A SEARCH FOR SEQUENCES OF MINING-INDUCED SEISMIC EVENTS AT THE

A C T A G E O P H Y S I C A P O L O N I C A

Vol. 52, No. 2 2004

A SEARCH FOR SEQUENCES OF MINING-INDUCED SEISMIC EVENTS

AT THE RUDNA COPPER MINE IN POLAND

Grzegorz KWIATEK

Institute of Geophysics, Polish Academy of Sciences ul. Księcia Janusza 64, 01-452 Warszawa

e-mail: [email protected]

A b s t r a c t

A detailed analysis of the Rudna copper mine’s seismic catalogue for 1980-2003, with a threshold local magnitude ML ≥ 1.3, allowed to distinguish several types of event sequences related to 345 stronger mining events of magnitude greater than 3.0. Events without aftershocks and foreshocks were observed as well as those where the number of aftershocks numbered more than ten, while foreshocks – several. Foreshocks were recorded for 58 events, nearly all of them several tens of minutes before the main seismic event. Aftershocks accompanied the 190 strongest events; the greatest number of aftershocks was 10 for an event of magnitude just over 3.0. For the two strongest events, of magnitudes ML = 4.1 and ML = 4.2, the number of aftershocks was radically different, 9 and 1, respec-tively. Different numbers of aftershocks were observed depending on the loca-tion of the main event in various mining areas, which is related to the differences in the seismicity of individual zones within the mine.

Non-parametric probability distribution functions of magnitude have been determined for the different seismogenic zones. In addition, the value of the b coefficient of the Gutenberg-Richter relation has been analyzed for each zone. These studies confirmed that seismicity varies within the mine.

Key words: aftershocks, foreshocks, seismic sequences, seismic hazard, b-value estimator.

mailto:[email protected]

G. KWIATEK 156

1. INTRODUCTION

Only a small part of studies on seismic event sequences concerns regions of mining -induced seismicity. For example, Gibowicz et al. (1979) analyzed the event of March 24, 1977, of magnitude ML = 4.5 at the Lubin copper mine in Poland. A total of 136 aftershocks of magnitude ML > –0.3 were recorded during two days after the main event. More than 30 of them were located, and their distribution was in good agree-ment with the plane of the main fault. The p coefficient of Omori’s law, describing the decreasing number of aftershocks with increasing time elapsed from the main shock, was approximately equal to 1.

In the Western Deep Levels gold mine in South Africa, four sequences of after-shocks were recorded by the local seismometric network (Gibowicz, 1997). These sequences overlapped, and lasted a total of 12 days. A total of 199 aftershocks with seismic moment magnitude MW ranging from –0.5 to 3.1 were recorded. The p coeffi-cient from Omori’s law ranged from 0.7 to 1.0.

Buben and Kozák (1999) studied sequences of events from the Kladno-Mayrau coal mine in the Czech Republic. They noted their great diversity: from single events, through events with one or several aftershocks, doublets, to swarm sequences.

McGarr and Green (1978) analyzed sequences of events related to two mining -induced events from the East Rand Propriety Mine in South Africa. A total of more than 140 aftershocks were recorded during the first hour from each of the events. In both cases, the decrease in the number of aftershocks with time was similar, but these shocks differed in that one of them was preceded by a more than seven-fold increase in seismic activity prior to the event.

A small number of aftershocks and a generally lower level of seismic activity af-ter the main shock was observed for the event of magnitude ML = 4.3 recorded at the Lubin mine on June 20, 1987 (Gibowicz et al., 1989). During one month after the main shock, only a few weak aftershocks occurred. This event is in obvious contrast to the event of March 24, 1977, mentioned earlier.

Such varied rock mass behaviour and the variety of event sequences it generates could be related to the specific character of mining-induced seismicity and to the mechanism generating such events. In natural seismicity, in the great majority of cases, the energy related to existing tectonic stress is released. In induced seismicity, the view is that, for example, the seismicity of mining regions could be the combined effect of accumulation of stress resulting from mining activity and its interaction with the regional stress field (Kijko et al., 1987). The most extreme example of such a dual-ity of mechanism could be the multi-modality of the Gutenberg-Richter relation distri-bution: the existence of several distribution modes. It is also possible that the bimodal-ity or multi-modality of distributions resulting from a specific mechanism could be caused by the activation of new and independent seismicity-generating processes, e.g., due to sudden changes of rock-mass properties or mining intensity (Gibowicz and Kijko, 1994).

