Page 1 of 14 Analysis of time of day seismicity at mine A 19th January 2010, revised 4th June 2014 Abstract All mining-induced seismic events can be viewed as aftershocks of stope blasts, or of previous events. The classical Omori law for the decay rate of aftershocks provides a good fit to seismic data over time scales of a few seconds to 13 days after stope blasts. This result is based on analysis of seismic data from mine A were centralised face blasting was practiced. The post-blast seismicity decays to a level close to a background level after several hours and then continues to decay. Therefore, seismicity during the day shift will be minimised by delaying the re-entry time after the blast as much as is practical. This could be achieved for example by initiating the blast as soon as the stope workers are well clear of their working areas. Few development blasts go off at the same time as the face blasts. As development blasts are not formally identified in the seismic data base, their presence complicates the seismic analysis. Furthermore, more than one half of the seismic events with Magnitudes less than 2.0 are lost during the face blast period between about 18:00 and 21:00, presumably due to difficulties in associating and analysing the seismicity during periods of very high event rate. Special effort will be needed to solve this problem when the system is upgraded. Background Mine A was on a system of centralised blasting. This system was introduced to concentrate a greater proportion of seismicity into the blast window. If all blasting takes place within a few minutes in each day, then the decay of seismicity can be studied to better understand the time-dependent rock mass response to blasting and advancing the face. This report consists of an analysis of a recent event catalogue that represent seismicity at Mine A after centralised blasting was well established. Current analysis Introduction The purpose of the current analysis was to identify the times of centralised blasting from the seismic records and to study the post-blast seismic response to look towards engineering applications such as re-entry times and understanding the time response to face advance or blasting. As the exact time of initiation of the daily blast was not available, a large part of my analysis consisted of a search for the time of the daily blast. In hindsight, if the blasting times were available and a simpler analysis followed, some of the results presented here might not have been forthcoming. The analysis involves a few forms of seismic analysis such as time of day, frequency-Magnitude distributions, and aftershock behaviour. Aftershock behaviour will be studied using the Omori power law behaviour that has been shown to describe the rate of post-blast seismicity (e.g. Spottiswoode, 1990, Lynch, 2005 and Kgarume et al 2010). The Appendix shows that all mining seismicity could be considered to be aftershocks of the face advance. Page 2 of 14 Data and software development Seismic data was provided by the mine. It consisted of 81552 events recorded between 1st May 2007 and 4th December 2009 inclusive. Only the 71327 events within an on-reef square 4608 m on a side in and around the study area of Spottiswoode et al (2009) were used in this study. The spatial distribution is indicated in Figure 1. The following analysis is based on these events. Figure 1 Plan view of seismicity at mine A superimposed on the mine outlines. Symbols indicate blast sequences, as identified in this study, in blue and M>2.5 events in yellow through to red. The following is a partial list of the processing of the seismic catalogue that I performed during this study. I needed to write over 700 lines of code to achieve it. The code has sufficient documentation to make it usable for other data sets and viable for alterations where needed. The reasons for this coding will appear within this report. 1. 2. 3. 4. 5. 6. For purposes of plotting seismicity, reduce the number of smaller events; List time differences and identify temporal clusters (Type 1 sequences); Measure the spatial spread of the temporal clusters; Split the temporal clusters into spatio-temporal clusters and list for 3D plotting; List number of events by Magnitude in categories of time of day and of temporal clusters; List the maximum number of events in each day and within time windows (5, 10, 15 … 60 minutes), yielding Type 2 sequences; 7. List the inferred blast times by day of week and by hour of day; 8. Stack seismicity according to the start of Type 2 sequences; and 9. Compare blast times estimated during step 2 with those estimated during step 6. I used EXCEL to plot values in tables of derived