Off-Fault Secondary Failure Induced by a Dynamic Slip Pulse

We develop a 2D slip-weakening description of a self-healing slip pulse that propagates dynamically in a steady-state configuration. The model is used to estimate patterns of off-fault secondary failure induced by the rupture, and also to infer fracture energies G for large earthquakes. This extends an analysis for a semi-infinite rupture (Poliakov et al. , 2002) to the case of a finite slipping zone length L of the pulse. The dynamic stress drop, when divided by the drop from peak to residual strength, determines the ratio of L to the slip-weakening zone length R . Predicted off-fault damage is controlled by that scaled stress drop, static and dynamic friction coefficients, rupture velocity, principal prestress orientation, and poroelastic Skempton coefficient. All damage zone lengths can be scaled by ![Graphic][1] , which is proportional G /(strength drop)2 and is the value of R in the low-rupture-velocity, low-stress-drop, limit. In contrast to the Poliakov et al. (2002) case R / L = 0, the region that supports Coulomb failure reaches a maximum size on the order of ![Graphic][2] when mode II rupture speed approaches the Rayleigh speed. Analysis of slip pulses documented by Heaton (1990) leads to estimates of G , each with a factor-of-two model uncertainty, from 0.1 to 9 MJ/m2 (including the factor), averaging 2–4 MJ/m2; G tends to increase with the amount of slip in the event. In most cases, secondary faulting should extend, at high rupture speeds, to distances from the principal fault surface on the order of 1 to 2 ![Graphic][3] ≈ 1–80 m for a 100-MPa strength drop; that distance should vary with depth, being larger near the surface. We also discuss gouge and damage processes. [1]: /embed/inline-graphic-1.gif [2]: /embed/inline-graphic-2.gif [3]: /embed/inline-graphic-3.gif

[1]  L. B. Freund,et al.  The mechanics of dynamic shear crack propagation , 1979 .

[2]  Richard H. Sibson,et al.  Interactions between Temperature and Pore-Fluid Pressure during Earthquake Faulting and a Mechanism for Partial or Total Stress Relief , 1973 .

[3]  Gutuan Zheng,et al.  Self-healing slip pulse on a frictional surface , 1995 .

[4]  D. Goldsby,et al.  Flash Melting of Crustal Rocks at Almost Seismic Slip Rates , 2003 .

[5]  Victor C. Li,et al.  Mechanics of shear rupture applied to earthquake zones , 1986 .

[6]  Paul Segall,et al.  Nucleation and growth of strike slip faults in granite , 1983 .

[7]  J. Rice,et al.  Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents , 1976 .

[8]  Rachel E. Abercrombie,et al.  Can observations of earthquake scaling constrain slip weakening , 2005 .

[9]  R. Sibson Generation of Pseudotachylyte by Ancient Seismic Faulting , 1975 .

[10]  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.

[11]  Terry E. Tullis,et al.  Self-healing slip pulses in dynamic rupture models due to velocity-dependent strength , 1996, Bulletin of the Seismological Society of America.

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

[13]  J. Hull Thickness-displacement relationships for deformation zones , 1988 .

[14]  James H. Dieterich,et al.  The frictional properties of a simulated gouge having a fractal particle distribution , 1989 .

[15]  Paul G. Richards,et al.  Quantitative Seismology: Theory and Methods , 1980 .

[16]  D. Pollard,et al.  8 – THEORETICAL DISPLACEMENTS AND STRESSES NEAR FRACTURES IN ROCK: WITH APPLICATIONS TO FAULTS, JOINTS, VEINS, DIKES, AND SOLUTION SURFACES , 1987 .

[17]  J. Rice,et al.  Dilatancy, compaction, and slip instability of a fluid‐infiltrated fault , 1995 .

[18]  T. Heaton Evidence for and implications of self-healing pulses of slip in earthquake rupture , 1990 .

[19]  Peggy A. Johnson,et al.  Rupture mechanism and interface separation in foam rubber models of earthquakes: a possible solution to the heat flow paradox and the paradox of large overthrusts , 1993 .

[20]  Kim B. Olsen,et al.  Three-Dimensional Dynamic Simulation of the 1992 Landers Earthquake , 1997 .

[21]  R. Madariaga,et al.  Dynamic modeling of the 1992 Landers earthquake , 2001 .

[22]  K. Broberg Cracks and Fracture , 1999 .

[23]  Michael F. Ashby,et al.  The damage mechanics of brittle solids in compression , 1990 .

[24]  James P. Evans,et al.  Fluid‐rock interaction in faults of the San Andreas system: Inferences from San Gabriel fault rock geochemistry and microstructures , 1995 .

[25]  T. Nagase,et al.  Fluidization and melting of fault gouge during seismic slip: Identification in the Nojima fault zone and implications for focal earthquake mechanisms , 2003 .

[26]  C. Scholz Wear and gouge formation in brittle faulting , 1987 .

[27]  K. W. Neale,et al.  Dynamic fracture mechanics , 1991 .

[28]  E. Yoffe,et al.  The moving Griffith crack , 1951 .

[29]  Yehuda Ben-Zion,et al.  Wrinkle-like slip pulse on a fault between different , 1997 .

[30]  J. Rudnicki,et al.  Mechanics of dip-slip faulting in an elastic half-space , 1995 .

[31]  A. Lachenbruch,et al.  Frictional heating, fluid pressure, and the resistance to fault motion , 1980 .

[32]  J. Rice,et al.  Conditions under which velocity-weakening friction allows a self-healing versus a cracklike mode of rupture , 1998, Bulletin of the Seismological Society of America.

[33]  R. Archuleta,et al.  Direct seismic energy modeling and application to the 1979 Imperial Valley earthquake , 2002 .

