Numerical Modelling of Structural Patterns in Tectonic Flow with Applications to the Neoarchean Crustal Dynamics

Abstract

We formulate a numerical framework, in both 2d and 3d, to model the structural patterns emerging from viscous tectonic flow by coupling a level set description of the material interface with a finite element flow solver. Our formulation has the advantage of straightforward extensibility to encompass complex rheology and versatile mesh geometry, as well as improved computational efficiency. A distinct novelty of our formulation is the capability to offer a fully dynamical approach to modelling structural patterns resulting from an inhomogeneous and non-steady tectonic flow. The model output, in the form of lithological distribution and deformation patterns, can be directly compared with the results of based geological mapping and structural analysis, thus offering the opportunity to ground-truth the abstract numerical models with concrete field observations.

As examples for the potential applications of our method, we apply our newly developed method to the modelling of the crustal dynamics of the Neoarchean granitoid-greenstone terranes in two case studies to shed light on the potential vertical- to horizontal-style tectonics. In the first case study, a field-based structural study is conducted in the Swayze greenstone belt in the Superior Craton and four generations (G1--G4) of ductile deformations are identified. Among them, G2 structures are associated with an oblique shearing kinematics with a granitoid-up/greenstone-down movement in the vertical direction and a dextral sense of shear in the horizontal direction, as well as an opposing plunge directions of L2 stretching lineation. The tectonic regime associated with G2 is interpreted to be the operation of vertical-style tectonism in the form of sagduction/diapirism under the backdrop of horizontal-style tectonism in the form of regional dextral simple shearing. To test this interpretation, an isothermal numerical model is constructed for the Swayze greenstone belt. The model replicates the observed lithological and deformation pattern, confirming the synchronous vertical and horizontal tectonism model as a viable regime to explain the observed structural patterns.

To further explore whether the synchronous vertical and horizontal tectonism is applicable to the Neoarchean crustal dynamics in general, a thermomechanical model is constructed in the second case study with both thermal and rheological conditions appropriate for the Neoarchean granitoid-greenstone terranes. As in the first case study, many aspects of the crustal architecture and structural patterns are comparable to the observations in Neoarchean terranes worldwide. Due to the high competency of the cold upper crust, the density-induced sinking of the supracrustal assemblages into the granitoid domes operates by active diachronous pointwise ``dripping'' at triple junctions or by sheet-like sagduction with higher rate of horizontal shearing. Furthermore, the transitional process of the crustal dynamics towards the modern-day conditions from the hotter Archean Earth is further explored by systematically decreasing the Moho heat flux, which results in a delayed initiation and a slower rate of the vertical tectonic process. The increase in the horizontal strain rate results in the promotion of sheet-like sagduction pattern, the elongation of granitoid domes, the preferential alignment of the high strain zones and the reduction of the rate of greenstone sagduction. It is therefore postulated that through the secular cooling of the crustal thermal condition, the role of density-induced sagduction/diapirism is suppressed, thereby completing the transition of the Earth's crustal dynamics from a dominantly vertical style in the early Earth's history to a present-day dominantly horizontal style, with the Neoarchean being the interlude period where both processes coexisted. Furthermore, taking into account that the Neoarchean lithospheric dynamics of the southeastern Superior Craton is interpreted to be terrane accretion under a plate tectonics-like regime, we conclude that the synchronous horizontal and vertical crustal dynamics is not contradictory to a framework of plate tectonics on a lithospheric scale. In fact, the Neoarchean transition in crustal dynamics may mirror a similar transition in lithospheric dynamics from the early stagnant-lid tectonics to the modern day plate tectonics.