Reply to comment by Y. Ben‐Zion on “Material contrast does not predict earthquake rupture propagation direction”

[1] Normal stress perturbations near the tip of a propagating mode II rupture along a bimaterial interface can introduce asymmetries in the rupture velocity and/or the slip-velocity function. In an informative theoretical study, Andrews and Ben-Zion [1997] demonstrated through numerical simulations that, for a constant coefficient of friction, these asymmetries can lead to emergence of a self-sustaining unilaterally propagating slip pulse. They called the phenomenon the ‘‘wrinkle pulse. ’’ The Andrews and Ben-Zion [1997] simulations are for a simplified dynamics in which the friction coefficient never weakens at or following the onset of sliding. This allowed the asymmetrical wrinkle pulse to dominate the dynamics, leading to unilateral rupture in the simulations. [2] The existence of the wrinkle pulse phenomenon itself is not in question here. Indeed, the wrinkle-pulse phenomenon plays an important part in our own bimaterial rupture simulations [Harris and Day, 1997, 2005], and we performed our own analytical study of slip-induced normal-stress perturbations to explain asymmetries in those simulations [Harris and Day, 1997]. The utility of the wrinkle-pulse concept is also clear in the work of A. M. Rubin and J.-P. Ampuero (Aftershock asymmetry on a bimaterial interface, submitted to J. Geophys. Res., 2006, hereinafter referred to as Rubin andAmpuero, submittedmanuscript, 2006), who use it to suggest a mechanism to explain the existence of asymmetric aftershock distributions [Rubin and Gillard, 2000]. It might also provide all or part of the slip-velocity and stressfield asymmetry required to explain observations that damage is concentrated preferentially on one side of strike slip faults in southern California [Dor et al., 2006], as discussed by Rubin and Ampuero (submitted manuscript, 2006). The question under discussion here, however, is simply whether thewrinkle pulse effect is likely to induce unilateral rupture in large, natural earthquakes. [3] The first suggestion that it might not do so derives from the numerical simulations of Harris and Day [1997]. These simulations were for mode II rupture, just as were those of Andrews and Ben-Zion [1997], and they used a similar methodology and a similar range of seismic velocity contrasts at the interface, yet Harris and Day [1997] found bilateral rupture in all cases. The wrinkle pulse was present and induced the expected asymmetry, but did not give rise to a preferred direction of unilateral rupture propagation. [4] This difference in conclusion about the relationship of the wrinkle pulse to rupture directivity, contrary to the implication of Ben-Zion’s [2006] commentary (and the suggestion given by Shi and Ben-Zion [2006]), has nothing to do with the use of artificial viscosity to regularize the numerical solution, but rather results from radically different assumptions about the frictional physics. Andrews and Ben-Zion [1997] considered the case of a constant coefficient of friction, while Harris and Day [1997] considered a friction coefficient that drops in value following the onset of sliding. The Harris and Day numerical simulations, and all others done since then [e.g., Andrews and Harris, 2005, 2006; Harris and Day, 2005; Shi and Ben-Zion, 2006; Rubin and Ampuero, submitted manuscript, 2006] are consistent in showing bilateral rupture whenever the friction coefficient is allowed to fall to a dynamic friction value that is below the minimum required to stabilize the fault under the initial static stress conditions, that is, to below t0/s0, where t0 and s0 are the initial values of shear and normal stress. When the friction coefficient does not weaken to below t0/s0, the wrinkle pulse dominates and a unilateral rupture mode can occur, albeit with very small slips and very short rise time (of the order of milliseconds) [see Shi and Ben-Zion, 2006]; when the friction coefficient does weaken in the above sense, the rupture is invariably bilateral. [5] This conclusion holds irrespective of whether the solution is regularized by viscous loss [Harris and Day, 1997, 2005] or by the addition of memory effects to the normal-stress dependence of the shear resistance [e.g., Ranjith and Rice, 2001; Cochard and Rice, 2000; Rubin and Ampuero, submitted manuscript, 2006]. It even holds for unregularized numerical solutions [Shi and Ben-Zion, 2006], although such solutions are highly suspect (because they include wavefield components with wavelength too short to be accurately modeled by grid-based numerical methods—the resulting numerical noise is very evident in the results in Shi and Ben-Zion [2006]). Nor is the conclusion altered when 3D effects are considered [Andrews and Harris, 2005; Harris and Day, 2005]. Furthermore, laboratory experiments allow for controlled material contrasts and controlled nucleation and initial stress conditions, and so provide a test of numerical and theoretical assertions about spontaneous rupture dynamics (e.g., A. Rosakis et al., Dynamic shear rupture in frictional interfaces: Speeds, directionality, and modes, submitted to Treatise on Geophysics, edited by H. Kanamori, 2006). Laboratory experiments of spontaneous rupture propagation on a fault that is the interface between two plastics, homalite and polycarGEOPHYSICAL RESEARCH LETTERS, VOL. 33, L13311, doi:10.1029/2006GL026811, 2006 Click Here for Full Article