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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]
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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.