data and MinView3D to plot seismicity. I will argue that Type 1 sequences are mostly development blasts and Type 2 sequences occur in response to face blasts. Page 3 of 14 Analysis The distribution of the number of events by Magnitude, commonly called the frequency-Magnitude distribution or Gutenberg-Richter plot, is shown for all the events in Figure 2. The seismic catalogue did not contain event Magnitudes, so Magnitudes were estimated using ML = a*log(Energy) + b*log(Moment) + c (1) where the coefficients a, b, c take recommended values of a = 0.344, b = 0.516, and c = -6.572 (Durrheim et al, 2007). Magnitude is abbreviated as M in this report. When tens of thousands of seismic events are plotted together, they appear very crowded, as seen in Figure 1. The crowding is especially acute for small Magnitude events so the number of smaller events was reduced. A factor of 10(M-4)/2 was used to reduce the number of events in the range M±0.05 as illustrated in Figure 2 and plotted spatially again in Figure 3. Freq-Mag with reduction using b=0.5 10000 b=0.5 N (M +- 0.05) 1000 all reduced 10(M-4)/2 100 b=1.0 10 1 -3 -2 -1 0 1 Magnitude 2 3 4 Figure 2 Distribution of events by Magnitude (“all”). “Reduced” has been adjusted by dividing all values by a line given by Log(N) = 2 – M/2 (equivalent to a “b” value of 0.5, or a factor of 10(M-4)/2) as shown. Figure 3 As for Figure 1 with the number of events reduced as suggested in Figure 2 Search for time of blasting: Part 1 I tried to identify the time of the centralised blasting by searching for times of high event rate. After studying the listing shown in part in Figure 4 (left), I selected an event rate of one event every 15s over nine or more events as these sustained event rates were distinctly higher during some periods than during others. As can be seen in Figure 4 (left and right), there were occasions when more than one such sequence occurred in a Page 4 of 14 day. This problem was not entirely unexpected as Kevin Riemer had noted that development blasting was often not tied in to the centralised blasting system and the seismic system recorded sequences of development blasts. The spread of each temporal cluster was measured in terms of the median inter-event distance, measured between the projections of events onto reef. As can be seen in Figure 5, there are clearly two populations, one with a spread of 100m or less that dominated the sequences that occurred between midnight (0:00) and 6:00 and then between 12:00 and 18:00. All values of median inter-event distance that exceeded 100m occurred between 18:00 and 21:00, corresponding to the peak in seismicity rate also shown in Figure 5. These temporal clusters consisted of 38% of all events and occupied only 0.30% of the total time. They contributed a negligible amount of the total amount of total seismic moment or energy release. Time to nine following events, s 1500 1000 500 0 0 5 10 15 20 Days after 2007/05/01 00:00:00 260 Cumulated number events Increasing event number Cumulated number events 2000 240 220 200 180 160 147500 148500 149500 150500 151500 Seconds after 2007/05/01 00:00:00 Figure 4 Method for selecting times of high event rate shown in text (left) and graphically (right). Right bottom is enlarged from the red box in right top. The lines at right bottom represent a high event rate that must be exceeded for 9 events or more in succession. Page 5 of 14 Space-time distributions of >= 10 event sequences spaced <=15s apart 25000 Number of events per hour hour Median inter-event distances 10000 1000 100 Distribution of all events events by by hour hour of of day day 20000 15000 10000 5000 0 0 10 00 03 06 09 12 15 18 21 6 12 Hour of day 18 21 24 00 Hour of day Figure 5 Median inter-event distributions of blast sequences (left) and distribution of all events by hour of day (right). Frequency-magnitude distributions The time and spatial variations in the clustered events as shown in Figure 5 suggests that it might be useful to divide events in terms of time clustering and space clustering. The frequency-Magnitude distributions in Figure 6 are based on these divisions: Time boundaries chosen as 6:00, 12:00, 18:00 and 21:00. Clustering with spread <=100m and spread >100m and events not included in the clusters. Figure 6 shows many distinct features: 1. The most distinctive feature is the contrast between the time-clustered data and the rest of the data at right. The time-clustered data at right showed a very sharp peak at M=-1.3 and few events with M>-0.6. The graph for all events also shows a hump at M=-1.3 that rises above the trend line marked “b=0.5”. This hump disappears when the time-clustered events are removed. 