Physics of Earth's Evolution

However the Earth came to its presently differentiated form, it must have obeyed our known physics:

Conservation of energy and momentumThe laws of thermodynamicsThe laws governing electromagnetism

EPSC 666 November 4, 2009... Olivia

Energetics

About 4.6 billion years ago, the primordial Earth condensed from a cloud of planetesimals with a composition not unlike that of the chondritic meteorites we find that have fallen to Earth. The gravitational potential energy available in this collapse could have brought the mass of Earth to a temperature exceeding 30000K –- a plasma primordial Earth?

Early Earth

Early Earth surely didn't exist in a gravity-bound plasma state; internal temperature was probably pretty much as it is today – perhaps a little cooler, perhaps a little hotter.

26Al 26Mg (t½ ~ 700k years; 1000K)The “Big Splat” (deep magma ocean)U, Th, K (long-lived; current sources)

Heat budget

Losses:1. Measured global cooling rate: ~30TW → 44TW* and

probably higher during the ancient past.2. Geomagnetic field loss (external): ~1 → 4TW

Sources:1. Radioactive decay: crust (6 → 9TW), upper mantle

(12 → 21TW), lower mantle (3 → 14TW)2. Entropy increase in mantle: (~3TW)3. From core into mantle: ( > 8.6TW + ~1 → 2TW)4. Remnant primordial gravitational energy: (~9 → 14TW)* In 2008, average rate of human energy consumption – all forms: 15

→ 16TW

New Theory of the Earth, Anderson, D.L, 2007, Cambridge

Earth model and T

Mao, H-K and Hemley, R, 2007 www.pnas.orgcgidoi10.1073pnas.0703653104

Modes of cooling

• Inner core: conduction cooling, freezing surface (an interior source 40K?)

• Outer core: very vigorous convection • D'' layer (lowermost mantle): conduction• Lower mantle ( > 660km depth): vigorous

convection• Upper mantle ( < 660km): convection• Lithosphere ( upper 0 – 200km): conduction

Convection

Convection continues to differentiate, to reorganize the Earth's mantle.Requirements for convection:Locally, the temperature gradient, dT(z)/dz, must exceed the adiabatic gradient:

dT(z)/dz > g αP

T / CP

The observed “vigour” of mantle convection suggests that the adiabatic gradient must be “substantially” exceeded:The Rayleigh number, Ra, the ratio of bouyant to viscous forces: Ra ~ 106

Temperature

Mao, H-K and Hemley, R, 2007 www.pnas.orgcgidoi10.1073pnas.0703653104

PREMDziewonski and Anderson (1981)