MINING-INDUCED SEISMIC EVENTS AT RUDNA 157

The aim of the present study is the identification, as best as possible, of existing event sequences related to seismicity induced by the mining operations at the Rudna mine located in the Lubin-Głogów Copper Region. The analysis is based on the mine’s seismic catalogue for the years 1980-2002. Any apparent differences in se-quences depending on the location of the main event or on the time of its occurrence have also been studied.

2. DATA

The Rudna mine’s seismic network is composed of 32 vertical Wilmore MK-II and MK-III seismometers. Most of the seismometers are located within the mined depos-its, with a few placed in the mine shafts. Seismic signals in analogue form are trans-mitted to a central station on the surface. The signals are then digitized with a fre-quency of 500 Hz by a 14-bit converter. The seismometers have a flat frequency re-sponse in the range from 0.5 to 150 Hz; the system’s dynamics does not exceed 70 dB (Domański et al., 2002).

The seismic catalogue covering the period from January 1, 1980, to March 3, 2002, was selected for analysis. The catalogue contains a total of 15,573 events with a maximum local magnitude ML = 4.2 (seismic energy ≈ 2×109J). Not all the seismic events in the catalogue have been located. The unlocated events with high magnitude were the rock mass response to blasting, and for these events location attempts were not undertaken during data processing by the mine’s seismic station.

The completeness threshold of the seismic catalogue was estimated from the fre-quency-magnitude relation shown in Fig. 1. Consequently, as a result of the break-down of the Gutenberg-Richter relation below the magnitude ML = 1.3, further analy-sis was continued on the remaining 12,983 events.

Fig. 1. The number of seismic events as a function of magni-tude for the period 1980-2002. The total number of events N = 15,573.

G. KWIATEK 158

3. THE CATALOGUE’S DIVISION INTO SEISMIC ZONES

Because the seismicity of the Rudna mine varies depending on the time and area of mining operations, which could influence the character of event sequences, the whole seismic catalogue was divided into groups called seismic zones, with the help of the space-time criteria (Orlecka and Lasocki, 2002). The surface distribution of event epicenters was studied first (Fig. 2). The visible concentration of events into clusters with a limited surface range is related to the chamber and pillar method of mining the copper deposits and the generation of shocks in the areas of mining operation.

Fig. 2. Surface distribution of epicenters of seismic events in 14 clusters corresponding to the areas.

The fact that the events were grouped in specific places allowed for the initial identification of 11 groups of events. Each of these groups was analyzed with respect to the seismic event frequency distribution. On this basis, the catalogue was divided further by means of dividing the groups where the mean seismic activity λ , under-stood as the number of events per unit of time, is homogeneous. This kind of division was aimed at ensuring a relatively uniform seismicity within each group. The events whose location was unknown were added to specific zones using the event date and the mining section identifier which defines the approximate location of the event. Ul-timately, 14 zones were identified (Fig. 2, Table 1), some of which are clearly sepa-rated in space-time terms. Two zones (2, 14) are not well identified in terms of event location (they overlap with zones 1 and 8), but they are easy to separate using the time


criterion (cf. Table 1). Table 1 lists the number of events in particular ranges of local magnitude value, including the events below the catalogue threshold. Table 2 lists the mean seismic activity, calculated both for all the events and the located events, the maximum observed magnitudes for a given zone and the average number of events in a given zone observed in the course of 2 days. Additional information includes the number of events above the local magnitude ML = 3.0, the percentage of the number of such events in relation to all events in a given zone, and the values of the maximum observed and estimated magnitude. All these elements will be explained in detail be-low. The greater number of unlocated events in zones 1, 7 and 10 could be addition-ally related to the lower quality of the seismometric network in the years 1980-1990.

Table 1

The number of events divided into 7 magnitude intervals for 14 seismic clusters. Full explanation is given in the text

