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 = jN 1 , where j is an activity ratio and N 1 is the measured number of events occurring during the first hour after the principal event. The average j values are in a well-defined range. Theoretically j B 0.8, and empirically j [ [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 = aN 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 [ [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.

Changes in mining‐induced seismicity before and after the 2007 Crandall Canyon Mine collapse

“…The p value statistic represents a power law aftershock decay rate as defined by the Modified Omori's law: where N ( t ) is the number of aftershocks per day, and k and c are constants [ Utsu , ]. This relation has been demonstrated to model aftershock decay rates observed for both naturally occurring and mining‐induced sequences of seismicity [ Vallejos and McKinnon , ]. A p value of 1.11 ± 0.06 (2 σ ) was computed for this catalog using ZMAP [ Wiemer , ].…”

“…A p value of 1.11 ± 0.06 (2 σ ) was computed for this catalog using ZMAP [ Wiemer , ]. According to Vallejos and McKinnon [], the median p value for 163 mining‐induced seismicity sequences observed in four Canadian hard‐rock mines was found to be 1.1, indicating close agreement. A prior study of seismicity at CCM found a p value of 0.8 ± 0.3 using only 15 events with M C > 1.6.…”

Investigation of coseismic and postseismic processes using in situ measurements of seismic velocity variations in an underground mine

“…The locations of the aftershocks stay reasonably constant over a 2 day period, and no systematic migration patterns were observed. The time distribution of the aftershocks follows Omori's law with a p value of 0.48, which seems low but is reasonable in a mine setting [ Vallejos and McKinnon , ].…”

Modelling the Dynamic Relationship Between Mining Induced Seismic Activity and Production Rates, Depth and Size: A Mine-Wide Hierarchical Model

“…For longer time periods, those of interest in this study, it has been shown that the exponential decay predominates over power-law decay (Otsuka 1985(Otsuka , 1987Souriau et al 1982) for aftershocks. Also, the decay times in this study are in the order of weeks as opposed to hours or days for major events in mines (Vallejos and Mckinnon 2010;Olivier et al 2015). Furthermore, as no single earthquake in our sequences is a main shock but the result of weakly production in the mine, the process may have a closer relation to that of earthquake swarms as opposed to aftershocks (see e.g.…”