Comment on “The wrinkle-like slip pulse is not important in earthquake dynamics” by D. J. Andrews and R. A. Harris

Abstract

[1] Andrews and Harris [2005] (hereinafter referred to as AH) found in several numerical simulations that effects associated with prescribed stress heterogeneities and timeweakening friction can suppress those generated dynamically by rupture on a bimaterial interface, and concluded that the wrinkle-like rupture mode is generally not important for earthquake dynamics. Their results are based on selective cases, rather than a systematic parameter-space study, and they do not form the basis for a general conclusion. Moreover, most of their cases are associated with conditions for which the bimaterial effects are weak due to combination of assumed parameter values, mixed rupture modes, relatively small propagation distance, and coarse grid. Considerations of a larger body of theoretical results and observations suggest that the wrinkle-like rupture may be relevant to earthquake dynamics. [2] Weertman [1980] showed analytically that mode II slip pulse on a bimaterial interface governed by Coulomb friction produces dynamic changes of normal stress that depend on the slip function, material properties and direction of rupture propagation. Subsonic propagation in the direction of slip of the compliant solid reduces dynamically the normal stress, whereas propagation in the opposite direction increases the normal stress. Adams [1995] showed analytically that mode II rupture on a bimaterial Coulomb interface has a strong dynamic instability that transfers energy during propagation to shorter wavelengths, leading to pulse sharpening and increasing slip velocity with propagation distance. The discussed effects are pure mode II phenomena on a bimaterial interface, and they do not exist for mode III rupture or in a homogeneous solid. For additional theoretical background, see Ranjith and Rice [2001] and Ben-Zion [2001]. [3] The analytical properties of mode II slip pulse on a bimaterial interface render numerical simulations of such rupture highly challenging. Very fine grid is needed to capture the sharp features associated with the pulse, while large propagation distance is required to reach a dynamic regime that is relatively free of initial transients and reflects the attractor of the evolving dynamic behavior. Andrews and Ben-Zion [1997] simulated mode II ruptures on a bimaterial Coulomb interface with a nucleation consisting of a localized stress drop having a favored propagation direction. They observed wrinkle-like slip pulses with properties compatible to the analytical results of Weertman and Adams. Similar pulses were found in subsequent simulations with increasing refinements and incorporation of additional physical ingredients, including a nucleation mechanism that generalizes the procedure of Andrews and Ben-Zion to a symmetrically expanding source without a preferred direction and slip-weakening friction [Shi and Ben-Zion, 2006]. [4] An assessment of the possible relevance of the wrinkle-like pulse to earthquake dynamics should focus on situations associated with mode II ruptures. Important such cases are large earthquakes on plate-bounding strikeslip faults. These earthquakes (referred to below as the ‘‘target’’ earthquakes) saturate the seismogenic zone, propagate predominately as mode II rupture, and are likely to be affected primarily by the elastic properties of the bounding crustal blocks (rather than the myriad of possible smallscale heterogeneities). As discussed below, the simulations of AH address in a rather limited way the dynamics of the large target earthquakes.