[34]  D. Goldsby,et al.  Low frictional strength of quartz rocks at subseismic slip rates , 2002 .

[35]  M. Zoback,et al.  New Evidence on the State of Stress of the San Andreas Fault System , 1987, Science.

[36]  J. Spray Pseudotachylyte controversy: Fact or friction? , 1995 .

[37]  Nobuki Kame,et al.  Simulation of the spontaneous growth of a dynamic crack without constraints on the crack tip path , 1999 .

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

[39]  A. Lachenbruch,et al.  Heat flow and energetic of the San Andreas fault zone , 1980 .

[40]  C. L. Prasher,et al.  Crushing and Grinding Process Handbook , 1987 .

[41]  Raul Madariaga,et al.  On the Self-Healing Fracture Mode , 2003 .

[42]  James P. Evans,et al.  Mesoscopic structure of the Punchbowl Fault, Southern California and the geologic and geophysical structure of active strike-slip faults , 2000 .

[43]  Steven M. Day,et al.  Effects of a low-velocity zone on a dynamic rupture , 1997, Bulletin of the Seismological Society of America.

[44]  L. Smith,et al.  Effects of frictional heating on the thermal, hydrologic, and mechanical response of a fault , 1987 .

[45]  J. Rice,et al.  Three-dimensional perturbation solution for a dynamic planar crack moving unsteadily in a model elastic solid , 1994 .

[46]  Y. Ben‐Zion,et al.  Characterization of Fault Zones , 2003 .

[47]  D. Andrews A fault constitutive relation accounting for thermal pressurization of pore fluid , 2002 .

[48]  G. Beroza,et al.  Inferring rate and state friction parameters from a rupture model of the 1995 Hyogo‐ken Nanbu (Kobe) Japan earthquake , 2001 .

[49]  J. Brune Fault-Normal Dynamic Unloading and Loading: An Explanation for "Non-Gouge" Rock Powder and Lack of Fault-Parallel Shear Bands Along the San Andreas Fault , 2001 .

[50]  Laboratory gouge friction: Seismic‐like slip weakening and secondary rate‐ and state‐effects , 2002 .

[51]  J. Rice,et al.  Crack front waves , 1998 .

[52]  J. Weertman,et al.  Unstable slippage across a fault that separates elastic media of different elastic constants , 1980 .

[53]  E. Johnson,et al.  On the initiation of unidirectional slip , 1990 .

[54]  Ronald L. Biegel,et al.  The kinematics of gouge deformation , 1987 .

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

[56]  K. Aki Characterization of barriers on an earthquake fault , 1979 .

[57]  J. D. Eshelby The elastic field of a crack extending non-uniformly under general anti-plane loading , 1969 .

[58]  F. Chester,et al.  Composite planar fabric of gouge from the Punchbowl Fault, California , 1987 .

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

[60]  Raul Madariaga,et al.  Complexity of seismicity due to highly rate‐dependent friction , 1996 .

[61]  K. Broberg On transient sliding motion , 1978 .

[62]  Gregory C. Beroza,et al.  Short slip duration in dynamic rupture in the presence of heterogeneous fault properties , 1996 .

[63]  R. Sibson Brecciation processes in fault zones: Inferences from earthquake rupturing , 1986 .

[64]  Gregory C. Beroza,et al.  Linearized inversion for fault rupture behavior: Application to the 1984 Morgan Hill, California, earthquake , 1988 .

[65]  J. R. Rice Flash heating at asperity contacts and rate-dependent friction , 1999 .

[66]  C. Wibberley,et al.  Internal structure and permeability of major strike-slip fault zones: the Median Tectonic Line in Mie Prefecture, Southwest Japan , 2003 .

[67]  J. Spray VISCOSITY DETERMINATIONS OF SOME FRICTIONALLY GENERATED SILICATE MELTS : IMPLICATIONS FOR FAULT ZONE RHEOLOGY AT HIGH STRAIN RATES , 1993 .

[68]  A. Argon,et al.  Physics of Strength and Plasticity , 1969 .

[69]  D. J. Andrews,et al.  Rupture velocity of plane strain shear cracks , 1976 .

[70]  Frederick M. Chester,et al.  Implications for mechanical properties of brittle faults from observations of the Punchbowl fault zone, California , 1986 .

[71]  Charles G. Sammis,et al.  An automaton for fractal patterns of fragmentation , 1991, Nature.

[72]  C. Wibberley Hydraulic diffusivity of fault gouge zones and implications for thermal pressurization during seismic slip , 2002 .

[73]  Paul Segall,et al.  Mechanics of discontinuous faults , 1980 .

[74]  F. Chester,et al.  Ultracataclasite structure and friction processes of the Punchbowl Fault , 1998 .

[75]  James P. Evans,et al.  Internal structure and weakening mechanisms of the San Andreas Fault , 1993 .

[76]  John R. Rice,et al.  Fault rupture between dissimilar materials: Ill-posedness, regularization, and slip-pulse response , 2000 .

[77]  J. Carlson,et al.  Rupture Pulse Characterization: Self-Healing, Self-Similar, Expanding Solutions in a Continuum Model of Fault Dynamics , 2000 .

[78]  B. Atkinson Fracture Mechanics of Rock , 1987 .

[79]  S. Ide Estimation of Radiated Energy of Finite-Source Earthquake Models , 2002 .

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

[81]  C. Sammis,et al.  The micromechanics of friction in a granular layer , 1994 .

[82]  Steven M. Day,et al.  Dynamics of fault interaction: parallel strike‐slip faults , 1993 .

[83]  J. Weeks,et al.  Roughness and wear during brittle faulting , 1988 .

[84]  The Fracture Energy of Earthquakes , 1975 .

[85]  Nobuki Kame,et al.  Effects of prestress state and rupture velocity on dynamic fault branching , 2002 .