the work presents an attempt of application of the hvsr...

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. 3 2004

APPLICATION OF THE HORIZONTAL TO VERTICAL SPECTRAL RATIO TECHNIQUE FOR ESTIMATING

THE SITE CHARACTERISTICS OF GROUND MOTION CAUSED BY MINING INDUCED SEISMIC EVENTS

Dorota OLSZEWSKA and Stanisław LASOCKI

Faculty of Geology, Geophysics and Environmental Protection, Department of Geophysics AGH University of Science and Technology

Aleja Mickiewicza 30, 30-059 Kraków, Poland e-mails: [email protected]; [email protected]

A b s t r a c t

The work presents an attempt of application of the horizontal-to-vertical spec-tral ratio (HVSR) method for estimating the local amplification of ground motion caused by mining seismic events in the Legnica Głogów Copper District. Amplify-ing properties of the surface layer are assessed from the ratio of amplitude spectra of the horizontal and vertical components of ground acceleration, recorded at the surface. The location of a local maximum of the ratio in the frequency band up to 8 Hz assigns the resonant frequency of the surface layer; the maximal value esti-mates the amplification factor at the measurement point.

The spectral ratio was evaluated for 219 ground acceleration records from ten recording stations. The HVSR curves for induced seismicity turned out to be similar to the typical HVSR-s for natural earthquakes. Amplification factors estimated by the HVSR method were used to reduce the observed peak ground accelerations (PGA-s) to the bedrock. The reduction significantly improved an agreement be-tween the PGA values order and the order of epicentral distances. The obtained re-sults suggest that the HVSR method can be successfully used to evaluate the local influence of the surface layer also for induced seismicity, in spite of the fact that in this case the conditions for application of the method essentially differ from the conditions met in natural seismicity.

Key words: site effects, site amplification, spectral ratio, HVSR method, induced seismicity.

mailto:[email protected]

D. OLSZEWSKA and S. LASOCKI

302

1. INTRODUCTION

The energy and mechanism of seismic events, as well as hypocentral distance and lo-cal soil conditions, are basic factors determining seismic effects on the ground. The site response is related to geological structure of the surface layer and manifests itself as an amplification of horizontal component of shaking. The effect is parameterised by the amplification factor, which is the ratio of acceleration amplitudes on the surface and on the firm rock. The smaller the seismic wave velocity in the surface layer, the larger the amplification factor value. This value is about one for a firm rock, and up to 20 for a poorly consolidated soil (Bard, 2002).

Various methods used to estimate the amplification factor are either analytical -numerical or empirical. The analytical-numerical methods make use of an assumed model of the subsurface. The model is based on seismic investigation, laboratory stud-ies or literature data (e.g., Mutke and Dworak, 1992; Dubiński and Mutke, 1998; At-kinson and Cassidy, 2000; Dubiński and Stec, 2002). The amplification factor is evaluated using empirical relations that link parameters of the assumed geological model (e.g., P- and S-wave velocities, thickness of layers, shaking frequencies, damp-ing factors, surface layer dispersion). The basic drawbacks influencing considerably the accuracy of analytical-numerical methods are as follows (Bard, 2002):

– the use of only plane incidence waves, – one dimensional and linear approach, – difficulties in setting reliable input parameters. An obvious way of empirical assessment of the amplification factor is simultane-

ous measurement of ground acceleration amplitude on the surface and on the bedrock. For this type of studies, sensors must be installed both on the surface and in a bore-hole, which is technically difficult and expensive. Therefore, this manner of amplifica-tion factor assessment is only occasionally used for ascertaining quality of other meth-ods (e.g., Satoh et al., 2001; Tsuboi et al., 2001).

Nakamura (1989; 2000) has suggested a simple and convenient way for estimat-ing the amplification factor. In his method, called HVSR (Horizontal to Vertical Spec-tral Ratio) method, the amplification is assessed from the ratio of amplitude spectra of the horizontal and vertical components of ground acceleration recorded on the surface. Nakamura’s method is at present the most popular tool to estimate site effects in natu-ral seismicity (e.g., Lermo and Chavez-Garcia, 1994; Nakamura and Saita, 1994; Konno and Ohmachi, 1998; Luzon et al., 2001; Satoh et al., 2001; Tsuboi et al., 2001; Giampiccolo et al., 2001; Dimitriu, 2002).

