Dynamic ruptures in recent models of earthquake faults

We discuss several problems of dynamic rupture relevant to mechanics of ear thquake faults, material sciences, and physics of spatially extended dissip ative systems. The problems include dynamic rupture along an interface sepa rating different elastic solids., dynamic rupture on a planar surface gover ned by strongly velocity-weakening friction, and elastodynamic calculations of long deformation history on a smooth fault in an elastic continuum. The se separate problems share a number of methodological and conceptual issues that form recurring themes in the paper. An important methodological issue for computational schemes is dependency of numerical results on the used g rid size. This arises inevitably in computer simulations when the assumed c onstitutive laws do not include a length scale (e.g., of shear or extension al displacement) over which material properties evolve. Such simulations do not have a stable underlying solution, to which they may converge with suf ficient grid refinement. However, they may provide rough approximations-lac king at present a rigorous foundation-to the behavior of systems containing elements of discreteness (associated with abrupt fluctuations) at scales r elevant to observations of interest. Related important conceptual issues ar e connections between. or when appropriate separation of, small scale pheno mena (e.g., nucleation of rupture, processes at rupture front) and large sc ale features of the response (e.g., overall space-time dimensions of ruptur e, statistics of many events). Additional recurring conceptual topics are c rack vs. pulse modes of dynamic rupture, the stress under which earthquake faults slip, and the origin of spatio-temporal complexities of earthquakes. These seemingly different issues probably have one or more common origins. Dynamic rupture on an interface between different solids. strongly velocit y-weakening friction on a homogeneous fault, and strong fault zone heteroge neities can all produce narrow self-healing slip pulses with low dynamic st ress (and low associated frictional heat) during the active part of slip. S trong fault heterogeneities probably play the dominant role in producing th e observed earthquake complexities, Improved understanding of the discussed problems will require establishing connections between discrete and contin uum descriptions of mechanical failure processes, generalization of current models to realistic three-dimensional dynamic models, and high-resolution laboratory and in-situ observations over broad scales of space and time. Th ese challenging problems provide by their subject matter and involved great difficulties important targets for multi-disciplinary research by engineer s, earth scientists, and physicists. (C) 2001 Elsevier Science Ltd. All rig hts reserved.