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Abstract Reconstructing fault surfaces from volumetric data is a longstanding challenge in geosciences. We present a novel 3D method based on the medial axis to transform a volumetric strain‐rate invariant field from long‐term geodynamic simulations into fault surfaces. In these geodynamic models, faults correspond to regions of locally high values of the second invariant of the strain‐rate commonly referred to as shear zones. The proposed workflow begins by normalizing the strain‐rate to define fault indicator field . An iso‐surface of a chosen value is then extracted to form an envelope around the shear zones. Using the shrinking ball algorithm (Ma et al., 2012,https://doi.org/10.1007/s00371‐011‐0594‐7), we compute the medial axis of this 3D envelope to generate a point cloud representing the geometric skeleton of the shear zones. We reconstruct fault surfaces by applying Delaunay triangulation followed by Laplacian smoothing. For models involving multiple intersecting faults, we perform a local principal component analysis (PCA) of the coordinates defining the medial axis and use the resulting eigenvectors to detect first‐order orientation variations, enabling the separation and individualization of faults. We demonstrate the generality and robustness of the method by applying it several diverse 3D geodynamic scenarios: A single strike‐slip fault, a branching strike‐slip fault in a restraining bend, a dense strike‐slip fault network, a rift system, and a subduction zone with a megathrust and a conjugate thrust fault. 

Abstract. Modelling the pressure in the Earth's interior is a common problem in Earth sciences. In this study we propose a method based on the conservation of the momentum of a fluid by using a hydrostatic scenario or a uniformly moving fluid to approximate the pressure. This results in a partial differential equation (PDE) that can be solved using classical numerical methods. In hydrostatic cases, the computed pressure is the lithostatic pressure. In non-hydrostatic cases, we show that this PDE-based approach better approximates the total pressure than the classical 1D depth-integrated approach. To illustrate the performance of this PDE-based formulation we present several hydrostatic and non-hydrostatic 2D models in which we compute the lithostatic pressure or an approximation of the total pressure, respectively. Moreover, we also present a 3D rift model that uses that approximated pressure as a time-dependent boundary condition to simulate far-field normal stresses. This model shows a high degree of non-cylindrical deformation, resulting from the stress boundary condition, that is accommodated by strike-slip shear zones. We compare the result of this numerical model with a traditional rift model employing free-slip boundary conditions to demonstrate the first-order implications of considering “open” boundary conditions in 3D thermo-mechanical rift models.