In this work we present an attempt of using the HVSR method for estimating the local amplification of ground motion caused by mining seismic events in the Legnica Głogów Copper District. For such sources, the initial conditions of the method’s application differ from the conditions met in natural seismicity problems. Firstly, because of short epicentral distances, individual phases cannot be identified in the

GROUND MOTION SITE CHARACTERISTICS 303

recorded signals. In particular, one cannot single out the S phase, which should be exclusively used to evaluate the spectral ratio. Secondly, the ground motion caused by mining seismic events has higher frequencies than that caused by earthquakes. As a result, the assumption of Nakamura’s method that the vertical component of ground motion is amplification free, can be significantly violated in the case of induced seis-micity. Finally, ground motion recording stations in the Legnica Głogów Copper Dis-trict in fact do not record the ground motion because their sensors are mounted not di-rectly in the ground but in concrete measurement wells. Both the magnitude and the sign of the distortion of resultant signals remain unknown. The obtained results of our investigations show, however, that in spite of these differences the HVSR method can be successfully used also in induced seismicity studies.

2. HVSR METHOD

In 1989 Nakamura suggested estimating the amplification factor from the ratio of am-plitude spectra of the horizontal to vertical components of ground acceleration re-corded on the surface (Nakamura, 1989). The relation between this ratio and the fre-quency is called the HVSR curve and has a peak within dominating frequencies of the recording. The peak amplitude is the amplification factor estimate, and its frequency is the principal frequency of surface layer. Furthermore, Nakamura ascertained that such a characteristic peak of the HVSR curve is strictly related to local geology, being in-dependent of source parameters and signal frequency. He also indicated that the HVSR method would give the most accurate results when the spectral ratio were evaluated from the horizontal and vertical component of S wave. Figure 1 presents an example of the HVSR curve obtained from ground motions caused by seven earth-quakes in Yokohama city (Tsuboi et al., 2001). The amplification factor is linked to the maximum located at about 6 Hz frequency of and its value is about 6.

Performance of HVSR method was checked through theoretical analyses (e.g., Lachet and Bard, 1994; Konno and Ohmachi, 1998; Luzon et al., 2001; Tsuboi et al., 2001) and empiric studies of microtremors and earthquakes (e.g., Lermo and Chavez-Garcia, 1994; Nakamura and Saita, 1994; Nakamura, 2000; Diagourtas et al., 2001; Satoch et al., 2001; Tsuboi et al., 2001). Investigations of individual component spec-tra of signals from the surface and bedrock indicated that the vertical component of ground motion was amplification free for lower frequencies. Such a result agrees with basic assumptions of the method (Lermo and Chavez-Garcia, 1994; Tsuboi et al., 2001). The frequency range in which the HVSR method gives correct estimates of the amplification factor is still under research. This range depends on the structure of the surface layer but generally should not exceed 6-8 Hz. Tsuboi et al. (2001) noticed on the basis of empirical and theoretical studies that the HVSR method gave correct am-plification factor values when the HVSR curve had only one peak. The HVSR curve with many peaks results from a complex structure of the surface layer, which can lead


304

to amplifying the vertical com-ponent of acceleration above the frequency of 2Hz. On the other hand, if HVSR is calculated from a full signal, an influence of the surface wave on the ratio can be significant in a low frequency area. Kokusho and Matsumoto (1997) maintained that if a re-sponse of the surface layer was linear then the estimation of am-plification factor by the HVSR method was correct. Otherwise, the amplification was underesti-mated.

In spite of doubts concern-ing its theoretical basis, the HVSR method is widely used for estimating site effects because it

is readily feasible, provides correct results, its interpretation is simple and the required measurements are not expensive. When the surface layer structure is relatively simple, values of the amplification factor obtained from the HVSR method correlate well with the values achieved from other surface methods (Atkinson and Cassidy, 2000). In more complicated geological situations, the credibility of the HVSR method is supe-rior (Ansal et al., 1997).

Fig. 1. HVSR curves for ground motion caused byseven earthquakes in Yokohama city (Tsuboi et al.,2001).

3. DATA

Measurements of ground motion caused by mining seismic events have been carried on in the Legnica Głogów Copper District for some years. The Mining and Engineer-ing Seismology Laboratory of Department of Geophysics in the AGH University of Science and Technology in Kraków is in possession of an extensive base of accelera-tion records from this region. The database comprises signals from 12 ground seismic stations owed by local communes and 21 stations owed by KGHM “Polska Miedź” S.A. All the recording stations have three-component accelerometers. The sensors are mounted either in the ground, on building foundations, or at selected points on upper storeys of the buildings.

