Self-organised criticality and fluid-rock interactions in the brittle field

The concept of self-organised criticality (SOC) has recently been suggested as a paradigm for the long-term behaviour of earthquakes, even though many of the currently-proposed models require some tuning of the state variables or local conservation rules to produce the universally-observed Gutenberg-Richter frequency-magnitude distribution witha b value near 1. For example, a systematic negative correlation is predicted between modelb values and the degree of conservation of local force after the slip of a single element in an elastic spring/block/frictional slider model. A similar relation is described here for a cellular automaton model with constitutive laws based on fracture mechanics. Such systems, although critical phenomena in the sense of producing order on all scales, are clearly not universal, and may not in general even be true examples of SOC. Nevertheless they adequately reproduce both the observed power-law (fractal or multifractal) scaling and its reported short-term fluctuation.We also present experimental and field evidence for similar systematic variations inb value with the degree of force conservation (expressed in terms of a normalised crack extension force) during subcritical crack growth involving the physical and chemical influence of pore fluids during a single cycle of failure both in tension and compression. We find that the level of conservation is strongly influenced by fluid-rock interaction under stress, allowing energy partition into processes such as: physico-chemical stress corrosion reactions; the dissolution and precipitation of mineral species on crack surfaces; and the purely mechnical phenomenon of dilatant hardening. All of these are known to occur in the Earth on a local scale, but few have been explicitly included in automaton models of seismicity. The implication is that over long time periods pore fluids may exert a strong physical and chemical influence on the universal state of SOC which the system evolves in a complex interplay of local feedback mechanisms keeping the system near criticality, perhaps most strikingly due to the valve action of faults. In the short term, crustal fluids might nevertheless be responsible for systematic local fluctuations about this average state.