3D Stresses and Velocities Caused by Continental Plateaus: Scaling Analysis and Numerical Calculations With Application to the Tibetan Plateau

Abstract

Abstract Understanding stresses is crucial for geodynamics since they govern rock deformation and metamorphic reactions. However, the magnitudes and distribution of crustal stresses are still uncertain. Here, we use a 3D numerical model in spherical coordinates to investigate stresses and velocities that result from lateral crustal thickness variations around continental plateaus like those observed for the Tibetan plateau. We do not consider any far‐field deformation so that the plateau deforms by horizontal dilatation and vertical thinning. We assume viscous creep, a simplified plateau geometry, and simplified viscosity and density distributions to couple the numerical results with a scaling analysis. Specifically, we study the impact of the viscosity ratio between crust and lithospheric mantle, a rectangular plateau corner, a stress‐dependent power‐law flow law and Earth's double curvature on the crustal stress field and horizontal velocities. Two orders of magnitude variation in crustal and lithospheric mantle viscosities change the maximum crustal differential stress only by a factor of ≈2. We derive simple analytical estimates for the crustal deviatoric stress and horizontal velocity which agree to first order with 3D numerical calculations. We apply these estimates to calculate the average crustal viscosity in the eastern Tibetan plateau as ≈1022 Pa · s. Furthermore, our results show that a corner strongly affects the stress distribution, particularly the shear stresses, while Earth's curvature has a minor impact on the stresses. We further discuss potential implications of our results to strike‐slip faulting and fast exhumation around the Tibetan plateau's syntaxes.