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Transcript
Topography of the earth’s surface Depth to the Moho under north america and environs Seismic structure of Greenland margin, and a related interpretive cartoon. Topography in continental mountain chains and plateaus Seismic structure beneath Himalayas First-order topography of the ocean floor Seismic velocity at 100 km depth Fast (blue) = stiff and dense ~ cold Slow (red) = soft and low-density ~ warm Seismic structure near a mid ocean ridge Fast (blue) = stiff and dense ~ cold Slow (red) = soft and low-density ~ warm Moho is hiding here at ~6 km Topography near ocean island chains Seismic structure of the deep mantle near hawaii • High topography = thick crust or warm mantle, and visa versa • Often crust is thick and mantle cold, and topography is still fairly high; Thus crustal thickness effect ‘trumps’ mantle temperature effect These observations reflect the role of isostacy in controlling topography [chalk board notes on isostacy and orographic cycle] WM Davis and the Geographic Cycle Incision Erosion Isostatic ‘event’ increases elevation (‘Uplift’) Mature Heat flow at the earth’s surface Temperature gradients near the earth’s surface Measurements from a geothermal area in Iceland The archetype for the outer 300 km of the Earth dT/dz ~ 1˚/40 meters, on average, near Earth’s surface [chalk board notes on heat production and conduction] Note that conduction also leads to a change in rheology between interior and outer shell What are the dynamics of the hot, viscous (fluid like) interior? Rayleigh number = Buoyancy Viscous drag acceleration Momentum diffusivity X Thermal diffusivity Thermal expansion Temperature contrast Length scale Kinematic viscosity Thermal diffusivity If > ~1000, convection ensues. The mantle is ~106 A numerical model of whole-mantle convection in a 2-D earth Lord Kelvin’s measurement of the age of the earth Take 1: a proof was presented in his Ph.D. thesis, but he burned his writings on this work after his thesis defense. It has never been recovered or reproduced. Lord Kelvin’s measurement of the age of the earth Take 2: directly determine age of the Earth by inverting the conductive temperature profile observed in its outer few km of crust Melting point of rock 1500 t2 t1 t0 T (˚C) ‘pinned’ by radiative balance of surface 0 Radial distance Jheat = k(dT/dx) dT/dt = k d2T/dx2 k = thermal diffusivity ~ 5x10-3 cm2/s (= ‘conductivity’/(densityxCv)) Solution not simple, but is approximated by x = (kt)0.5, where x = distance from surface to mid-point in T profile. x ~ 30 km; t ~ 20 million years Lord Kelvin’s measurement of the age of the earth Take 3: determine the age of the Sun using principles of gravitation and thermodynamics; infer this to be the maximum age of the Earth. I: Measure flux of energy at earth’s surface (best above atmosphere directly facing sun) =1340 Js-1m-2 II: Integrate over area of a sphere with radius equal to distance from earth to sun (assumes sun emits energy isotropically) area = 4π(1.5x1011)2; power = 3.8x1026 Js-1 If dJ/dt is a constant: (dJ/dt)xAge ≤ mass of sun x initial energy content (‘E’, in J/Kg)) Age ≤ (2x1030 Kg)/(3.8x1026) x E Age ≤ 5000 x E Lord Kelvin’s measurement of the age of the earth Take 3, continued: Age of sun ≤ 5000 x initial energy content of sun in J/Kg Case 1: If sun’s radiance is driven by a chemical reaction, like combustion, then it’s highest plausible initial energy content is ~ 5x107 J/Kg If the sun is a ball of gasoline, it is ≤ 2.5x1011 s, or 8000 years, old Case 2: Sun’s radiance is dissipating heat derived from its initial accretion: Potential energy of pre-accretion cloud… converts to kinetic energy when cloud collapses… turns into heat if collisions between accreting material are inelastic Case 3: Sun’s accretion, continued: Total mass M at center-of-mass location, i -GMimj Potential energy = R ji (plus any contained in rotation or other motion of cloud) Rji Component particle mass m at location j Solution depends on the distribution of mass and velocity in the cloud before its collapse to form the sun One simple solution supposes all constituent masses arrived at the sun with a velocity equal to the escape velocity from the Sun today: V = (2GMs/R)0.5 = 618 km/s i0.5miv2 = 0.5Ms(6.18x105)2 0.5MsxV2 Age ≤ 3.8x1026 J/s Age ≤ 1015 s ~ 30 Million years Q.E.D.: Physicists rule; geologists drool