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

Abstract

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 = κN1, where κ is an activity ratio and N1 is the measured number of events occurring during the first hour after the principal event. The average κ values are in a well-defined range. Theoretically κ ≤ 0.8, and empirically κ ∈ [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 TMC at the maximum curvature point, which is a function of Omori’s law parameters. For a time sequence obeying an Omori process, TMC marks the transition from highest to lowest event rate change. Using solely the aftershock decay rate, therefore, we recommend TMC 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 TMC can be estimated without specifying a p value by the expression: TMC = aN1b, where a and b are two parameters dependent on local conditions. Both parameters presented well-constrained empirical ranges for the sites analyzed: a ∈ [0.3–0.5] and b ∈ [0.5–0.7]. These findings provide concise and well-justified guidelines for event rate re-entry protocol development.