Processes associated with earthquakes are known to occur over a wide variety of spatial and temporal scales. Figure 1 illustrates this point. For example, frictional processes, the primary nonlinearity associated with earthquakes, are known to be physically significant from the molecular scale, on time intervals of less than 10-8 seconds and lengths of Angstroms (), to plate motion scales, on time intervals of 106 years and lengths in excess of 1000 km. The physical processes directly associated with faulting and seismology, including nucleation and quasistatic crustal deformation, occur over time intervals of fractions of seconds to thousands of years, and lengths of meters to a hundreds of km. By contrast, experiments on frictional sliding of rock samples are carried out over laboratory scales extending over typical time intervals of 10-3 seconds to days, and over length scales of cm to m. Figure 1 indicates that in terms of length scales, processes of faulting, seismology and crustal deformations are as far removed from laboratory experiments on rock samples, as these laboratory rock processes are from those on the molecular scale. There are no reliable means presently available to relate results observed on one set of scales to those on another. It is therefore of critical importance to develop an experimental numerical capability that can help to span these large ranges in scales, so that the applicability of physical (and chemical) processes on one scale can be evaluated for their importance on other, distinctly different scales. An example is the need to determine whether empirical or theoretical friction laws developed to describe the nonlinearity of sliding on one temporal and spatial scale applies to sliding on other scales.
Within the region of spatial and temporal scales in figure 1 describing earthquakes (denoted ``faulting and seismology''), there exist additional ``sub-scales'' that describe additional heirarchies of processes. These include, but are not limited to, the following:
1. Individual earthquakes on a single planar fault. Processes that may be important include inertia; stress transfer via waves and comparison to quasistatic stress transfer calculations; elastic heterogeneity at small scales (elastic wave scattering); quasistatic and dynamic friction; the pore fluid flow; and wearing and evolution of the sliding surface. Important to have friction models for both the quasistatic and dynamic regimes based upon velocity-, slip-, or rate and state-weakening processes.
Time Scales: 10-1 sec to 102 sec Space Scales: 10-1 km to 102 km
2. Multiple earthquakes on several faults. Processes that may be important include quasistatic and dynamic friction; pore fluid flow; dynamic stress transfer via waves; quasistatic/static stress transfer via elasticity and viscoelasticity; earth rheology; Coulomb Failure Functions; Viscoelastic Coulomb Failure Functions; stress shadows; geometry of faults; and how faults influence one another.
Time Scales: 10 sec to 108 sec Space Scales: 10-1 km to 103 km
3. Statistics, correlations, and space-time patterns of earthquakes in large populations of earthquakes on large fault systems. Processes that may be important include quasistatic friction; pore fluid flow; quasitatic/static stress transfer; earth rheology; sub- gridscale faults (sources of noise); plate-tectonic stress loading processes; and evolution in fault geometry due to fracturing of fresh rock. Since space-time correlations in populations of earthquakes are of primary interest, only processes on time scales longer than an earthquake source time are important, because all smaller time scales are coarse-grained out of the problem. Scaling, critical phenomena and nucleation processes are clearly relevant on these time and space scale, as is obvious from observations of the Gutenberg-Richter relation, Omori's law, and so forth.
Time Scales: 102 sec to 1012 sec Space Scales: 10-1 km to 103 km
4. Physics of fault gouge formation, role of granula media in geologic structure of faults, heat flow questions. Processes that may be important include comminution; formation and mechanics of granular gouges; formation of stress ``bridges'' between sides of faults; fluid infiltration; fracturing and abrasion of intact rock; and spatial-temporal evolution of fault geometries. These processes are primarily associated with the formation of geologic fault structures, and their influence on heat flow and thermomechanics of slip.
Time Scales: 10-1 sec to 106 years Space Scales: 10-6 km to 1 km
It will clearly not be possible to address all of these problems in a single proposal, or perhaps even within a single computational or physical framework. Choices must therefore be made as to which problem(s) to address in a given proposal, and in which priority. These choices and priorities will be determined in consideration of a given funding target of opportunity.