Positive and negative feedback in the earthquake cycIe: the role of pore fluids on states of criticality in the crust

Fluids exert a strong physical and chemical control on local processes of rock fracture and friction. For example they may accelerate fracture by stress corrosion reactions or the development of overpressure (a form of positive feedback), or retard fracture by time-dependent stress relaxation or dilatant hardening (negative feed-back), thereby introducing a variable degree of local force conservation into the process. In particular the valve action of dynamic faulting may be important in tuning the Earth to a metastable state of incipient failure on all scales over several cycles, similar to current models of Self-Organised Criticality (SOC) as a paradigm for eartiquakes However laboratory results suggest that ordered fluctuations about this state may occur in a single cycle due to non conservative processes involving fluids which have the potential to be recognised, at least in the short term, in the scaling properties of earthquake statistics. Here we describe a 2-D cellular automaton which uses local rules of positive and negative feedback to model the effect of fluids on failure in a heterogeneous medium in a single earthquake cycle. The model successfully predicts the observed fractal distribution of fractures, with a negative correlation between the predicted seismic b-value and the local crack extension force G. Such a negative correlation is found in laboratory tests involving (a) fluid-assisted crack growth in tension (b) water-saturated compressional deformation, and (c) in field results on an intermediate scale from hydraulic mining-induced seismicity all cases where G can be determined independently, and where the physical and chemical action of pore fluids is to varying degrees a controlled variable. For a finite local hardening mechanism (negative feedback), the model exhibits a systematic increase followed by a decrease in the seismic b-value as macroscopic failure is approached, similar to that found in water-saturated laboratory tests under controlled «undrained» conditions, and where dilatancy hardening is independently known to be a local mechanism of negative feedback. A similar pattern is suggested from selected field observations from natural seismicity, albeit with a lesser degree of statistical significance