This chapter starts with the time characteristics of seismic activity, the coefficient of variation, and proportional variability and progresses to stationary Poisson processes, probabilities of exceedance, and mean recurrence times. In this section, there are two practical examples. The first one compares seismic hazard between three mines with different volumes of rock extracted over the same time period at different depths, and it is done in the logE domain. It shows the utility of plotting the cumulative potency vs. the cumulative volume of rock extracted as an indication of seismic hazard. The second example compares the seismic hazard characteristics of two mostly overlapping seismic and rock extraction data sets selected from the same mine, and it is done in the logP domain. Having partial data on the volume of rock extraction, it postulates that apart from increasing extraction ratio, the more concentrated production blasting at greater depth may have contributed to the observed increase in seismic hazard. The rest of this chapter is dedicated to the seismic rock mass response to step loading, mainly by production blasting and by larger seismic events. Seismic rock mass response to blasting is driven strongly by the stress level in rock surrounding the blast and by the volume of rock blasted. In most cases, rock extraction by blasting induces and triggers seismic events immediately and in close proximity to the blast. In some cases, the rate of activity follows typical aftershock sequences that can be described by the simple Omori law or by the stretched exponential relaxation function. Here, the non-stationary Poisson process needs to be invoked to assess the probabilities of having larger events during the aftershock sequences. Two examples of seismic hazard assessment after large events are presented. In practice, mines frequently group blasts to optimise the required exclusion time after blasting. It is important then to schedule blasting sequences to limit the overlap of seismic relaxation. If larger blasts are too frequent and/or too close to each other, i.e. if the next blast is still during the excitation phase of the previous one, it may push a larger and larger part of the system into the sub-critical stage. There is also the possibility that such blasting may induce a larger seismic event that would not have happened otherwise, as opposed to advancing the clock for events that are almost ready to be triggered. This issue is addressed in the section Seismic Rock Mass Response and Blasting Sequence, where the defined proximity index may help to test whether the preferred time differences and distances between blasts sequence of a planned sequence are at an acceptable level.

Time Distribution and Seismic Hazard

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2025年

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Aleksander J. Mendecki

摘要

This chapter starts with the time characteristics of seismic activity, the coefficient of variation, and proportional variability and progresses to stationary Poisson processes, probabilities of exceedance, and mean recurrence times. In this section, there are two practical examples. The first one compares seismic hazard between three mines with different volumes of rock extracted over the same time period at different depths, and it is done in the logE domain. It shows the utility of plotting the cumulative potency vs. the cumulative volume of rock extracted as an indication of seismic hazard. The second example compares the seismic hazard characteristics of two mostly overlapping seismic and rock extraction data sets selected from the same mine, and it is done in the logP domain. Having partial data on the volume of rock extraction, it postulates that apart from increasing extraction ratio, the more concentrated production blasting at greater depth may have contributed to the observed increase in seismic hazard. The rest of this chapter is dedicated to the seismic rock mass response to step loading, mainly by production blasting and by larger seismic events. Seismic rock mass response to blasting is driven strongly by the stress level in rock surrounding the blast and by the volume of rock blasted. In most cases, rock extraction by blasting induces and triggers seismic events immediately and in close proximity to the blast. In some cases, the rate of activity follows typical aftershock sequences that can be described by the simple Omori law or by the stretched exponential relaxation function. Here, the non-stationary Poisson process needs to be invoked to assess the probabilities of having larger events during the aftershock sequences. Two examples of seismic hazard assessment after large events are presented. In practice, mines frequently group blasts to optimise the required exclusion time after blasting. It is important then to schedule blasting sequences to limit the overlap of seismic relaxation. If larger blasts are too frequent and/or too close to each other, i.e. if the next blast is still during the excitation phase of the previous one, it may push a larger and larger part of the system into the sub-critical stage. There is also the possibility that such blasting may induce a larger seismic event that would not have happened otherwise, as opposed to advancing the clock for events that are almost ready to be triggered. This issue is addressed in the section Seismic Rock Mass Response and Blasting Sequence, where the defined proximity index may help to test whether the preferred time differences and distances between blasts sequence of a planned sequence are at an acceptable level.