Number of events Seismic

zone Time interval ML < 1.3 ML ≥ 1.3

ML < 1.8 ML ≥ 1.8 ML < 2.3

ML ≥ 2.3 ML < 2.8

ML ≥ 2.8 ML < 3.3

ML ≥ 3.3 ML < 3.8 ML ≥ 3.8 Total

1 1 Jan 1980 – 20 Oct 1990 403 1702 345 126 82 6 – 2664

2 since 22 Feb 1994 63 130 92 39 21 2 – 347

3 since 20 Nov 1984 374 1286 506 169 49 18 – 2402

4 12 May 1998 – 26 Feb 2000 44 25 21 16 1 – – 107

5 since 19 Apr 1986 297 923 370 179 60 19 – 1848

6 since 28 Mar 1988 106 236 93 33 21 3 – 492

7 10 Dec 1983 – 10 Feb 1994 122 360 30 12 1 – – 525

8 since 21 Apr 1996 23 65 39 32 19 6 1 185

9 since 4 Apr 1985 165 712 126 61 29 17 2 1112

10 14 Nov 1981 – 23 Oct 1992 333 1234 135 85 60 4 – 1851

11 since 26 Nov 1999 83 196 132 55 41 6 – 513

12 since 3 Jan 1980 569 1677 690 365 132 21 2 3456

13 21 Jan 1994 – 15 Apr 2001 5 21 11 4 11 1 – 53

14 1 Apr 1993 – 24 May 1994 3 6 3 2 1 3 – 18

Total number 2590 8573 2593 1178 528 106 5 15573

G. KWIATEK 160

4. PRELIMINARY ANALYSIS OF THE CATALOGUE

First of all, the level of seismicity in the identified seismogenic zones was estimated in order to provide an idea as to the frequency of the events in specific magnitude ranges. The average event return period T(ML), known from probabilistic seismic hazard analysis, was used

( )

1( )1 ( )L

L

T MF Mλ

=−

, (1)

which means the average time interval between events of magnitude MLF is the cumu-lative distribution function (CDF) of the magnitude determined for a given zone, and λ denotes the mean seismic activity for a given group of events.

Relation (1) shows that knowledge of the probability distribution function (PDF) of magnitude and its CDF (e.g., Orlecka-Sikora and Lasocki, 2002) is of key impor-tance for the obtained values of mean return period. In studies of natural seismicity, the Gutenberg-Richter distribution with parameter b, modified by an upper and lower limit on the magnitude, can be applied. For mining-induced seismicity, the relation of the logarithmic decrease of the number of events with increasing magnitude is gener-ally not preserved, and the distribution itself can be bi- or multi-modal (Kijko et al., 1987), as the superposition of two (or more) components of low- and high-energy. As one of the reasons for this inhomogeneous distribution, Gibowicz and Kijko (1994) mention the complex geological structure (faults, dykes, rock layers with their own elasticity parameters), and the stress-generating phenomena (mining operations, natu-ral tectonic stress).

In view of the above distribution limitations, the non-parametric estimator of CDF has been used (Kijko et al., 2001) together with the adaptation kernel (Lasocki, 2001), where the sought CDF takes the form:

( )

min

min

1 min max

max min

1

max

0 for

ˆ for ,

1 for

L L

i inL L L L

i iiL L L Li in

L L L L

i ii

L L

M M

M M M Mh h

F M M M MM M M M

h h

M M

Φ Φα α

Φ Φα α

=

=

⎧ <⎪⎪ ⎡ ⎤⎛ ⎞ ⎛ ⎞− −

−⎪ ⎢ ⎥⎜ ⎟ ⎜ ⎟⎪ ⎝ ⎠ ⎝ ⎠⎣ ⎦= ≤⎨

⎡ ⎤⎛ ⎞ ⎛ ⎞− −⎪ −⎢ ⎥⎜ ⎟ ⎜ ⎟⎪ ⎝ ⎠ ⎝ ⎠⎣ ⎦⎪⎪ >⎩

∑

∑≤ (2)

where is the magnitude threshold, is the unknown upper limit of the mag-nitude range, Φ(·) is the standard Gaussian CDF, and the coefficient h, called the smoothness parameter, is chosen according to the MISE criterion – minimization of the average integral square error (Kijko et al., 2001). The coefficients α

minLM max

LM

i modify the shape of Φ(·) so that individual observations (in higher magnitude ranges) have a


greater influence on the shape of the CDF estimator. To determine the unknown upper limitation on the magnitude, the following estimator is proposed (Kijko and Graham, 1998):

(3) ( ),max

,min

,max ,maxˆ d

obsL

L

Mnobs

L L LM

M M f M M= + ⎡ ⎤⎣ ⎦∫ ,L

where is the maximum observed magnitude in a given seismogenic zone. ,maxobsLM

The calculated estimators of maximum magnitude and mean return period T(ML) for events of magnitude ML ≥ 3.0 are listed in Table 2. These parameters have not been calculated for zones 4, 13 and 14 because the analysis was carried out for zones in which the number of events exceeded 250. The only exception is zone 8, for which further calculations were important, as it seems to be characterized by strong seismic-ity and a relatively high share of events of magnitudes exceeding ML = 3.0.