2. The peak at M=-1.3 is clearly visible in two of the time bands at left, namely {12-18} and {18-21} hours, but is not visible at time periods {21-6} and {6-12} hours. Note that there was much less time clustering at these latter times than in the two active time bands within {12-21} hours. 3. The b-value for 2.0≤M≤4.0 is about 1.0 whereas it drops to 0.5 for -0.6≤M≤2.0. 4. The b-value of 0.5 for -0.6≤M≤2.0 is very pronounced for the three time periods outside of {18-21}. However, the data for the period {18-21} hours has fewer events with M<1.3 than would be expected if b=0.5 applied. If the data fell on a perfect b=0.5 line, as sketched in the dashed red construction line then many more events would have been recorded in the hours {18-21}. In fact, 5124 were recorded whereas 11120 would have been expected for -0.6≤M≤2.0, an apparent loss of events of over 50% in this time period and Magnitude range. Page 6 of 14 10000 b=0.5 All b=0.5 1000 100 b=0.5 <100m >100m N (M+-0.05) N (M+-0.05) 1000 10000 All {6-12} {12-18} {18-21} {21-6} Time ranges in hours Not clustered Groups of >=9 events <=15s apart 100 b=1.0 b=1.0 10 10 1 1 -3 -2 -1 0 1 Magnitude 2 3 4 -3 -2 -1 0 1 Magnitude 2 3 Figure 6 Frequency-Magnitude distributions by time of day in hours and by temporal and spatial clustering The temporal clusters were then split into spatial clusters through successive agglomeration of events within 100m of one another. Despite the large values of the median inter-event distances, with many exceeding 1000m (Figure 5), the temporal clusters broke into only a few spatial sub-clusters, most often only two spatial sub-clusters, as seen in Table 1. Table 1 Distribution of spatial sub-clusters with temporal clusters Number of spatial sub-clusters per temporal cluster 1 2 3 4 Number of temporal clusters 1345 243 24 7 I now refer to these spatial sub-clusters of the temporal clusters as spatio-temporal clusters. Figure 7 Spatio-temporal clusters of events. Size scales with Magnitude and colour ranges from blue to red for increasing time. Search for time of blasting: Part 2 Part 1 of the search for the time of blasting yielded sequences of events that were spread from 12:00 to 21:00 and from 00:00 to 06:00, were spatially localised and had small Magnitudes (almost all with M<-0.6). This is the familiar pattern for development blasting and not for the seismicity that follows face blasting. The familiar pattern is normally shown as a histogram of the number of events in each hour of the day (Figure 5). 4 Page 7 of 14 I attempted to look the times of face blasting using the same approach that I used to identify the Type 1 sequences using events with M>-0.6, but without much success. I then found more success by searching for the maximum number of events with M>-0.6 within fixed time periods, namely 5, 10, 15, …, 60 minutes. Figure 8 shows the maximum number of events that took place within some of the chosen time periods in Mondays through to Fridays. Through a process of iteration and inspection, I selected the “best” estimate of the time of each daily blast to be the largest number of days within a time period while keeping the number that fall earlier than 16:00 or later than 22:00 from Monday to Friday below one percent of the total. The selection used for identifying blast times was four events within 10 minutes. 41.3% of days were not identified and 0.5% of identified times fell outside of the expected time window. The time of day distribution of types 1 and 2 estimates of blasting time is shown in Figure 9 and compared on a day to day basis in Figure 10. Frequency of occurrence of events within selected time windows Number of days 200 150 100 5 10 15 20 30 40 50 0 0 4 8 12 16 20 Maximum number within N minutes Figure 8 Histogram of the maximum number of events with M>-0.6 in each day that occurred within time periods of N=5, 10, 15, 20, 30 and 40 minutes. The arrows indicated expected tendencies for events that cluster in time. Distribution of types 1 and 2 event sequences Number of "blast" events 600 500 400 1 300 2 200 100 0 0 6 12 Hour of day 18 24 Figure 9 Time of day distribution of types 1 and 2 event sequences. Figure 10 is annotated as if the two ways of identifying blasting are sensitive to development and face blasting for types 1 and 2 respectively. The text boxes contain speculative suggestions regarding the difference in time between the development blasts and the inferred face blasting. Further discussion is provided in the Discussion below. Page 8 of 14 Cumulated percent 100 Development blasting slightly delayed after face blasting 75 Night shift development blasting ? 50 Development blasting 12:00 to 18:00 and face blasting 18:00 to 21:00 Early face blasting? 