A new hybrid numerical scheme for modelling elastodynamics in unbounded media with near-source heterogeneities

The Finite Difference (FD) and the Spectral Boundary Integral (SBI) methods have been used extensively to model spontaneously propagating shear cracks in a variety of engineering and geophysical applications. In this paper, we propose a new modeling approach, in which these two methods are combined through consistent exchange of boundary tractions and displacements. Benefiting from the flexibility of FD and the efficiency of spectral boundary integral (SBI) methods, the proposed hybrid scheme will solve a wide range of problems in a computationally efficient way. We demonstrate the validity of the approach using two examples for dynamic rupture propagation: one in the presence of a low velocity layer and the other in which off-fault plasticity is permitted. We discuss possible potential uses of the hybrid scheme in earthquake cycle simulations as well as an exact absorbing boundary condition

[1]  J. Lysmer,et al.  Finite Dynamic Model for Infinite Media , 1969 .

[2]  David M. Boore,et al.  Comparison of two independent methods for the solution of wave-scattering problems: Response of a sedimentary basin to vertically incident SH waves , 1971 .

[3]  Yoshiaki Ida,et al.  Cohesive force across the tip of a longitudinal‐shear crack and Griffith's specific surface energy , 1972 .

[4]  J. Rice,et al.  The growth of slip surfaces in the progressive failure of over-consolidated clay , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  D. J. Andrews,et al.  Rupture propagation with finite stress in antiplane strain , 1976 .

[6]  Keiiti Aki,et al.  A numerical study of two-dimensional spontaneous rupture propagation , 1977 .

[7]  Steven M. Day,et al.  DYNAMIC RUPTURE IN A LAYERED MEDIUM: THE 1966 PARKFIELD EARTHQUAKE , 1980 .

[8]  Steven M. Day,et al.  Three-dimensional finite difference simulation of fault dynamics: Rectangular faults with fixed rupture velocity , 1982 .

[9]  J. Virieux,et al.  Dynamic faulting studied by a finite difference method : Bull seismol soc am, V72, N2, April 1982, P345–369 , 1982 .

[10]  Jacobo Bielak,et al.  Symmetric finite element and boundary integral coupling methods for fluid-solid interaction , 1991 .

[11]  Raul Madariaga,et al.  Dynamic faulting under rate-dependent friction , 1994 .

[12]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[13]  J. Rice,et al.  A spectral method for three-dimensional elastodynamic fracture problems , 1995 .

[14]  Philippe H. Geubelle,et al.  Numerical analysis of dynamic debonding under anti-plane shear loading , 1997 .

[15]  Dan Givoli,et al.  Dirichlet-to-Neumann Maps for Unbounded Wave Guides , 1998 .

[16]  D. Komatitsch,et al.  Introduction to the spectral element method for three-dimensional seismic wave propagation , 1999 .

[17]  J. Rice,et al.  Elastodynamic analysis for slow tectonic loading with spontaneous rupture episodes on faults with rate‐ and state‐dependent friction , 2000 .

[18]  James R. Rice,et al.  Dynamic shear rupture interactions with fault bends and off-axis secondary faulting , 2002 .

[19]  Jean-Paul Ampuero Étude physique et numérique de la nucléation des séismes , 2002 .

[20]  S. Franke,et al.  Comparison of meteor radar and Na Doppler lidar measurements of winds in the mesopause region above Maui, Hawaii , 2005 .

[21]  James R. Rice,et al.  Off-Fault Secondary Failure Induced by a Dynamic Slip Pulse , 2005 .

[22]  S. Day,et al.  Comparison of finite difference and boundary integral solutions to three‐dimensional spontaneous rupture , 2005 .

[23]  Jean-Pierre Vilotte,et al.  Influence of the rupture initiation on the intersonic transition: Crack‐like versus pulse‐like modes , 2006 .

[24]  M. Dumbser,et al.  An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes - I. The two-dimensional isotropic case with external source terms , 2006 .

[25]  Shuo Ma,et al.  Radiated seismic energy based on dynamic rupture models of faulting , 2006 .

[26]  P. Moczo,et al.  The finite-difference time-domain method for modeling of seismic wave propagation , 2007 .

[27]  Hideo Aochi,et al.  3D finite-difference dynamic-rupture modeling along nonplanar faults , 2007 .

[28]  Luis A. Dalguer,et al.  Staggered-grid split-node method for spontaneous rupture simulation , 2007 .

[29]  Jean Virieux,et al.  Dynamic non-planar crack rupture by a finite volume method , 2006 .

[30]  J. Rice,et al.  Off-fault plasticity and earthquake rupture dynamics: 1. Dry materials or neglect of fluid pressure changes , 2008 .

[31]  J. Ampuero,et al.  Spectral element modeling of spontaneous earthquake rupture on rate and state faults: Effect of velocity‐strengthening friction at shallow depths , 2008 .

[32]  Michael S. Riley,et al.  University of Birmingham Controls on the formation and stability of gas hydrate-related bottom-simulating reflectors (BSRs): A case study from the west Svalbard continental slope , 2008 .

[33]  Martin Käser,et al.  Dynamic rupture modeling on unstructured meshes using a discontinuous Galerkin method , 2009 .

[34]  J. Rice,et al.  Earthquake ruptures with thermal weakening and the operation of major faults at low overall stress levels , 2009 .

[35]  Jean-Paul Ampuero,et al.  Pulse-like ruptures induced by low-velocity fault zones , 2011 .

[36]  E. Dunham,et al.  Earthquake Ruptures with Strongly Rate-Weakening Friction and Off-Fault Plasticity, Part 1: Planar Faults , 2011 .

[37]  Francisco J. Sánchez-Sesma,et al.  A 3D hp‐adaptive discontinuous Galerkin method for modeling earthquake dynamics , 2012 .

[38]  J. Ampuero,et al.  Three‐dimensional dynamic rupture simulation with a high‐order discontinuous Galerkin method on unstructured tetrahedral meshes , 2012 .

[39]  F. Dupros,et al.  Finite difference simulations of seismic wave propagation for understanding earthquake physics and predicting ground motions: Advances and challenges , 2013 .

[40]  Jeremy E. Kozdon,et al.  Simulation of Dynamic Earthquake Ruptures in Complex Geometries Using High-Order Finite Difference Methods , 2013, J. Sci. Comput..

[41]  D. Helmberger,et al.  Earthquake ruptures modulated by waves in damaged fault zones , 2014 .

[42]  Xiao Ma,et al.  Effect of off-fault low-velocity elastic inclusions on supershear rupture dynamics , 2015 .

[43]  Setare Hajarolasvadi A new hybrid numerical scheme for simulating fault ruptures with near fault bulk inhomogeneities , 2016 .

[44]  W. Ellsworth,et al.  Stress drop estimates of potentially induced earthquakes in the Guy‐Greenbrier sequence , 2016 .

[45]  A Model for Athermal Strain Localization in Dry Sheared Fault Gouge , 2017, 1701.03087.

[46]  Arash Khosravifar,et al.  A finite difference method for off-fault plasticity throughout the earthquake cycle , 2017 .