Omori’s Law Applied to MiningInduced Seismicity a

Authors: J A Vallejos S D McKinnon

Publish Date: 2009/12/22

Volume: 167, Issue: 1-2, Pages: 91-106

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Abstract

This paper describes a detailed study of the Modified Omori’s law nt = K/c + t p applied to 163 mininginduced 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 mininginduced 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 powerlaw behavior The p value differs from sequence to sequence with most 98 ranging from 04 to 16 The parameter K can be satisfactorily expressed by K = κN 1 where κ is an activity ratio and N 1 is the measured number of events occurring during the first hour after the principal event The average κ values are in a welldefined range Theoretically κ ≤ 08 and empirically κ ∈ 03–05 These two findings enable us to develop a realtime event rate reentry protocol 1 h after the principal event Despite the fact that the Omori formula is temporally selfsimilar 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 reenter 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 wellconstrained empirical ranges for the sites analyzed a ∈ 03–05 and b ∈ 05–07 These findings provide concise and welljustified guidelines for event rate reentry protocol developmentWe would like to thank two anonymous referees for their critical reviews which led to improvements in the manuscript This research was supported by a grant from the Workplace Safety and Insurance Board WSIB of Ontario The authors wish to acknowledge the permission of the four mines studied to publish this work

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