25 0 -24 -18 -12 -6 0 6 12 18 24 Blast times (face - development), hours Figure 10 Cumulated differences between the times of inferred face blasting and development blasting. Time-dependent response of seismicity to face blasting The blast times estimated in the previous section were used to stack cumulated seismicity to estimate an average behaviour of seismicity after the blasts. The stacking process was explained by Kgarume et al (2010) and by Spottiswoode (2009). Cumulated seismicity is shown below in terms of time as a linear scale on the left and as a log scale on the right. For example, data for each day of the week is shown in Figure 11. Linear and logarithmic scales were chosen to illustrate the applicability, or otherwise, of the following model for the amount of seismicity following a blast: n(t ) B K (c t ) p (2) Where n(t) = number of events per second and B, K and p are constants. The first part of Equation (2) represents a constant rate of background seismicity and the second part is the well-known Omori relationship. Kgarume et al (2010) found that the value of p at the study area was so close to 1.0 that we can assume that p=1.0. Equation (2) can then be integrated to: t n(t )dt Bt k (log 10 (c t ) log 10 (c)) 0 (3) Bt k (log 10 (1 t / c) Where k=ln(10)×K. k is preferred to K here as it can be measured directly off the linear-log plots on the right of Figure 11 and Figure 12. The numerical labels within regular pentagons in Figure 11 and Figure 12 are interpreted here as: 1. A high initial rate of seismicity at values of time t over the first few hours This appears as a log-type curve on the linear scale on the left and a straight line on the logarithmic scale at the right; 2. A constant background rate after a few hours. This appears as a straight line on the linear scale on the left and an exponential curve on the logarithmic scale at the right; 3. An accelerated rate soon before 24 hours. This is more obvious on the left-hand graphs and is caused by the next day’s blast taking place less than 24 hours after the current day’s blasts. Page 9 of 14 As can be seen in Figure 11, a c value of 40s provides a reasonably linear behaviour for the earliest post-blast events of over 2½ orders of magnitude in time (from 40s to 10 000s). This is strong support for the assumption of p = 1.0. Also note that the seismicity following blasting during each day of the week was similar, both in terms of the Omori decay and the background rate. Events as aftershocks of face advance Events as aftershocks of face advance 30 25 Cumulated events / day Cumulated events / day 30 3 20 15 Mon Wed Fri 2 10 Tues Thur Sat 1 5 20 6 12 18 24 30 36 42 Tues Thur Sat 3 15 2 10 5 0 0 Mon Wed Fri 25 1 0 48 10 Time after estimated face blast, hr 100 1000 10000 100000 40s+time after estimated face blasts, hr 1000000 Figure 11 Cumulated seismicity with time on a linear (left) and log (right) scale, stacked for each day of week. The numbers in the pentagon are explained in the text. I stacked the data further by averaging the seismicity following the blasting from Mondays to Fridays. I then followed a visual curve-fitting exercise in EXCEL by applying Equation (3) to the stacked data, as shown in Figure 12. As the first event in a sequence is assumed to be the time of the face blasts, stacking generates one event at t=0: a small correction was needed in the curve-fitting to incorporate this offset. The event rate as the slope of the modelled curves in Figure 12 is shown in Figure 13. Hours are used for the time scale for greater ease of engineering interpretation. Comparison between model & data Comparison between model & data 25 3 {Mon-Fri} Model 20 Cumulated events / day Cumulated events / day 25 15 2 10 5 1 {Mon-Fri} Model 20 15 10 5 0 0 0 6 12 18 24 10 Time after estimated face blast, hr 100 1000 10000 100000 40s+time after estimated face blasts, s Figure 12 Comparison between observed and modelled seismicity following the inferred blasting time 10000 50 Modelled event rate (M>-0.6) Modelled event rate (M>-0.6) Events/day Events/day 40 30 20 1000 100 10 10 0 0 3 6 9 12 15 18 21 24 1 0.01 Hours after face blast Figure 13 Event rate derived from modelled seismicity as shown in Figure 12 0.1 1 10 Hours after face blast 100 Page 10 of 14 To avoid any dependence of size distributions on time of day, including overcoming the difficulties posed by missed small events during the blasting period, data for M>1.0 events only is shown in Figure 14 and Figure 15. The main difference is that the Omori-type behaviour dominates the seismicity rate for longer, leading to even more benefit for lengthening the re-entry period after the