Table 2

Results of statistical analysis of seismicity in 14 clusters

Seis

mic

zon

e

Tota

l num

ber o

f ev

ents

(abo

ve

the

thre

shol

d)

Mea

n ac

tivity

λ

Mea

n nu

mbe

r of

eve

nts p

er

2 da

ys

h fa

ctor

Max

imum

ob

serv

ed m

ag-

nitu

de

Max

imum

es

timat

ed m

ag-

nitu

de

Mea

n re

turn

pe

riod

Estim

ated

b-

valu

e

Num

ber o

f ev

ents

M

L>3.

0 Pe

rcen

t of

even

ts

ML>

3.0

Num

ber o

f ev

ents

(lo

cate

d, a

bove

th

e th

resh

old)

Perc

enta

ge o

f un

loca

ted

even

t

1 2261 0.58 1.2 0.02 3.52 3.61 3.42 1.16±0.02 41 1.8 858 62

2 284 0.10 0.2 0.06 3.64 3.75 6.49 0.67±0.04 14 4.9 226 20

3 2028 0.32 0.6 0.03 3.65 3.82 5.39 0.92±0.02 38 1.9 1464 28

4 63 0.05 0.1 – 3.01 – – – 1 1.6 58 8

5 1551 0.27 0.5 0.03 3.66 3.76 4.08 0.82±0.02 46 3.0 1083 30

6 386 0.08 0.2 0.05 3.61 3.87 13.26 0.86±0.02 13 3.4 319 17

7 403 0.11 0.2 0.03 2.89 2.94 ∞ 1.78±0.09 0 0.0 178 56

8 162 0.08 0.2 0.07 4.16 4.34 4.74 0.54±0.04 14 8.6 135 17

9 947 0.15 0.3 0.03 3.85 3.96 6.08 1.01±0.03 34 3.6 626 34

10 1518 0.38 0.8 0.02 3.48 3.61 3.63 1.30±0.03 36 2.4 729 52

11 430 0.11 0.2 0.04 3.66 3.80 5.23 0.65±0.02 25 5.8 303 30

12 2887 0.36 0.7 0.03 4.09 4.46 3.79 0.81±0.02 68 2.4 1867 35

13 48 0.02 0.0 – 3.61 – – – 11 22.9 39 19

14 15 0.04 0.1 – 3.45 – – – 4 26.7 10 33

Total 12983 345 7895 39

G. KWIATEK 162

The values of the maximum magnitude estimators in some zones differ substan-tially from the maximum magnitudes actually observed in these zones, though usually the difference between these values is about 0.1-0.2.

Statistically the most frequently observed events of magnitude ML ≥ 3.0, on the average every 3.5 months, occur in zones 1, 10 and 12, and the least frequent events are in zone 6, where the mean return period is more than 13 months; consequently, a similar order of time interval between stronger events should be expected. Detailed data related to this part of the analysis are presented in Table 2.

5. SEISMIC EVENT SEQUENCES

The catalogue provides 345 events with magnitude exceeding ML = 3.0; they were marked as “main shocks”. Table 3 lists the main shocks with magnitude equal to or greater than 3.5. All the zones display a more or less constant or slowly changing seismic activity, i.e., there is a certain constant or slowly changing level of the coeffi-cient λ for a given zone. It has been assumed in the present paper that aftershocks are all events occurring after a given main shock, and particular attention is paid to their frequency of occurrence. The first qualitative analysis showed that for some of the main events, directly (up to a few hours) after their occurrence, there appear several or even more than ten events in a given zone, where the activity of the whole sequence is substantially greater than the zone’s seismic “background”. It seems that a sensible period for aftershocks observation should be up to a few days for the strongest events. These observations are compatible with other authors (e.g., Gibowicz et al., 1979; Buben and Kozak, 1999; Gibowicz, 1997). For the Lubin mine event of March 24, 1977, of magnitude ML = 4.5, Gibowicz et al. (1979) found more than 130 aftershocks during 3-4 days after its occurrence, but most of the aftershocks occurred on the back-ground of the main event’s record. Therefore, one can expect that the number of after-shocks after strong events from the analyzed seismic catalogue will not exceed a dozen or so events. A similar several-day period of observation of aftershocks was also chosen by Buben and Kozák (1999), who analyzed aftershock sequences at the Kladno-Mayrau coal mine. Meanwhile, a much longer, nearly one month, observation period was applied for studying the aftershocks of the Lubin event of June 20, 1987, of magnitude ML = 4.3 (Gibowicz et al., 1989). In this case, however, only 28 after-shocks were recorded, and only a few of these during the first hours after the occur-rence of the main event.

