Precursory deformation and fracture before brittle rock failure and potential application to volcanic unrest

Small-magnitude earthquakes and ground deformation are the precursors most frequently recorded before volcanic eruptions. Analogous signals (using acoustic emissions) have also been reported before the bulk brittle failure of crustal rock in the laboratory. Models based on laboratory and field data have focused on precursory behavior during deformation under a constant stress. A new model is proposed for extending analyses to deformation under an increasing stress. It describes how precursory time series can be determined from a parent relation between fracturing and stress, together with time-dependent changes in applied stress and rock resistance. The model applies to rock in which these stresses do not interact with each other and occupy volumes much smaller than the total volume being deformed. It identifies how the amounts of fracturing observed during deformation are controlled not only by stress concentrations at macroscopic heterogeneities, such as crack tips but also by rock composition, temperature, confining pressure, and the distribution of energy among atoms. The results appear to be scale independent, and so may be used to investigate whether the approach to bulk failure is limited by changes in applied stress or in rock weakening. When applied to pre-eruptive data from Hawaii, the analysis suggests that precursory signals are controlled by an increase in applied stress, rather than by creep deformation under a constant stress.