GE 11a 2014, Lecture 6 Conduction, the lithosphere and isostacy

Transcription

1 GE 11a 2014, Lecture 6 Conduction, the lithosphere and isostacy

2 To zero th order, the earth s surface is bimodal in height with respect to sea level

3 Similar things are also true for the moon and Mars, though we will end up deciding it reflects something unique (and uniquely important) on Earth Moon Mars

4 The Catastrophists view of the North Atlantic

5 Cartoon of crust and lithosphere on the board

6 A shaggy dog story about the first organized thought on this subject: Lord Kelvin s response to uniformitarianism+catastrophism Lord Kelvin looking into a box First quantitative estimates of the ages of celestial objects based on modern physical theory (I.e., Newtonian physics, thermodynamics, Fick s laws and the kinetic theory of gases). Engaged a mature scientific community and discredited lax logic of Uniformitarian dating Arguments of this kind are still made to date astrophysical events, processes on other planets, and poorly sampled geologic events

7 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.

8 Lord Kelvin s measurement of the age of the earth Take 2: 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 -1 m -2 II: Integrate over area of a sphere with radius equal to distance from earth to sun (assumes sun emits energy isotropically) area = 4π(1.5x10 11 ) 2 ; power = 3.8x10 26 Js -1 If dj/dt is a constant: (dj/dt)xage mass of sun x initial energy content ( E, in J/Kg)) Age (2x10 30 Kg)/(3.8x10 26 ) x E Age 5000 x E

9 Lord Kelvin s measurement of the age of the earth Take 2, 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 ~ 5x10 7 J/Kg If the sun is a ball of gasoline, it is 2.5x10 11 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

10 Potential energy = -GM i m j R ji Case 2: Sun s accretion, continued: Total mass M at center-of-mass location, i (plus any contained in rotation or other motion of cloud) R ji 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 = (2GM s /R) 0.5 = 618 km/s i0.5m i v 2 = 0.5M s (6.18x10 5 ) 2 0.5M s xv 2 Age 3.8x10 26 J/s Age s ~ 30 Million years

11 Lord Kelvin s measurement of the age of the earth Take 3: directly determine age of the Earth by inverting the conductive temperature profile observed in its outer few km of crust 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

12 Lord Kelvin s measurement of the age of the earth Take 3: 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 T ( C) 0 t 1 t 2 Radial distance J heat = k(dt/dx) dt/dt = k d 2 T/dx 2 t 0 pinned by radiative balance of surface k = thermal diffusivity ~ 5x10-3 cm 2 /s (= conductivity /(densityxc v )) 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 Q.E.D.: Physicists rule; geologists drool

13 Note that conduction also leads to a change in rheology between interior and outer shell

14 What are the dynamics of the hot, viscous (fluid like) interior? Rayleigh number = Buoyancy Viscous drag X Momentum diffusivity Thermal diffusivity acceleration Thermal expansion Temperature contrast Kinematic viscosity Thermal diffusivity Length scale If > ~1000, convection ensues. The mantle is ~10 6

15 A numerical model of whole-mantle convection in a 2-D earth