The ground motion data that were used in this work had been gathered by ten recording stations: seven located in town Polkowice and single in villages Rudna, Rynarcice and Tarnówek. Location of the recording stations is presented in Fig. 2. Table 1 presents summarized information concerning the processed data.


Table 1 Data used in the analysis

Station coordinates Location of recording station

Station ID number x y

Recording period

Number of records

Polkowice ul. Akacjowa 4 20 30 548 5 882 22 Jan 2000

– 21 May 2002 20

Polkowice ul. 3-go Maja 8 22 31 130 5 546 9 Jan 2000

– 21 May 2002 48

Polkowice ul. Miedziana 9 23 30 864.5 5 756 9 Jan 2000

– 21 May 2002 34

Polkowice ul. Sosnowa 14 26 30 531 6 722.5 8 Jan 2000

– 21 May 2002 19

Polkowice ul. Hubala 40 30 500 5 520 31 Oct 2001

– 17 Mar 2003 22

Polkowice ul. Kolejowa 41 31 500 5 950 25 Jan 2002

– 28 Mar 2003 27

Rudna 60 31 300 18 290 24 Jan 2002 – 28 Mar 2003 8

Rynarcice 61 27 330 15 470 17 Nov 2002 – 28 Mar 2003 11

Polkowice os. Skalniaków 63 31 440 5 680 17 Sep 2002

– 28 Mar 2003 20

Tarnówek 62 32 300 12 050 17 Sep 2002 – 28 Mar 2003 10

The measurement points given in Table 1 are served by three different kinds of recording equipment. ID numbers 20, 22, 23, 26 are WORS 3CM stations (Jake2, Ka-towice make), ID-s 40 and 41 are AMAX99 stations (Central Mining Institute, Ka-towice make), and ID-s 60, 61, 62, 63 are field stations of SEJS-NET system (Mirek, 2001). We analysed only such signals whose horizontal peak ground acceleration (PGA) was greater than 0.05 m/s2 in the case of WORS 3CM and 0.04 m/s2 in the case of AMAX99 and SEJS-NET stations, respectively. In this way, records with consider-able portion of noise were not studied. Besides, the dominant frequency of every used signal was in the range from 4 to 8 Hz, and the energy of its source was not less than 106J. Altogether 219 signals were selected for processing.


306

Fig. 2. Location of the recording stations. Coordinates are provided in the local seismic (min-ing) system.

The following data subgroups were also extracted from the analysed data: – Subgroup 1: Signals generated by stronger seismic events whose energy was

greater than or equal to 108J; there were 56 such records; – Subgroup 2: Stronger signals of either horizontal or vertical PGA greater than

0.5 m/s2; there were 25 such records.

4. ESTIMATION OF THE AMPLIFICATION FACTOR

The horizontal component of acceleration, h(t), is defined as

( ) ( ) ( )ix yh t h t h t= + , (1)

where hx(t) and hy(t) are the x and y components of acceleration, respectively, and i is the imaginary unit. Spectra of the horizontal and vertical components of ground accel-eration were evaluated using the fast Fourier transform (FFT). The spectrum ratio, HVSR, is an absolute value of the ratio of horizontal to vertical component amplitude spectra, smoothed with the five-point moving average.

The HVSR curves for signals from the recording stations 20, 22, 23, 26, 40, 41, 60, 61, 62, 63 are shown in Fig. 3. Heavy lines represent the averages of all individual HVSR-s. It is seen that the spectral ratios from signals recorded by the same station are similar to a great extent. The similarity includes the number of local extremes, their locations and amplitudes. The similarity between the HVSR-s from the same


place is also satisfactory in Fig. 4, where the average HVSR-s from all analysed sig-nals (solid line), from the signals caused by stronger sources (subgroup 1 – dotted line) and from the stronger signals (subgroup 2 – dashed line) are presented. Larger amplitudes and additional peaks for lower frequency in the spectral ratios related to stronger events and stations 20 and 22 can be connected with the influence of Rayleigh waves.

The HVSR curves of records from different stations differ significantly. The dif-ferences are distinctly visible in the average HVSR-s in both Figs. 3 and 4.

The obtained results indicate that the HVSR-s of ground motion caused by min-ing seismic events follow basic assumptions of the Nakamura method, that is, they are related to a sensor location and local properties of the place. Moreover, they depend neither on the source size/frequency, nor on the hypocentral distance and propagation path.

