Omori's Law Applied to Mining-Induced Seismicity and Re-entry Protocol Development

This paper describes a detailed study of the Modified Omori's law n(t) = K/(c + t) (p) applied to 163 mining-induced aftershock sequences from four different mine environments in Ontario, Canada. We demonstrate, using a rigorous statistical analysis, that this equation can be adequately used to describe the decay rate of mining-induced aftershock sequences. The parameters K, p and c are estimated using a uniform method that employs the maximum likelihood procedure and the Anderson-Darling statistic. To estimate consistent decay parameters, the method considers only the time interval that satisfies power-law behavior. The p value differs from sequence to sequence, with most (98%) ranging from 0.4 to 1.6. The parameter K can be satisfactorily expressed by: K = kappa N (1), where kappa is an activity ratio and N (1) is the measured number of events occurring during the first hour after the principal event. The average kappa values are in a well-defined range. Theoretically kappa a parts per thousand currency sign 0.8, and empirically kappa a [0.3-0.5]. These two findings enable us to develop a real-time event rate re-entry protocol 1 h after the principal event. Despite the fact that the Omori formula is temporally self-similar, we found a characteristic time T (MC) at the maximum curvature point, which is a function of Omori's law parameters. For a time sequence obeying an Omori process, T (MC) marks the transition from highest to lowest event rate change. Using solely the aftershock decay rate, therefore, we recommend T (MC) as a preliminary estimate of the time at which it may be considered appropriate to re-enter an area affected by a blast or large event. We found that T (MC) can be estimated without specifying a p value by the expression: T (MC) = a N (1) (b) , where a and b are two parameters dependent on local conditions. Both parameters presented well-constrained empirical ranges for the sites analyzed: a a [0.3-0.5] and b a [0.5-0.7]. These findings provide concise and well-justified guidelines for event rate re-entry protocol development.