For a more precise estimate of the time period for observation of foreshocks and aftershocks, and in view of the expected small number of foreshocks and aftershocks, events occurring up to 10 days before and after events of magnitude ML > 3.0 were analyzed. The method used was that of “combining” (Jones and Molnar, 1979) se-quences of events originating from many shocks, because the predicted number of events in a sequences for single events would have been too small. The rule assumed


Table 3

List of main shocks with magnitude equal to or greater than 3.5. Local time and local coordinates are used, ML is the local magnitude

Location Date Time

X [m] Y [m] ML

Seismic zone

1988 Feb 16 14h54m42s 31974 4216 3.52 1 1993 Oct 02 21 59 28 27813 7317 3.65 5 1994 Feb 03 19 44 15 29002 7945 3.61 6 1994 Feb 26 21 39 42 34308 5877 3.65 3 1994 Apr 13 12 20 11 32717 4483 3.64 2 1994 Apr 30 13 12 21 29866 4775 3.82 12 1994 Jun 04 16 54 56 27369 8929 3.66 11 1995 May 26 04 57 26 – – 3.73 9 1995 Nov 25 06 03 16 28452 6952 3.57 5 1998 Jun 26 05 03 53 31255 9915 3.77 8 1998 Nov 06 13 13 43 30112 6167 3.52 12 1998 Dec 04 05 06 28 – – 3.65 12 1999 Jan 05 05 00 04 – – 3.60 9 1999 Jan 29 02 12 23 31260 9921 3.70 8 1999 Apr 28 16 21 54 30205 5944 3.55 12 1999 Aug 23 03 20 48 27428 8375 3.58 11 1999 Dec 04 05 04 59 – – 3.71 12 1999 Dec 19 06 19 59 31247 10724 3.70 8 1999 Dec 31 21 44 42 30048 6150 3.55 12 2000 Jan 22 21 30 34 28898 6629 3.66 5 2000 Mar 13 13 08 46 – – 3.55 9 2000 Jun 09 12 52 50 33373 6679 3.61 13 2000 Jul 18 05 45 25 31165 9966 4.16 8 2001 Jan 20 21 02 19 – – 3.52 9 2001 Oct 02 13 02 11 32260 9297 3.64 9 2001 Oct 19 16 44 14 31800 5474 3.61 12 2001 Oct 30 09 32 19 33287 8334 3.57 9 2002 Jan 24 21 05 14 32180 9513 3.85 9 2002 Feb 16 16 25 43 32794 8464 3.83 9 2002 Feb 18 08 13 26 27621 8450 3.55 11 2002 Feb 20 12 27 03 30131 6168 4.09 12

here was that sequences of events related to a given shock should belong to the same seismogenic zone, and for foreshocks the additional criterion was that any occurring foreshocks should be at most 250 meters from the main event. Next, the sequences accompanying 345 events and prepared in this way were combined into one graph

G. KWIATEK 164

presented in Fig. 3. The horizontal axis denotes the time before (for foreshocks) or after (for aftershocks) a given event in days, and the vertical axis denotes the number of events in the selected time intervals. The mine’s constant average level of seismic-ity is visible and the sudden increase in the number of events both before and after the main shock. The generally smaller number of foreshocks is related to the above-mentioned additional distance criterion. It is worth mentioning that seismic activity for nearly all the zones during two days does not exceed a single event (Table 1), which means that if the number of foreshocks/aftershocks in the assumed time interval sub-stantially exceeds the average seismicity level of a given zone, this may not be just a coincidence linked to the data’s statistical dispersion, but more likely is a sequence of correlated events.

Fig. 3. Cumulative number of aftershocks (a) and foreshocks (b) as a function of time after and before the occurrence of main shocks.

After preliminary analysis of sequences of events related to main shocks, the seismic catalogue was analyzed with the help of an automatic algorithm with regard to the occurrence of aftershocks and foreshocks. Additionally, a search was made for sequences of several events with short time intervals and short distances between them. The following criteria for searching the catalogue for event sequences were adopted:

− Foreshocks: an event or events occurring up to 2 days before the main shock, belonging to the same zone as the main shock, and occurring at a distance of up to 250 meters from the main event.

− Aftershocks: events occurring up to 2 days after the main shock, belonging to the same seismogenic zone.

− Event series: a successive event or events of magnitude equal to at least 90% of the magnitude value of the main shock, with the time interval between pairs of events


no longer than 2 days, and a distance of up to 250 meters from the first shock in the analyzed sequence.

