle (Asthenosphere): Viscosity η ≈ 3–5 × 10²⁰ Pa·s.
- Lower Mantle (Below 660 km): Viscosity η ≈ 1–3 × 10²² Pa·s (a factor of 30 to 100 stiffer than the upper mantle).
3. Peripheral Forebulge Collapse and Sea-Level Fingerprints
While the central glaciated domes (e.g., Hudson Bay in Canada and the Gulf of Bothnia in Sweden) are rebounding upward at rates exceeding 10 to 12 mm/year, their peripheral forebulges are collapsing downward.
Subsidence along the US Mid-Atlantic Coast
Regions positioned on the collapsing peripheral bulge of the ancient Laurentide ice sheet—such as the Chesapeake Bay and New York/New Jersey coastlines—are experiencing natural land subsidence of 1 to 2 mm/year. When combined with modern climate-driven sea-level rise, this GIA subsidence significantly accelerates coastal flood risk.
The Planetary Scale Metric
Peak Rebound Velocity: Gulf of Bothnia v > 10 mm/year | Upper Mantle Viscosity: η ≈ 4 × 10²⁰ Pa·s | Remaining Rebound in Hudson Bay: ~ 100–150 meters
| Rebound Region | LGM Ice Thickness | Modern Vertical Motion | GIA Kinematic Domain |
|---|---|---|---|
| Gulf of Bothnia (Sweden/Finland) | ~ 2.5–3.0 km | +9.0 to +11.0 mm / yr | Core uplift zone (Fennoscandian) |
| Hudson Bay (Canada) | ~ 3.5–4.0 km | +10.0 to +13.0 mm / yr | Core uplift zone (Laurentide) |
| Chesapeake Bay / Mid-Atlantic (USA) | 0 km (Ice-free) | -1.0 to -2.0 mm / yr | Collapsing peripheral forebulge |
| Southern North Sea / Netherlands | 0 km (Ice-free) | -0.5 to -1.5 mm / yr | Collapsing peripheral forebulge |
4. Key Takeaways and Geophysical Summary
- Viscoelastic Recovery: Melting of 3-km-thick ice sheets triggers time-dependent mantle fluid relaxation governed by Maxwell rheology.
- Mantle Viscosity Constraint: Post-glacial rebound rates calibrate upper mantle viscosity at ~4 × 10²⁰ Pa·s and lower mantle viscosity at ~10²² Pa·s.
- Forebulge Subsidence: Regions surrounding ancient ice margins (e.g., US East Coast, Netherlands) are actively subsiding as the peripheral bulge drains back toward the center.
- Ongoing Adjustment: Hudson Bay and Scandinavia have over 100 meters of vertical rebound remaining, which will take another 10,000 years to reach complete equilibrium.
