Comparing thin-sheet models with 3-D multilayer models for continental collision

Abstract

Various models have been proposed to explain tectonic deformations during continent collision. A frequently applied model is the thin viscous sheet model which is however not fully 3-D and assumes a priori diffuse thickening as the dominant deformation style. We compare a fully 3-D multilayer numerical model with a corresponding thin viscous sheet numerical model for the scenario of continent indentation. In our comparison we focus on the three basic viscous deformation styles thickening, buckling (folding) and lateral crustal flow. Both numerical models are based on the finite element method (FEM) and employ either a linear or power-law viscous rheology. The 3-D model consists of four layers representing a simplified continental lithosphere: strong upper crust, weak lower crust, strong upper mantle and weak lower mantle. The effective viscosity depth-profile in the 3-D model is used to calculate the depth-averaged effective viscosity used in the thin-sheet model allowing a direct comparison of both models. We quantify the differences in the strain rate and velocity fields, and investigate the evolution of crustal thickening, buckling and crustal flow resulting from the two models for two different phases of deformation: (1) indentation with a constant velocity and (2) gravitational collapse after a decrease of the indenting velocity by a factor of 5. The results indicate that thin-sheet models approximate well the overall large-scale lithospheric deformation, especially during indentation and for a linear viscous rheology. However, in the 3-D model, additional processes such as multilayer buckling and lower crustal flow emerge, which are ignored in the thin-sheet model but dominate the deformation style in the 3-D model within a range of a few hundreds of kilometres around the collision zone and indenter corner. Differences between the 3-D and thin-sheet model are considerably larger for a power-law viscous than for a linear viscous rheology. Buckling and lower crustal flow are significant in the 3-D model with power-law viscous rheology. For example, fibre strain rates due to buckling can be several hundred per cent different to the depth-averaged strain rate and the lateral mass flow of lower crustal material can be up to six times more than the flow of upper crustal material. Our results also show that the horizontal velocity fields of the upper crust and upper mantle remain nearly identical in the 3-D model during indentation despite their mechanical decoupling due to an intermediate weak lower crust. This result questions the validity of using similarities between velocities from the surface global positioning system (GPS) and mantle shear wave splitting data as evidence for a mechanically coupled lithosphere. 3-D multilayer models provide a more complete picture of continental collision than thin-sheet models as they enable studying the timing, locality and relative importance of different processes simultaneously which is especially important for the hundreds of kilometre scale around the collision zone and indenter corners. 3-D models are, however, still computationally challenging and we, therefore, also present results of a computational performance test of several solution algorithms.