Dynamic ruptures in recent models of earthquake faults.pdf

Journal of the Mechanics and Physics of Solids 49 (2001) 2209–2244 /locate/jmps Dynamic ruptures in recent models of earthquake faults Yehuda Ben-Zion ? Department of Earth Sciences, University of Southern California, Los Angeles, CA 90089-0740, USA Abstract We discuss several problems of dynamic rupture relevant to mechanics of earthquake faults, material sciences, and physics of spatially extended dissipative systems. The problems include dynamic rupture along an interface separating di0erent elastic solids, dynamic rupture on a pla- nar surface governed by strongly velocity-weakening friction, and elastodynamic calculations of long deformation history on a smooth fault in an elastic continuum. These separate problems share a number of methodological and conceptual issues that form recurring themes in the pa- per. An important methodological issue for computational schemes is dependency of numerical results on the used grid size. This arises inevitably in computer simulations when the assumed constitutive laws do not include a length scale (e.g., of shear or extensional displacement) over which material properties evolve. Such simulations do not have a stable underlying solution, to which they may converge with su3cient grid re4nement. However, they may provide rough approximations—lacking at present a rigorous foundation—to the behavior of systems containing elements of discreteness (associated with abrupt 7uctuations) at scales relevant to observations of interest. Related important conceptual issues are connections between, or when appropriate separation of, small scale phenomena (e.g., nucleation of rupture, processes at rupture front) and large scale features of the response (e.g., overall space–time dimensions of rupture, statistics of many events). Additional recurring conceptual topics are crack vs. pulse modes of dynamic rupture, the stress under which earthquake faults slip, and the origin of spatio-temporal com- plexities of earthquakes. These seemingly