The amplification factor is estimated by the local maximum of HVSR curve in the frequency range from 3 to 8 Hz. Abscissa of this maximum is a resonate fre-quency of the surface layer at the measurement point.

Two maxima for a frequency of 5.7 and 8.5 Hz, respectively, can be singled out in the HVSR for station 20 (Fig. 3a). The value of the first maximum is the amplifica-tion factor estimate for the point of station location equal to 2.7.

The HVSR curve for station 22 has a maximum of about 6 Hz (Fig. 3b). The maximal value, the amplification factor estimate for the station location, is 4.4.

A HVSR maximum for station 23 is about 6.7 Hz and the maximal value that es-timates the amplification factor at this point is 4.3 (Fig. 3c).

Change of the spectral ratio with frequency for station 26 (Fig. 3d) is more complicated and the dispersion of individual HVSR curves about their average is greater than for the above cases. It is possible to single out a HVSR maximum at about 3.7 Hz. The maximal value is 5.3. The complicated character of the spectral ratio causes, however, that the amplification factor estimation is uncertain.

The HVSR curve for station 40 (Fig. 3e) also suggests a complex character of the surface layer at this point. From the average spectral ratio one can identify two maxima at a frequency of about 5.5 and 8 Hz, respectively. Large dispersion of individual HVSRs about the average (heavy line) is visible. For the first maximum at 5.6 Hz, the HVSR value is about 2.3.

It is also possible to distinguish two maxima in the HVSR curve for station 41 (Fig. 3f): for frequencies of 5.6 and 7.4 Hz, respectively. In this case, the amplification can be estimated more accurately than for station 40, because the individual HVSR curves are less dispersed. The HVSR value for the first peak is 2.3.

The most complicated in character is the spectral ratio for station 60 (Fig. 3g). Many peaks above 2 Hz indicate that the subsurface in this place is complex.


308

Fig. 3. Spectral ratios of ground motion for differentrecording stations. Heavy line denotes the average ra-tio.


Fig. 4. Average spectral ratios for different recordingstations. Solid line – the average ratio from all sig-nals; dotted line – the average ratio from the signalscaused by sources of energy ≥ 108J; dashed line – theaverage ratio from the signals of PGA > 0.5 m/s2.


310

Two maxima can be distinguished in the HVSR for station 61 (Fig. 3h). Their lo-cations are 4.5 and 6.3 Hz, respectively. Shapes of the individual HVSR curves sug-gest that the amplification factor is related to the second maximum. The HVSR value for the second maximum, that is the amplification estimate, is 5.

The HVSR curves for station 62 (Fig. 3i) have a number of slight maxima above the frequency of 5Hz, indicating the complexity of the subsurface at this point. The amplification factor cannot be unequivocally determined. An approximated value of the amplification from the first peak would be 5.2.

In the HVSR curve for station 63 (Fig. 3j) one can single out two maxima for frequencies of 5.9 and 7.6, respectively. Hence, the surface layer is also complex. An estimated value of the amplification from the first maximum equals 3.3.

Table 2

Estimated values of the amplification factor obtained by the HVSR method

Station ID number 20 22 23 26 40 41 61 62 63

Amplification factor estimate 2.7 4.4 4.3 5.3 2.3 3.4 5.0 5.2 3.3

The HVSR curves for stations 40, 41, 60, 61, 62 and 63 are complicated. The most complicated one is for station 60 (Fig. 3g). Unequivocal estimation of the ampli-fication factor for this place was not possible. The complexity of HVSR in all these cases is not only a result of local complexities of the subsurface but also is caused by the fact that the number of recorded and processed signals from these stations was smaller than the number of signals from stations 20, 22 and 23.

Eventually, we estimated the amplification factor for nine points. The estimates are presented in Table 2.

5. EVALUATION OF SIGNIFICANCE OF THE AMPLIFICATION FACTOR ESTIMATES

Contrary to common expectations, the descending order of PGA-s of ground motion induced by one source at different places often does not correspond to the ascending order of epicentral distances. The reasons for that might be the source directivity, dif-ferences in the signals paths and differences in local amplification on the surface layer at sensor locations.


The site effect can be removed by reducing the measured PGA-s to the bedrock, that is, by dividing the measured values by appropriate amplification factors. Such a reduction should largely improve the correlation between the PGA-s and epicentral distances.

