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<p>On Earth, different geodynamic features form in response to a tectonic event. Continental plateaus, such as the Tibetan Plateau, are formed in a collisional environment and they are characterized by an unusually large crustal thickness, which generates lateral variations of gravitational potential energy per unit area (GPE). These GPE variations cause the thickened crust to flow apart and thin by gravitational collapse. Although plateau and lowland are in isostatic equilibrium, the lateral GPE variations must be balanced by horizontal differential stresses, which prevent the plateau from flowing-apart instantaneously. However, the magnitude and distribution of differential stress around plateau corners for three-dimensional (3-D) spherical geometries relevant on Earth remain disputed. Due to the ellipticity of the Earth, the lithosphere is mechanically analogous to a shell, characterized by a double curvature. Shells exhibit fundamentally different mechanical characteristics compared to plates, having no curvature in their undeformed state. Understanding the magnitude and the spatial distribution of strain, strain-rate and stress inside a deforming lithospheric shell is thus crucial but technically challenging. Resolving the stress distribution in a 3-D geometrically and mechanically heterogeneous lithosphere requires high-resolution calcuations and high-performance computing.</p> <p>Here, we present numerical simulations solving the Stokes equations under gravity. We employ the accelerated pseudo-transient finite-difference (PTFD) method, which enables efficient simulations of high-resolution 3-D mechanical processes relying on a fast iterative and implicit solution strategy of the governing equations. The main challenges are to guarantee convergence, minimize the iteration count and ensure optimal execution time per iteration. We implemented the PTFD algorithm using the Julia language. The Julia packages ParallelStencil.jl and ImplicitGlobalGrid.jl enable optimal parallel execution on mulitple CPUs and GPUs and ideal scalability up to thousands of GPUs.</p> <p>The aim of this study is to quantify the impact of different lithosphere curvatures on the resulting stress field. To achieve this, we use a simplified plateau geometry and density structure implemented in a spherical coordinate system. The curvature is modified by varying the radius of the coordinates system, without altering the initial geometry. We particularly focus on stress magnitudes and distributions in the corner regions of the plateau.</p>

Diapirism is crucial for heat and mass transfer in many geodynamic processes. Understanding diapir ascent velocity is vital for assessing its significance in various geodynamic settings. Although analytical estimates exist for ascent velocities of diapirs in power-law viscous, stress weakening fluids, they lack validation through 3D numerical calculations. Here, we improve these estimates by incorporating combined linear and power-law viscous flow and validate them using 3D numerical calculations. We focus on a weak, buoyant sphere in a stress weakening fluid subjected to far-field horizontal simple shear. The ascent velocity depends on two stress ratios: (1) the ratio of buoyancy stress to characteristic stress, controlling the transition from linear to power-law viscous flow, and (2) the ratio of regional stress associated with far-field shearing to characteristic stress. Comparing analytical estimates with numerical calculations, we find analytical estimates are accurate within a factor of two. However, discrepancies arise due to the analytical assumption that deviatoric stresses around the diapir are comparable to buoyancy stresses. Numerical results reveal significantly smaller deviatoric stresses. As deviatoric stresses govern stress-dependent, power-law, viscosity analytical estimates tend to overestimate stress weakening. We introduce a shape factor to improve accuracy. Additionally, we determine characteristic stresses for representative mantle and lower crustal flow laws and discuss practical implications in natural diapirism, such as sediment diapirs in subduction zones, magmatic plutons or exhumation of ultra-high-pressure rocks. Our study enhances understanding of diapir ascent velocities and associated stress conditions, contributing to a thorough comprehension of diapiric processes in geology.

<p>Strain localization and associated softening mechanisms in a deforming lithosphere are important for subduction initiation or the generation of tectonic nappes during orogeny. Many strain localization and softening mechanisms have been proposed as being important during the viscous, creeping, deformation of the lithosphere, such as thermal softening, grain size reduction, reaction-induced softening or anisotropy development. However, which localization mechanism is the controlling one and under which deformation conditions is still contentious. In this contribution, we focus on strain localization in viscous material due to the generation of anisotropy, for example due to the development of a foliation. We numerically model the generation and evolution of anisotropy during two-dimensional viscous simple shear in order to quantify the impact of anisotropy development on strain localization and on the effective softening. We calculate the finite strain ellipse during viscous deformation. The aspect ratio of the finite strain ellipse serves as proxy for the magnitude and evolution of anisotropy, which determines the ratio of normal to tangential viscosity. To track the orientation of the anisotropy during deformation we apply a director method. We benchmark our implementation of anisotropy by comparing results of two independently developed numerical algorithms based on the finite difference method: one algorithm employs a direct solver and the other a pseudo-transient iterative solver. We will present results of our numerical simulations and discuss their application to natural shear zones.</p>

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