face blasting. Comparison between model & data Comparison between model & data 5 {Mon-Fri} Model 4 Cumulated events M>1. / day Cumulated events M>1. / day 5 3 2 1 0 {Mon-Fri} Model 4 3 2 1 0 0 6 12 18 24 10 100 Time after estimated face blasts, hr 1000 10000 100000 30s+time after estimated face blasts, s Figure 14 Comparison between observed and modelled seismicity following the inferred blasting time, M>1.0 events only. 20 1000 Modelled event rate (M>1.0) Modelled event rate (M>1.0) 100 Events/day Events/day 15 10 5 10 1 0 0 3 6 9 12 15 18 Hours after face blast 21 24 0 0.01 0.1 1 10 Hours after face blast 100 Figure 15 Event rate derived from modelled seismicity as shown in Figure 14. Mine A stopped all production over the Easter weekend and the Christmas-New Year period each year. This gave us the opportunity to study the seismicity following blasting over longer periods than 24 hours during the week or 48 hours from Saturday to Monday. Estimated values of B and k are listed in Table 2 and post-blast seismicity over the year-end break shown in Figure 16. Table 2 Table of values of k and c for seismicity following blasting Period Days after blast 1 B, events/day k, events/decade Mondays to Fridays Number of periods stacked, or start of blast 396 3.5 7.6 Saturdays 64 2 3.5 6.5 Easter 2008 2008/03/20 16:33:02 4 1.8 1.3 Easter 2009 2009/04/09 14:56:27 5 2.6 0.75 Christmas 2007 2007/12/21 17:47:38 13 3.2 2.5 Christmas 2008 2008/12/23 17:47:19 13 2.6 1.3 Page 11 of 14 Seismicity rate around year-end break 600 Y07/09 Y08/09 600 400 Y07/09 bl bl 800 Cumulated M>-0.6 events Cumulated M>-0.6 events Seismicity rate around year-end break 1000 blasts before and after year-end break 200 Y08/09 Sunday 500 blasts before and after year-end break 0 -30 -20 -10 0 10 20 30 40 Days after break 400 -5 0 5 10 Days after break 15 20 Figure 16 Influence of the cessation of mining over the Christmas-New Year period. Discussion and Conclusions Centralised stope blasting has provided us with the opportunity of considering whether all mining-induced seismicity could be considered to be aftershocks of production blasts. Indeed, post-blast seismicity on a daily basis follows the Omori aftershock pattern (n(t) = K/(c+t)p). As previously reported by Kgarume et al (2010), the value of p is close to 1.0. This allows us to use a standard spread-sheet program (EXCEL) to plot cumulated seismicity against c+t to find a suitable value for the constant c. The constant c is a function of event Magnitude and therefore most likely to be caused by the effective Magnitude threshold being elevated at times of high event rate. This is underscored by the apparent loss of more than half of events with M<2.0 during the blasting time. When Omori’s law is studied for aftershocks of earthquakes, it is widely recognised that the constant c reflects incomplete recording of seismic events that occur within the coda waves of earthquakes. In other words, seismic networks miss many events. The situation when applying Omori’s law to stope blasting is somewhat different as the blasting can take up to many minutes to complete. Seismic events with M<-0.6 are currently unusable for understanding induced seismicity as most of them are development blasts. All mining-induced seismic events can be viewed as aftershocks of stope blasts, or of previous events. The classical Omori law for the decay rate of aftershocks provides a good fit to seismic data over time scales of a few seconds to 13 days after stope blasts. Mature mining takes place within a cloud of seismicity that is induced not only by the most recent production blasts, but also within the decay of seismicity from earlier face blasts. As the seismicity that immediately follows the face blast occurs in volumes of rock with a combination of high stress and high stress change, one would expect that further mining would move the active areas out of the aftershock zone and therefore that this zone would only exist for a limited amount of time. It is perhaps surprising that this could be as long as several months, as suggested by the amount and character of seismicity that takes place during the end-ofyear break. Recommendations The post-blast seismicity decays to a level close to a background level after several hours and then continues to decay. Therefore, seismicity during the day shift will be minimised by delaying the re-entry time after the blast as much as is practical. This could be achieved for example by initiating the blast as soon as the stope workers are well clear of their working areas. Any investment in improving the seismic network needs to be used to overcome the problems of event loss and misidentification of