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.

TJs & Internal Plate Deformation (1) Plate Tectonics basic simplifying assumption that plates are perfectly rigid. However real plates do sometimes have internal plate deformation (e.g. Juan de Fuca) (2) Triple Junctions (TJs) are places where 3 plates meet. Their kinematic and geometric evolution can be predicted from plate tectonics principles as long as the 3 plates maintain constant velocities.

Juan de Fuca & TJs

Mantle Plumes & Hotspots Intraplate volcanism on oceanic plates often forms a pattern of linear chains of islands/seamounts The conventional picture for the formation of these changes is that they reflect the melting of mantle that is locally upwelling beneath the focus of volcanism in a mantle plume This hypothesis offers, in particular, a simple explanation for why the chains on different plates can all be viewed as being created by plates that move over multiple nearly stationary mantle plumes – upwelling plumes that are nearly stationary with respect to each other…. forming a ‘hotspot’ reference frame with respect to which absolute plate motions are inferred

Seamoount Trails

Hotspot Tracks

Conceptual model for hotspot volcanism

On Pressure Pressure is a force/area [a stress] Pressure is a tensor. (the force depends on the direction of the surface. However the magnitude of the force is independent of direction. P (tensor) Normal vector Force

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 2h h P F rhs = Ph/2 F lhs = Ph P

How big? Continental crust is ~40km thick Continental shelves and their adjacent oceanic abyssal plains differ in elevation by ~5-6km (say 5000m for this estimate) 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 (height difference) = 5.5TN Net horizontal stress associated with isostasy  = F/40000m = 0.14GPa i.e. = ~5,000/40,000 (1/8) of the pressure at the depth of compensation Implication: Lithosphere can elastically support stresses at least of order 0.14GPa (atmospheric pressure = 0.1 MPa, 1400 times less). In other words, crustal rocks do not typically creep under differential stresses of order 1400 atmospheres

Review for Prelim 1 Prelim will be roughly 2/3 non-quantitative questions and 1/3 quantitative ones Questions can cover all material to date— but there will be no mathematical derivations (e.g. ‘show this math expression to be true’) Will be closed book exam, but you will be given a sheet with all formulas that you would need to use — and many more useless ones so you will need to recognize what expression is used for what Study suggestions: – Review notes & problem sets (quantitative problems will be based on notes & problems) – Review handouts: e.g. Einstein handout on origin of meanders – Review the ‘review questions’ at the end of each chapter in the Marshak assigned reading (some non-quantitative questions will be taken from these questions)

Review for Prelim 2 – Material Covered What is a mineral? What are diagnostic differences between igneous, sedimentary, & metamorphic rocks, and how are they formed? What is origin of global atmosphere & ocean circulation patterns? El Nino? Monsoon seasons? What is global distribution of water? What is the meaning of residence time? Darcy’s Law — what is it? What do various terms in this relation mean? Groundwater flow & relation to water table, Aquifers, Artesian Basins & basin-scale groundwater flow… There will be a quantitative question or two on some aspect of Darcy’s Law & groundwater flow

Review for Prelim 3 – Material Covered What is the origin of stream meanders? — read the little handout on Einstein’s explanation for the formation of stream meanders Seafloor spreading, origin of seafloor magnetic anomalies, Wilson cycle Plate tectonics, Transform fault, fracture zones, ridges, trenches, subduction zones, relative and absolute plate motions Mid-ocean ridge volcanism, arc volcanism, hotspot volcanism Seafloor depth vs. age, thermal model of plate cooling with seafloor age, volume & density changes associated with cooling… (quantitative) Isostasy, implications for depth vs. age, difference between ocean & continent heights… (quantitative)

Stress - Generalization of Force to a Volume Normal stress (force/area perpendicular to a surface -- like pressure) Shear stress (force/area parallel to a surface) x z  xx  xz or  xz Direction of force Direction of normal vector to surface

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

Why we know Earth can be viscous (postglacial rebound)

Main mechanisms for creep: Movement of imperfections in crystal lattice (dislocations & vacancies)