The sequences of events recorded at the Rudna mine selected in this way were divided into 4 main groups:

group 1 (00) – the main event was not preceded by any foreshocks in a given zone, and there are no aftershocks within the assumed time;

group 2 (0F) – the main event was preceded by foreshocks, there were no aftershocks;

group 3 (A0) – the main event was followed by aftershocks, there were no foreshocks;

group 4 (AF) – foreshocks and aftershocks occurred before and after the main event, respectively.

For 155 events, there were no aftershocks according to the assumptions made earlier, while 190 main events were followed by a certain number of aftershocks. Fifty-eight events were preceded by one or more foreshocks.

Foreshocks

In the group of 345 events analyzed, only 58 were preceded by foreshocks, where the majority – 43 main events – had 1 foreshock, 12 events had 2 foreshocks each, and there were three single events each with 3, 4 and 5 foreshocks, respectively. The sur-face distribution of the foreshocks for all events seems random, as none of the seismic zones displays any substantially different frequency of occurrence of main events with foreshocks. Most of the catalogued foreshocks occurred shortly (within a few minutes or so) before the main event.

Doublets

Among the analyzed events, 5 formed pairs of events, and one – a trio of events. In nearly all cases the time between the first and second (or third) shock ranged from a few to a dozen or so minutes. Upon comparing the data with the mean return period of events with ML ≥ 3.0 previously determined for the zones, these pairs of events cannot be considered accidental (given that in most cases the mean return period of events with ML > 3.0 exceeded one month), but rather are evidence of the gradual release of accumulated energy in a series of two or three shocks. The most characteristic exam-ple of such a series is one recorded in zone 5, which occurred on November 23, 1999, and comprised three events of magnitudes ML = 3.4, 3.1 and 3.2. The time intervals between these events were as follows: between the first and the second about 9 min-utes, and between the second and the third about 2 minutes, whereas the mean return period of events with this order of magnitude for zone 5 is just over 4 months.

G. KWIATEK 166

Aftershocks Table 4

Number of main shocks Nm and the corresponding number

of aftershocks Na observed after each main shock

Nm Na

150 0 108 1 42 2 21 3 13 4 1 5 1 6 2 7 0 8 1 9 1 10

The distribution of the number of aftershocks following the main event is presented in Table 4. In most cases, the number of aftershocks did not exceed 1-2, with only a few events followed by a greater number of aftershocks. No clear relation was observed between the magnitude of a given main event and the number of aftershocks. More-over, there are examples of events with similar magnitudes with a very different number of after-shocks. For the strongest event in the selected catalogue (ML = 4.2), there was just one after-shock in the assumed time interval, whereas for another event with a comparable magnitude (ML = 4.1) the number of recorded aftershocks was 9. The greatest number of aftershocks, 10, was actually catalogued for an event of magnitude ML = 3.0.

Fig. 4. Surface distribution of main shocks with the number of their aftershocks marked by different colours shown at the right-hand side. The radius of circles is proportional to mag-nitude.

Figure 4 presents the surface distribution of main events together with the num-ber of aftershocks observed after their occurrence. The other events in the analyzed seismic catalogue are marked in gray. The size of a point and its colour, respectively,


denote the magnitude ML of the main event and the number of its aftershocks. The image is characterized by a weak but visible differentiation of the zones in terms of the number of aftershocks following the main shocks. There is a relatively smaller number of observed aftershocks in zones 8, 9, 10 and 11 compared to zone 1 or 12. These differences are not caused by weaker seismicity in these zones (the differences between the λ values are smaller than between the numbers of aftershocks), but by its special character, and therefore the character of seismicity in the individual zones was the next element of the study.

6. THE CHARACTER OF SEISMICITY OF THE SELECTED ZONES

For zones in which the number of analyzed events above the catalogue’s threshold was at least 250, the value of the b coefficient of the Gutenberg-Richter relation was calculated by the maximum likelihood method (Page, 1968)

( ) (

( ))max min max min

minmax min

exp ( )1 ,1 exp ( )

L L L LL L

L L

M M M MM M

M M

ββ β

− − −= − +

− − − (4)

where β = b ln(10), using relation (3) for the recursive calculation of the b coefficient estimator. Graphs of the estimator of the PDF of magnitude were additionally pre-pared applying the following relation (Lasocki, 2001):

1

1 1ˆ ( )in

L LL

i ii

M Mf M Knh h hα α=

⎡ ⎤⎛ ⎞−= ⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦∑ , (5)

where K(·) is a standard Gaussian PDF, as well as the values of the maximum magni-tude estimator, using relation (3). The collective data are presented in Table 2. The PDF of magnitude and the maximum magnitude estimator were also calculated for zone 8 because of the zone’s strong seismicity; the maximum magnitude estimator, however, could involve a greater error than in the other cases. The PDFs for individual zones were normalized and are shown collectively in Fig. 5.

