Source: Dissertation Abstracts International, Volume: 75-09(E), Section: B.

Adviser: David Bercovici.

The question of why plate tectonics occurs on Earth, but not on the other planets of our solar system, is one of the most fundamental issues in geophysics and planetary science. I study this problem using numerical simulations of mantle convection with a damage-grainsize feedback (grain-damage) to constrain the conditions necessary for plate tectonics to occur on a terrestrial planet, and how plate tectonics initiates.

In Chapter 2, I use numerical simulations to determine how large a viscosity ratio, between pristine lithosphere and mantle, damage can offset to allow mobile (plate-like) convection. I then use the numerical results to formulate a new scaling law to describe the boundary between stagnant lid and plate-like regimes of mantle convection. I hypothesize that damage must reduce the viscosity of shear zones in the lithosphere to a critical value, equivalent to the underlying mantle viscosity, in order for plate tectonics to occur, and demonstrate that a scaling law based on this hypothesis reproduces the numerical results. For the Earth, damage is efficient in the lithosphere and provides a viable mechanism for the operation of plate tectonics. I apply my theory to super-Earths and map out the transition between plate-like and stagnant lid convection with a "planetary plate-tectonic phase" diagram in planet size-surface temperature space. Both size and surface temperature are important, with plate tectonics being favored for larger, cooler planets. This gives a natural explanation for Earth, Venus, and Mars, and implies that plate tectonics on exoplanets should correlate with size, incident solar radiation, and atmospheric composition.

In Chapters 3 and 4 I focus on the initiation of plate tectonics. In Chapter 3, I develop detailed scaling laws describing plate speed and heat flow for mantle convection with grain-damage across a wide parameter range, with the intention of applying these scaling laws to the early Earth in Chapter 4. Convection with grain-damage scales differently than Newtonian convection; whereas the Nusselt number, Nu, typically scales with the Rayleigh number, Ra, to the 1/3 power, for grain-damage this exponent is larger because increasing Ra also enhances damage. In addition, Nu and plate velocity are also functions of the damage to healing ratio, (D/H); increasing D/H increases Nu (or plate speed) because more damage leads to more vigorous convection.

In Chapter 4, I demonstrate that subduction can be sustained on the early Earth, that the style of subduction at this time was different than modern day plate tectonics, and that such subduction (or proto-subduction) can initiate rapidly after magma ocean solidification. The scaling laws from Chapter 3 show that, though either higher interior mantle temperatures or higher surface temperatures lead to slower plates, proto-subduction, with plate speeds of at least 1.5 cm/yr, can still be maintained in the Hadean, even if the primordial atmosphere was CO2 rich. Furthermore, when the interior mantle temperature is high (e.g. above ≈ 2000 K), the mode of subduction switches to a "sluggish subduction" style, where downwellings are more drip-like than slab-like and plate boundaries are more diffuse. Numerical models of post-magma ocean mantle convection, and a scaling analysis based on the results of these models, demonstrate that proto-plate tectonics likely initiates within ∼100 Myrs of magma ocean solidification. Combined with the conclusion that proto-subduction could be maintained on the early Earth, my results are consistent with evidence for Hadean subduction from zircon data, and indicate that the subduction inferred from zircons may have been distinct from modern day plate tectonics. After the initiation of proto-subduction, which occurs as a rapid overturn of the whole lithosphere, mobile lid convection takes place as non-plate tectonic "sluggish subduction" As both the mantle interior and climate cool, modern style plate tectonics develops. The rapid, initial subduction event may help hasten the onset of modern style plate tectonics by drawing excess CO 2 out of the atmosphere and cooling the climate.