Modelling tectonic flow with discontinuous Galerkin level set method: Case studies and applications for the Neoarchean crustal dynamics

We present a new numerical method to simulate the structural patterns emerging from the long-term large-deformation tectonic flows in both two and three spatial dimensions.  The domains of different material properties are each represented by a level set function discretized on a Eulerian mesh with the discontinuous Galerkin method. The level sets are advected by a velocity field provided by a coupled Stokes flow solver. Our method accurately captures the material interface by the adaptive mesh refinement, reduces the computational expenses compared to the traditional particle-in-cell method and offers straightforward handling of geometric splitting and merging.  Under the unified finite element framework, our method promises the flexibility in the choice of mesh geometry as well as the potential for extending to complex rheology.  With passive tracers geat and around areas of interest, the finite strain of the flow field can be integrated through any time interval within the total simulation time.  The strain ellipsoids thus obtained offers the possibility for ground-truthing the simulated deformation patterns with the field structural analysis.  Our results demonstrate identical physical behaviour when compared with established structural geology and geodynamic benchmarks.

The style of the crustal dynamics on the Archean Earth has been subject to controversy on whether a vertical tectonic style in the form of Rayleigh-Taylor instability, induced by an inverted density profile, prevails in the early history of the Earth and if so, how the transition to the present-day plate tectonics, characterized by dominantly horizontal movement, is manifested in the rock record.  Equipped with our modelling scheme, we construct numerical models to simulate the lithological distributions and deformation patterns resulted from a synchronous operation of vertical tectonism and horizontal shearing. The latter can be viewed as a possible result of some far-field tectonic boundary condition (e.g. oblique convergence).  Many aspects of the simulation in terms of the map pattern, foliation/lineation trend and strain distribution compare favorably with the field observations in Neoarchean granitoid-greenstone terranes in the Superior Province as well as worldwide.  Therefore, it is concluded that the vertical and horizontal tectonism are not mutually exclusive tectonic regimes  The symbiosis of both tectonic processes is a viable mechanism for establishing the crustal architecture and the deformation pattern we see today in many Neoarchean terranes and might represent a transition from the former to the latter in the Neoarchean.