Using the Nakamura spectral ratio method we estimated the amplification factor for nine different locations. If these estimates reflect the actual amplification then the order of PGA-s reduced to the bedrock should significantly improve its correlation with the order of epicentral distances. To test this effect, we considered all signals re-corded by stations 20, 22, 23, 26, 40, 41, 60, 61, 62 and 63 and selected those fulfill-ing the following criteria:

– they were generated by the same source and recorded by at least three stations, – at least three monitoring stations were approximately situated more or less on

the same ray beginning from the source location.

The second condition was meant to make testing independent of the source directivity and path effects.

For 28 seismic events, ground motion signals recorded by three stations satisfied the above conditions. For other 7 events, the conditions were met by two three-station sets. Altogether, 42 signal triplets were selected. For every triplet we evaluated epi-central distances, PGA and PGA reduced to the bedrock with the respective amplifica-tion estimates from Table 2. The results are presented in Table 3.

The similarity of PGA and epicentral distance orders within every triplet was pa-rameterised by:

– the Spearman rank correlation coefficient

( )( ) ( ) ( ) ( )

( )( ) ( ) ( )( ) ( )

3 3 3

1 1 1

2 23 3 3 32 2

1 1 1 1

13

1 13 3

,i i i i

i i i

i i ii i i i

NR r NR a NR r NR ar a

NR r NR a NR a NR r

ρ = = =

= = = =

⎡ ⎤ ⎡ ⎤− ⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦=⎧ ⎫⎧ ⎫⎛ ⎞ ⎛⎪ ⎪⎪ ⎪− −⎨ ⎬⎨ ⎬⎜ ⎟ ⎜

⎝ ⎠ ⎝⎪ ⎪⎪ ⎪⎩ ⎭⎩ ⎭

∑ ∑ ∑

∑ ∑ ∑ ∑ i⎞⎟⎠

, (2)

where NR(ri) is the rank of i-th epicentral distance and NR(ai) is the rank of i-th PGA, i = 1, 2, 3. For the ideal agreement of orders in a triplet, ρ(r, a) = –1. An increase of orders similarity is expressed by a decrease of ρ(r, a);

– the coefficient of order similarity

3

1

( , ) 4 ( ) ( )ii

w r a NR r NR a=

= − −∑ i . (3)

For the ideal orders agreement w(r, a) = 0. An increase of orders similarity is ex-pressed by a decrease of w(r, a).


312

Table 3 Epicentral distances, measured PGA and PGA reduced to the bedrock with amplification factor

obtained from the Nakamura method

Event occurrence time

Source energy [J]

Station ID number

Epicentral distance [m]

Measured PGA[m/s2]

Reduced PGA [m/s2]

