Part II

1. Part II

2. Seismotectonics • Kanimori (1977) estimated that earthquakes release (use) about 5 x 1017 J per year. The theoretical limit of the annual energy available from the convective heat engine is about 5.4 x 1020 J per year. The work “done” by earthquakes accounts for only about 0.1% of the annual energy available to the convection engine. • What else? • Moving masses laterally across the geoid requires no work apart from the resistance or friction of the motions. Lifting masses above the geoid requires work. On long time scales, we believe that the topography of the Earth is approximately stable: uplift and erosion are in balance. The energy required to uplift the topography must somehow be provided by the convection engine.

3. Seismotectonics • The heat engine that is expressed in mantle convection works on the body and surface of the Earth. • It is not an especially thermodynamically “efficient”: its theoretically limiting efficiency is determined by the temperature differences at the bottom and top of the circulating mantle. • We might expect, then, that the convection engine could accomplish “work” at the rate of about 17TW. This is a tremendous power to move and uplift continents, spread ocean basins, lift mountain-building magmas above the surface and fracture surface rocks in earthquakes.

4. Powering mantle convection The mantle engine's power derives from several possible sources: • A chondritic Earth should contain enough U, Th and K to account for much of the heat flow from the surface. McDonough, 2003

5. Powering mantle convection - II The mantle engine's power derives from several possible sources: • A chondritic Earth should contain enough U, Th and K to account for much of the heat flow from the surface. • Total present-day instantaneous combined radiogenic heat source estimate for the BSE (bulk silicate Earth): 12.7 – 31TW. Anderson, 2009 *It has been argued that the atmospheric mass of argon (1.29% of the atmospheric mass) entirely derives from the decay of 40K during the history of the Earth. Presently, 40K comprises 0.0117% (atom count) of natural K.

6. 40K -> 40Ar, 40Ca

7. Core convection and the geodynamo • Compensation for the continuing dissipation of the geomagnetic field requires a continuous power input of ~0.5-4TW (various estimates) to maintain the field. • The convective engine of the core provides this power input. • The temperature gradient under which this engine operates is (we have) estimated to range from about 5100K to 4300K. • The theoretically limiting efficiency of this engine – it is this engine that drives the geodynamo – is then: • ~77% of the power available in the convective engine is exhausted into the mantle. This corresponds to a heat flow out of the core into the mantle of at least 1.8TW and possibly more than 14TW if all the available power of the convection drive feeds the geodynamo. There are myriad other losses. Caveat If we believe our temperature profile, we might accept Andersons's 9mW/m2 heat flow from the core into the mantle ... But! Note that our argument is really a circular one. We have obtained our temperature on the basis of Anderson's heat flow estimate: ~9TW

8. Powering core convection We tread on very soft ground of assumption here. • Latent heat of fusion of inner core: depends upon the rate and history of freezing of the core. We may argue that the core started freezing 3.5Ga or as recently as 1Ga. • Radioactive isotopes in the core and, preferentially, incorporated into the inner core. 40K is the best candidate. • Chemical differentiation releasing light elements into the outer core as Fe-Ni crystallize to form the inner core. • A small metallic fissile U-Th core at the centre of the inner core... probably fanciful but possibly testable. • Fossil primordial heat assembled during accretion. Properly, simply the continuing cooling of the overlying mantle... sometimes seen as “entropy increase”. 0.1 - 1TW 0.1 - 1TW 0.1 - 1TW 0 - 1TW Probably enough

9. Formation of the oceanic crust and lithosphere The ocean basin deepens with distance from the spreading ridge as a consequence of isostatic adjustment

10. Ocean bathymetry GEBCO The ocean ridges are the shallowest regions of the basins; they are also the youngest!

11. Mathematical-physical theory v

12. Mathematical-physical theory - II v

13. Mathematical-physical theory - III

14. Mathematical-physical theory - IV Much manipulation (Sandwell; 2001) takes us here:

15. The error function:erf(x) Explore this special function on Wolfram|Alpha

16. What happens at a subduction trench? We have seen how the oceanic crust and upper-mantle lithosphere form and deepen as the plate spreads from a ridge. The Earth remains finite in area so that lithospheric plate has to be consumed back into the volume of the Earth somewhere... Where? Along “subduction zones”. How does subduction work?

17. Forces acting of lithospheric plates

18. Exploring some tectonic stories and maps http://pubs.usgs.gov/gip/dynamic/understanding.html http://earthquakescanada.nrcan.gc.ca/zones/cascadia/mega-eng.php http://earthquakescanada.nrcan.gc.ca/zones/cascadia/strain-eng.php http://denali.gsfc.nasa.gov/dtam/data/ftp/gtam.gif http://denali.gsfc.nasa.gov/dtam/seismic/ http://denali.gsfc.nasa.gov/dtam/data/ftp/dtam.gif http://www.gps.caltech.edu/~dla/images/n_polar.jpg http://www.gps.caltech.edu/~dla/images/s_polar.jpg http://www.gps.caltech.edu/~dla/images/oblique.jpg

19. Plate tectonics!