There is a generally apparent tendency for an increase in the number of strong events and in seismic hazard in the northeastern direction, which is easily visible when observing changes in the maximum magnitude estimator value. This tendency is com-patible with the observations of Orlecka and Lasocki (2002). The character of seismic-ity itself in various zones is different. Several groups can be identified. The most lin-ear characteristics of the PDF of magnitude is found in zones 1, 3, 5, 6 and 12. For these zones, the value of the b coefficient is close to 1, and the non-parametric distri-bution only slightly deviates from a linear one. The next group could comprise zones 2, 8 and 11, characterized by low values of b (b ≈ 0.5). In these zones, the proportion between weak and strong events is disturbed in favour of strong events. Zone 8 in particular could pose a serious hazard, where despite a relatively short period of min-

G. KWIATEK 168

Fig. 5. Frequency-magnitude relations for 11 seismic clusters shown in Fig. 2. The number of events N for each cluster is also shown.

ing operations, several strong events have already occurred, including the largest event of magnitude ML = 4.2 mentioned earlier. The number of weaker events is relatively small in these zones, as shown in Fig. 4 in the form of a smaller number of recorded aftershocks. Distinctly bimodal distributions are present in zones 9 and 10 where, even though the values of b are high (b = 1.2, 1.3), the estimated maximum magnitude es-timators are very high (ML

max = 4.4 and 4.0). In these zones, the number of aftershocks occurring after strong events is slightly higher than in the previous group. Zone 7 is characterized by weak seismicity, with b = 1.78. No events with local magnitude ex-ceeding ML = 3.0 occurred in this zone.

In summary, specific danger of the occurrence of strong seismic events is present in zones 8, 9 and 10, which are characterized by a high value of the maximum magni-tude estimator, a small number of weak events compared to strong events, and bimo-dality of the distribution of the Gutenberg-Richter relation. It is worth noting that the differences in the number of aftershocks depending on the seismogenic zone coincides with the character of a given zone’s seismicity, which is especially visible for zones 8, 9, 10 and 11. In these zones, there occur a relatively large number of strong events and a relatively small number of weak ones, which is manifested by the smaller number of aftershocks.


7. b COEFFICIENT VARIABILITY WITH TIME

To study the change in b values with time, separate calculations were performed for each seismic zone, where the number of events in each zone had to be greater than 150.

Data from one zone were sorted by their date of occurrence. For the first, 150-element group of events that occurred the earliest, the b coefficient from the Guten-berg-Richter relation was calculated according to the method outlined earlier. The result was assigned to the “middle” of the calculated time interval; the arithmetic average of the time of the first and last event in the analyzed group. The next step involved removing the 3 oldest events and replacing them with 3 new ones, the next from the catalogue for the given zone. The b coefficient was calculated once again for this group; the procedure was repeated until the analyzed set for a given zone was exhausted. The choice of group size (150 elements) was based on a compromise be-tween the amount of data necessary for a credible calculation of the b coefficient and the level of detail of the obtained result (smaller group – stronger influence of single events).

Fig. 6. Time variation of the b coefficient from the frequency-magnitude relations estimated for overlapping moving windows containing 150 events with a step of every 5 events.

G. KWIATEK 170

The detailed results of these calculations are presented in Fig. 6. The image is characterized by a gradual decrease of the b coefficient estimator with time (which lasted from 1 to even 5 years) in the early stage of the seismogenic zone’s develop-ment. Events with smaller magnitudes dominate at this time. In the next stage, the value of the b coefficient estimator changes very slowly (zones 2, 3) if at all, and sta-bilizes around a certain value (12.5). One disturbing fact is that for newly formed zones 2, 8 and 11 the b estimator is low from the very beginning, which suggests a tendency for the occurrence of strong events in these zones and a small number of aftershocks.

8. CONCLUSIONS

The analysis of the Rudna mine’s seismic catalogue allowed to observe and then iden-tify several groups of event sequences: from events with no foreshocks or aftershocks, to events with a large number of aftershocks exceeding the average seismicity level.

Foreshocks occurred in a relatively small group of events (17% of all the ana-lyzed sequences). Nearly all the foreshocks occurred from a few to a dozen or so min-utes before the main shock.

