Modeling Earth's Engine: Utilizing Innovative Numerical Schemes to better Understand Plate Tectonics and Mantle Convection On Earth

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Between Earth's crust and core lies the mantle, a 2,900 km-thick layer of hot rock that comprises greater than 80% of Earth's volume. Carrying Earth's internal heat to the surface, the convecting mantle creeps like tar on a hot day. This overturning is the 'engine' that drives our dynamic Earth; ultimately, all large- scale geological activity is driven by mantle convection (Davies, 1992). Quantitative modelling of this process is thus essential for understanding Earth's dynamics, structure, and evolution, from earthquakes and volcanoes to the forces that build mountains and break continents apart.

While sluggish in human terms, mantle convection is actually an extremely vigorous process. Indeed, the mantle's Rayleigh number, a dimensionless parameter quantifying the vigour of convection, is of order 109, which is almost that of a pot of boiling water. Accurate modelling of mantle convection is thus extremely challenging, because kilometre-scale features, such as subducting plates/slabs and upwelling mantle plumes, must be resolved within the thousand-kilometre-scale mantle. Consequently, despite the large computing clusters available today, with current methods it is difficult to accurately simulate the whole mantle at its true dynamical regime.

The Project:

To overcome this obstacle to a better understanding of mantle convection on Earth and other planets, the proposed research will further enhance and test a recently developed computational framework for mantle dynamics, Fluidity (Davies et al. 2011, Kramer et al. 2012). The code:

  • Employs an unstructured mesh with non-uniform resolution, so that regions of dynamical activity, or specific interest, can be modeled at a higher resolution than is required by the large-scale flow.
  • Employs state-of-the-art adaptive mesh methods, to automatically resolve fine-scale features as they develop. This minimizes computational cost by reducing resolution where possible; computational power is automatically concentrated in the most active regions of the domain (Davies et al. 2007).
  • It takes advantage of load-balanced domain decomposition algorithms, in order to run on parallel machines with distributed memory.

The modificatios central to the proposed project include:

  1. Incorporation of 500 Myr of plate motion histories as a surface boundary condition.
  2. Incorporation of complex rheologies (grain-size and histroy dependent - damage), such that 'plates' can be generated and analysed self-consistently within a global framework.

The modified code will subsequently be applied in examining a range of processes relating to mantle convection and plate tectonics, focusing upon mantle/lithosphere interaction, including: (i) how surface plates modulate underlying mantle flow; (ii) how plate tectonics has evolved over Earth's history; (iii) why plate tectonics is unique to Earth, among the terrestrial planets.

Figure 2: A 2-D thermo-mechanical dynamic subduction simulation from Fluidity. Temporal snapshots of: (a) temperature; (b) viscosity; (c) the dominant deformation mechanism; and (d) the underlying computational mesh, from a case where subducting/overriding plates are initially 100/20 Myr old at the trench, respectively (black squares indicate initial trench location). White lines in panel (a) mark isotherms from 600-1400 K at 200 K intervals. Black (b/c) and red (d) lines mark the location of the 1300K isotherm. In this class of subduction model, the slab's buoyancy and distinct rheological properties arise self-consistently, through variations in temperature, pressure and strain-rate, with deformation accommodated through a composite diffusion creep (diff), dislocation creep (disl), Peierls creep (P) and yielding (YS) law. In the example shown, the slab's excess density drives subduction and trench retreat over time. Upon interaction with the transition zone, the descending slab temporarily stalls and deforms (b/c), before slowly sinking into the lower mantle (d). Note that throughout its descent, the slab maintains a strong core (b), which is a requirement from observations of Benioff seismicity. The underlying computational mesh is adapted at fixed intervals during the simulation, with zones of high resolution analogous to regions of dynamic significance. A local resolution of ~500m is required to resolve the slab's strong core and the interface between subducting and overriding plates (modified from Garel et al. 2014).

The Candidate:

The successful applicant will hold a 1st class degree (or equivalent) and have a strong record in a numerate subject such as mathematics, computer sciences, physics, geophysics or engineering. Experience in computer programming is desirable. The student will join a large and active international group, with collaborators at Imperial College London, Columbia University, New York and the University of Sydney.

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