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

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 approximate to 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 approximate to 1022 Pa center dot 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. This study focuses on understanding the stresses in the Earth's crust, which is crucial for understanding how rocks deform and undergo chemical reactions. However, there is still uncertainty about the exact magnitudes and distribution of these stresses, especially in three dimensions (3D). To estimate long-term stresses in the lithosphere, scientists often use observed variations in the thickness of the Earth's crust around continental plateaus, like the Tibetan plateau which has an average altitude of approximately 5 km. The plateaus we study will flow apart under gravity on geological time scales to reduce the altitude difference between the plateau and neighboring lowlands, a process often termed gravitational collapse. Here, a 3D numerical model is used to explore the magnitudes and distribution of stress around these plateaus. The study considers factors like variations in the viscosity (a measure of a material's resistance to flow) of different parts of the lithosphere and the Earth's curvature. We derive simple mathematical equations to estimate the crustal stress and horizontal velocity and we test these estimates with the results of the performed 3D numerical calculations. The results further show that Earth's curvature has a minor impact on the stress distribution. We study systematically the impact of different crustal and lithospheric mantle viscosities on stresses and velocities Simple analytical estimates for crustal deviatoric stress and horizontal velocity agree with 3D numerical results The double curvature of the Earth has a minor impact on the 3D stress distribution around the Tibetan plateau