DOI: 10.1029/2023jb027143 ISSN: 2169-9313

A Diffuse Interface Method for Earthquake Rupture Dynamics Based on a Phase‐Field Model

Jorge N. Hayek, Dave A. May, Casper Pranger, Alice‐Agnes Gabriel
  • Space and Planetary Science
  • Earth and Planetary Sciences (miscellaneous)
  • Geochemistry and Petrology
  • Geophysics


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.

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