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Explore the principles of pressure, isostasy, and horizontal forces in Earth science, including implications for rock deformation, mantle viscosity, and postglacial rebound. Learn about key evidence and mechanisms supporting these concepts.
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nonsequitur Science searches for the true by tying to eliminate the untrue. “It is a process of separating the demonstrably false from the probably true.” [Lynton Caldwell] Authentic science operates on the assumption that a concept can be shown to be false. Falsification occurs when a concept either is shown to be logically inconsistent or is demonstrated to run counter to direct observations.
Pressure, Isostasy, and Horizontal Forces • Each column isostatic equilibrium has the same weight of overburden at its base (equal pressure) • If the mean densities and heights of each column are different, there will be a net horizontal force on the material (isostasy only reflects a vertical force balance) h Isostasy (same overburden at base) leads to net horizontal force Ph/2 h/2 Ph Flhs = Frhs = Ph/4 2 2 P P
How big? • Continental crust is ~40km thick • Continental shelves and their adjacent oceanic abyssal plains differ in elevation by ~5-6km (5000m) • Mean density of continental crust is 2800 kg/m3 (2.8Mg/m3) • Pressure at base of continents (compensation depth) is 2800 kg/m3 x 10 m/s2 x 40,000m = 1.1GPa (1.1GN/m2) • Net horizontal force F =1.1GPa x 5000m / 2 = 2.75TN • Net horizontal stress associated with isostasy = F/40000m = 0.07GPa i.e. = ~2,500/40,000 (1/16) of the pressure at the depth of compensation • Implication: Lithosphere can elastically support stresses at least of order 70 MPa (atmospheric pressure = 0.1 MPa, 700 times less). In other words, crustal rocks do not typically creep under differential stresses of order 700 atmospheres (and may be even stronger)
Earth’s Rheology: Visco-elastic • Rock becomes viscous at depth (below lithosphere) • Rock is elastic/brittle when cold (lithosphere) Analogy to rock deformation: Bragg’s bubble model Elastic Viscous ~1011 Pa (100GPa) ~1021 Pa-s (1ZPa-s)
Earth’s Rheology: Visco-elastic Analogy to rock deformation: Bragg’s bubble model Elastic Viscous
Main mechanisms for creep: Movement of imperfections in crystal lattice (dislocations & vacancies)
How do we know Earth’s mantle is viscous? • Isostasy exists (implies underlying mantle must flow to balance changes in crustal thickness/load) — but no direct inference for how viscous • Post-glacial rebound (Areas covered by icesheets ~12,000 years ago are still rising ~m/100yr. Also see rebound from removal of large lakes and mountain glaciers) • Uniform plate motions measured by GPS (no ‘jerks’ in motion of plate interiors, implies ‘fluid’ movement with underlying mantle) • At ~1200°C+ temperatures, rocks exhibit viscous creep (flow) in laboratory experiments
Evidence for Pleistocene lakes (western US) Shoreline of Lake Bonneville
Postglacial Rebound Shoreline of Lake Bonneville
PGR • Finland and Sweden are rising today • Holmström, 1869, pointed out that Sweden is rising with respect to the Baltic (comparison of historic water levels in harbors). In the 1800s it was noticed that • Lakes and Canels in Finland rose (and rose faster near the W. Coast than inland). • Raised beaches were also remarked upon (e.g. Gotland)
Isostasy - PGR • Nansen, 1928 - quantified the uplift rates of beachfronts in Gotland (100 m in 10.000 years) • Daly, 1934 - suggested that postglacial rebound was the cause of this • Haskell, 1937 - quantified the uplift over an infinite halfspace mantle Van Bemmelen & Berlage (1935) (Vening-Munesz, 1937)used uplift history to suggest a weak asthenosphere layer above a more viscous lower mantle • 300m of uplift have already occurred in Fennoscandia, ~20m remains to be uplifted to reach isostatic equilibrium.
Postglacial Rebound (uplift rates) Shoreline of Lake Bonneville
Postglacial Rebound Shoreline of Lake Bonneville
postglacial rebound (cont.) w d Velocity Gradient: W/d Stress: Upward ‘buoyancy’:
Horizontal Velocity Component (at kx=Pi/2) Flow Solutions Depth kz Depth Vertical Velocity Component (at kx=0) Depth kz
Flow due to sinusoidal loading (view 1) 50% kz 80% 90% kx
Flow due to sinusoidal loading (view 2) 50% kz 80% 90% kx
Depth of Flow Flow Depth Depends on wavelength of load (k = 2/): 50% of flow above kz = 1.68, i.e. z < 0.27 80% of flow above kz = 3, i.e. z < 0.48 Depth kz Depth Vertical Velocity Component (at kx=0) Depth kz
What happens to hot rising blobs in mantle convection? asthenosphere Once formed, what removes an asthenosphere layer? • plate accretion&subduction • Slab dragdown
Pressure, Isostasy, and Horizontal Forces • Each column isostatic equilibrium has the same weight of overburden at its base (equal pressure) • If the mean densities and heights of each column are different, there will be a net horizontal force on the material (isostasy only reflects a vertical force balance) h Isostasy (same overburden at base) leads to net horizontal force Ph/2 h/2 Ph Flhs = Frhs = Ph/4 2 2 P P
Dynamic Isostasy — Compensation of Pressure effects of lateral flow w h P a m d
Good depth vs. age fit of seafloor relief means that dynamic topography must have a relatively small effect on seafloor depth (J. Sclater & coworkers, 1980s) All oceans depth vs. age Ravine et al., in prep.