events. Page 12 of 14 References Durrheim, R.J., Cichowicz, A., Ebrahim-Trollope, R., Essrich, F., Goldbach, O., Linzer, L., Spottiswoode, S.M., Stankiewicz, T. and van Aswegen, G. (2007) Minimising the Rockburst Risk (Phase 2): Output 3 - Guidelines, Standards and Best Practice for Seismic Hazard Assessment and Rockburst Risk Management, Safety in Mines Research Advisory Committee, Final Project Report, 6 March 2007 Kgarume, T.E., Spottiswoode, S.M. and Durrheim, R.J. (2010) Statistical properties of mine tremor aftershocks, Pageoph Special Issue: Induced Seismicity. Lynch, R.A. (2005) Proactive approaches to rock mass stability and control, MHSC final report for project SIM 02 03 02. SM Spottiswoode. (2000) Aftershocks and foreshocks of mine seismic events. 3rd international workshop on the application of geophysics to rock and soil engineering, GeoEng2000, Melbourne Australia. Spottiswoode, S.M., Linzer, L.M. and Majiet, S. (2008) Energy and stiffness of mine models and seismicity, Accepted by 1st Southern Hemisphere International Rock Mechanics Symposium, Perth, Australian Centre of Geomechanics, 16-19 September 2008, pp693-707. Spottiswoode, S.M., Milev, A., Linzer, L.M. and Majiet, S. (2009) Evaluation of the design criteria of Regularly Spaced Dip Pillars (RSDP) based on their in-situ performance, Final Project Report for Mine Health and Safety Council, contract SIM 04 03 01. Page 13 of 14 Appendix: Are all mine events aftershocks of blasting or of one another? In the main body of the report, seismicity was accurately modelled as a constant background level superimposed on Omori power-law behaviour after the daily face blast. What is source of the “constant background level”? This Appendix will consider whether the background seismicity could be the tails of Omori-type seismicity rate. Equation (3) can be rewritten and extended, as shown in Equation (4), to represent seismicity following many days cumulated seismicity. t n n(t )dt k n (log 10 (1 (t n 24hrs) / c)) log 10 (1 n 24hrs / c)) (4) n 0 0 Where n=0 represents today and n>0 is earlier days, kn is set as 10.0 when there has been a blast on day n and set as zero if no blast has occurred, and c = 20s. The second term of Equation (4) removes all the seismicity up until the moment before today’s blast. The effect of previous days blasting is shown in Figure 17 in which the modelled seismicity following 16 powers of two ( 1 to 32768). Figure 17 illustrates the short-term and long-term behaviour of Equation (4) that matches the data: At short times, cumulated seismicity increases as the logarithm of t+c at small times (t <~one hour) as illustrated in Figure 17 (right) while cumulated seismicity increases approximately lineally at long times (t >~three hours) (Figure 17, left). The approximate linearity at long times is underscored when the difference between the first and last day in is taken (Figure 17, left). Effect of long-term Omori response Effect of long-term Omori response 200 200 Cumulated events per day 160 140 1 year 120 1 month 100 1 week 1 day 80 60 40 ear 90 y 20 s- firs y t da Cumulated events per day 90 years 180 90 years 180 160 140 1 year 120 1 month 100 1 week 80 1 day 60 40 20 0 0 0 6 12 18 24 1 10 Hours after blast 100 1000 10000 100000 seconds after blast Figure 17 Application of equation (4) for power of two in the number of days (n). I now extend the comparison between observed and modelled seismicity over the normal 24-hour production cycle to the end-of year break. The upper part of Figure 18 is copied from Figure 16 to allow visual comparison with modelled seismicity when a 10-day break is taken after 900 days of mining. Two characteristics not observed during normal production are seen to be in common between the observed and modelled curves in Figure 18: 1. The rate of seismicity slows down by a similar amount; and 2. The rate of seismicity after the break is slightly less than before the break. Page 14 of 14 Seismicity rate around year-end break 600 Y07/09 Y08/09 800 600 400 Y07/09 bl bl Cumulated M>-0.6 events Cumulated M>-0.6 events Seismicity rate around year-end break 1000 blasts before and after year-end break 200 0 500 blasts before and after year-end break 400 -30 -20 -10 0 10 20 30 40 -5 0 5 10 Days after break Days after break 8000 6000 4000 2000 Events 15 20 4200 Long break and Sundays Cumulated seismicity Cumulated seismicity Y08/09 Sunday bl Sunday Long break and Sundays 3800 3400 3000 Events bl Sunday 2600 0 0 10 20 30 40 Days 50 60 70 25 30 35 40 45 Days Figure 18 Influence of the cessation of mining over the Christmas-New Year period (above) and seismicity modelled using the Omori law following daily blasts over 100 days (below).