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) Isostasy (same overburden at base) leads to net horizontal force P  h/2 22  h h/2 P F rhs = Ph/4 F lhs = P 2 Ph

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/m 3 (2.8Mg/m 3 ) Pressure at base of continents (compensation depth) is 2800 kg/m 3 x 10 m/s 2 x 40,000m = 1.1GPa (1.1GN/m 2 ) 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  ~10 11 Pa (100GPa)  ~10 21 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

Modern ice sheets (Antarctica)

Modern ice sheets (Greenland)

Pleistocene ice sheets (North)

Evidence for Pleistocene ice sheets (N.A.)

Pleistocene lakes (western US)

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)

Gotland

Finnland (1)

Sweden (1)

Sweden (2)

Isostasy - PGR Nansen, quantified the uplift rates of beachfronts in Gotland (100 m in years) Daly, suggested that postglacial rebound was the cause of this Haskell, 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.

Angermann Uplift

Ice vs. Time

Sealevel Rise

Daly

Postglacial Rebound (uplift rates) Shoreline of Lake Bonneville

Postglacial Rebound Shoreline of Lake Bonneville

Why we know Earth can be viscous (postglacial rebound)

postglacial rebound (cont.) w d Velocity Gradient: W/d Stress: Upward ‘buoyancy’:

Horizontal Velocity Component (at kx=Pi/2) Depth Vertical Velocity Component (at kx=0) Depth kz Flow Solutions

Flow due to sinusoidal loading (view 1) 50% 80% 90% kz kx

Flow due to sinusoidal loading (view 2) 50% 80% 90% kx kz

Depth Vertical Velocity Component (at kx=0) Depth kz Depth of Flow Flow Depth Depends on wavelength of load (k = 2  / ): 50% of flow above kz = 1.68, i.e. z < % of flow above kz = 3, i.e. z < 0.48

What happens to hot rising blobs in mantle convection? Once formed, what removes an asthenosphere layer? plate accretion&subduction Slab dragdown asthenosphere

asthenosphere flow & entrainment

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) Isostasy (same overburden at base) leads to net horizontal force P  h/2 22  h h/2 P F rhs = Ph/4 F lhs = P 2 Ph

Dynamic Isostasy — Compensation of Pressure effects of lateral flow hh dd PP aa ww mm

Good depth vs. age fit of seafloor relief means that dynamic topography must have a relatively small effect on seafloor depth All oceans depth vs. age Ravine et al., in prep. (J. Sclater & coworkers, 1980s)

Effects of buoyant asthenosphere

Lab Models

Numerical/Lab Comparison