In the case of 32% of the events, seismic activity after the main shock was higher than the expected average seismic activity, but the number of aftershocks exceeded a few to a dozen in the case of only a small number of events. It should be noted that the obtained results are certainly underestimated. First of all, the analysis of these se-quences was based on the mine’s seismic catalogue and not on seismograms, which could mean an underrated number of recorded foreshocks and aftershocks (e.g., Gi-bowicz et al., 1979). Secondly, a completeness threshold was applied to the analyzed catalogue for the purpose of greater objectivity of the search for sequences, which resulted in the removal of smaller events.

No correlation was found between the number of recorded aftershocks and the magnitude of the main. In particular, completely different types of sequences were observed for events whose magnitudes differed only slightly.

Changes in the number of events in a sequences were observed depending on the zone where they occurred, i.e., for some zones there was an overall tendency for the occurrence of a greater number of aftershocks, whereas for other zones this tendency was smaller, which could be related to the level of seismic activity. The estimated shapes of the magnitude PDF estimator, the determined b coefficient of the Guten- berg-Richter relation and its changes with time for individual seismogenic zones, showed that the value of the b estimator depends on the shape of the PDF and the number of aftershocks.

A c k n o w l e d g m e n t . I would like to thank Professor S.J. Gibowicz for valuable remarks and comments which helped me to notice some interesting fea-tures of mining-induced seismicity in Rudna copper mine.


R e f e r e n c e s

Buben, J., and J. Kozák, 1999, Foreshock and aftershock sequences of rockburst in coal mine Kladno-Mayrau, Publs. Inst. Geophys. Pol. Acad. Sc. M-22 (310), 95-102.

Domański, B., S.J. Gibowicz and P. Wiejacz, 2002, Source time functions of seismic events induced at a copper mine in Poland: empirical Green’s function approach in the fre-quency and time domains, Publs. Inst. Geophys. Pol. Acad. Sc. M-24 (340), 5-27 (in Polish with English abstract and figure captions).

Gibowicz, S.J., 1997, An anatomy of seismic sequence in a deep gold mine, Pure appl. geo-phys. 150, 393-414.

Gibowicz, S.J., and A. Kijko, 1994, An introduction to mining seismology, Academic Press, San Diego.

Gibowicz, S.J., A. Bober, A. Cichowicz, Z. Droste, Z. Dychtowicz, J. Hordejuk, M. Kazi-mierczyk and A. Kijko, 1979, Source study of the Lubin, Poland, tremor of 24 March 1977, Acta Geophys. Pol. 27, 3-38.

Gibowicz, S.J., J. Niewiadomski, P. Wiejacz and B. Domański, 1989, Source study of the Lubin, Poland, mine tremor of 20 June 1987, Acta Geophys. Pol. 37, 111-132.

Jones, L.M., and P. Molnar, 1979, Some characteristics of foreshocks and their possible relationship to earthquake prediction and premonitory slip on faults, J. Geophys. Res. 84, 3596-3608.

Kijko, A., and G. Graham, 1998, Parametric-historic procedure for probabilistic seismic haz-ard analysis. Part I: Estimation of maximum regional magnitude mmax, Pure Appl. Geophys. 150, 393-414.

Kijko, A., B. Drzęźla and T. Stankiewicz, 1987, Bimodal character of the distribution of ex-treme seismic events in Polish mines, Acta Geophys. Pol. 35, 157-166.

Kijko, A., S. Lasocki and G. Graham, 2001, Non-parametric seismic hazard analysis in mines, Pure appl. geophys. 152, 413-442.

Lasocki, S., 2001, Quantitative evidences of complexity of magnitude distribution in mining induced seismicity: Implication for hazard evaluation. In: G. van Aswegen, R.J. Dur-rheim and W.D. Ortlepp (eds.), “Rockburst and Seismicity in Mines”, SAIMM, Jo-hannesbourg, 543-550.

McGarr, A., and R.W.E. Green, 1978, Microtremor sequences and tilting in a deep mine, Bull. Seism. Soc. Am. 68, 1679-1697.

Orlecka-Sikora, B., and S. Lasocki, 2002, Clustered structure of seismicity from the Legnica -Głogów Copper district, Publs. Inst. Geophys. Pol. Acad. Sc. M-24 (340), 105-119 (in Polish with English abstract and figure captions).

Page, R., 1968, Aftershocks and microaftershocks of the great Alaska earthquake, Bull. Seism. Soc. Am. 58, 1131-1168.

Received 20 October 2003 Accepted 27 October 2003

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A SEARCH FOR SEQUENCES OF MINING-INDUCED SEISMIC EVENTS AT THE