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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 In traditional modeling approaches, earthquakes are often depicted as displacement discontinuities across zero‐thickness surfaces embedded within a linear elastodynamic continuum. This simplification, however, overlooks the intricate nature of natural fault zones and may fail to capture key physical phenomena integral to fault processes. Here, we propose a diffuse interface description for dynamic earthquake rupture modeling to address these limitations and gain deeper insight into fault zones' multifaceted volumetric failure patterns, mechanics, and seismicity. Our model leverages a steady‐state phase‐field, implying time‐independent fault zone geometry, which is defined by the contours of a signed distance function relative to a virtual fault plane. Our approach extends the classical stress glut method, adept at approximating fault‐jump conditions through inelastic alterations to stress components. We remove the sharp discontinuities typically introduced by the stress glut approach via our spatially smooth, mesh‐independent fault representation while maintaining the method's inherent logical simplicity within the well‐established spectral element method framework. We verify our approach using 2D numerical experiments in an open‐source spectral element implementation, examining both a kinematically driven Kostrov‐like crack and spontaneous dynamic rupture in diffuse fault zones. The capabilities of our methodology are showcased through mesh‐independent planar and curved fault zone geometries. Moreover, we highlight that our phase‐field‐based diffuse rupture dynamics models contain fundamental variations within the fault zone. Dynamic stresses intertwined with a volumetrically applied friction law give rise to oblique plastic shear and fault reactivation, markedly impacting rupture front dynamics and seismic wave radiation. Our results encourage future applications of phase‐field‐based earthquake modeling.