Jorge Nicolas Hayek , Dave A May, Casper Pranger, Alice-Agnes Gabriel 

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.