20 1811 0.2 0.074 22 2481 0.211 0.048 22 Jan 2000

21:30:34 2.10×108

23 2151 0.23 0.053 20 562 0.03 0.011 22 1166 0.026 0.006 19 Feb 2000

21:40:50 1.1×105

23 833 0.03 0.007 20 527 0.03 0.011 22 1160 0.035 0.008 22 Feb 2000

13:01:08 2.4×105

23 822 0.04 0.009 20 538 0.07 0.026 23 744 0.08 0.019 9 Mar 2000

1:56:19 2×106

22 1061 0.057 0.013 20 1853 0.11 0.041 22 2519 0.167 0.038 25 Mar 2000

21:52:40 4.5×107

23 2193 0.12 0.028 20 604 0.15 0.056 22 1251 0.183 0.042 23 Apr 2000

0:16:07 5.7×106

23 912 0.21 0.049 20 1940 0.09 0.033 22 2611 0.144 0.033 2 May 2000

20:05:14 9.6×107

23 2280 0.13 0.030 20 1009 0.12 0.044 22 1664 0.083 0.019 3 May 2000

22:48:10 2×106

23 1346 0.09 0.021 20 1891 0.06 0.022 22 2563 0.083 0.019 20 Jun 2000

18:31:09 7.9×107

23 2230 0.09 0.021 20 931 0.1 0.037 22 269 0.42 0.095 15 Nov 2000

6:28:56 3.3×107

23 592 0.23 0.053 20 556 0.35 0.130 22 1225 0.294 0.067 27 Jan 2001

12:19:58 4.3×107

23 888 0.471 0.110 20 1056 0.342 0.127 22 1683 0.149 0.034 28 Mar 2001

23:25:09 2.3×107

23 1383 0.231 0.054 20 694 0.316 0.117 22 1333 0.289 0.066 3 Apr 2001

13:05:48 6.2×107

23 996 0.336 0.078


Table 3 (continuation) 22 638 0.735 0.167 23 959 0.432 0.100 21 Jun 2001

2:58:43 3.5×107

20 1299 0.17 0.063 20 685 0.122 0.045 22 1310 0.076 0.017 13 Jul 2001

21:14:25 1.4×107

23 974 0.086 0.020 20 554 0.12 0.044 22 1218 0.049 0.011 5 Aug 2001

19:18:15 4.0×106

23 879 0.127 0.030 20 1215 0.201 0.074 22 543 1.109 0.252 23 881 0.626 0.146

17 Aug 2001 18:47:36 3.1×107

26 1810 0.108 0.020 20 900 0.252 0.093 22 1565 0.149 0.034 30 Aug 2001

3:10:42 1.6×107

23 1226 0.16 0.037 20 1351 0.063 0.023 22 679 0.237 0.054 23 1015 0.181 0.042

8 Sep 2001 23:15:28 5.0×106

26 1916 0.063 0.012 23 1034 0.187 0.043 22 702 0.318 0.072 20 1372 0.079 0.029

11 Oct 2001 14:21:44 2.9×106

26 1918 0.048 0.009 23 2374 0.14 0.033 20 2088 0.067 0.025 22 2704 0.091 0.021

12 Oct 2001 11:46:13 7.5×107

26 1443 0.19 0.036 23 978 0.513 0.119 20 1317 0.273 0.101 19 Oct 2001

16:44:14 1.7×108

22 674 0.55 0.125 23 995 0.167 0.039 22 661 0.3 0.068 31 Oct 2001

5:55:40 4.4×106

20 1332 0.066 0.024 23 2404 0.05 0.012 22 2734 0.049 0.011 21 Nov 2001

3:03:57 6.4×107

26 1476 0.07 0.013 20 749 0.057 0.021 22 1387 0.036 0.008 22 Jan 2002

12:33:53 7.2×105

23 1049 0.051 0.012 20 2248 0.096 0.036 22 2903 0.104 0.024 25 Jan 2002

10:09:41 1.3×107

23 2565 0.091 0.021


314

Table 3 (continuation) 20 3422 0.199 0.074 40 3732 0.041 0.018 16 Feb 2002

16:25:43 4.5×108

41 3060 0.187 0.055 20 1348 0.036 0.013 22 676 0.12 0.027 19 Feb 2002

21:33:39 2.0×106

23 1012 0.098 0.023 20 981 0.133 0.049 22 1653 0.107 0.024 20 Feb 2002

12:46:53 1.0×106

23 1320 0.128 0.030 20 1294 0.041 0.015 22 632 0.173 0.039 23 970 0.128 0.030

18 Mar 2002 7:34:51 1.1×106

26 1930 0.038 0.007 20 2380 0.1 0.037 22 3000 0.103 0.023 23 2669 0.102 0.024

20 Mar 2002 9:24:06 1.6×108

26 1739 0.124 0.023 23 2218 0.095 0.022 26 3126 0.076 0.014 20 2547 0.049 0.018

23 Mar 2002 18:42:18 7.8×106

22 1879 0.18 0.041 22 1574 0.102 0.023 23 1895 0.055 0.013 26 Apr 2002

21:19:01 5.2×106

26 2674 0.04 0.008 63 3144 0.058 0.018 40 3800 0.077 0.033 2 Dec 2002

17:38:18 7.9×107

41 3577 0.069 0.020 40 2354 0.023 0.010 41 2723 0.112 0.033 24 Jan 2003

5:11:30 4.7×108

63 3290 0.051 0.015

The values of parameters ρ and w obtained for the studied triplets of signals are presented in Table 4. These values were used to verify the following two null hy-potheses:

• ( ) ( )( )10 0 , z ,H E r a E r aρ ρ≤⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦ , where ( )0 ,E r aρ⎡ ⎤⎣ ⎦ and ( ),zE r aρ⎡ ⎤⎣ ⎦ are

the expected values of rank correlation coefficient of the epicentral distance with the observed and reduced PGA, respectively.

• ( ) ( )( )20 0 , and , have the same probabilistic distributionzH w r a w r a , where

and are the coefficients of orders similarity of the epicentral dis-tance and the observed and reduced PGA, respectively.

(0 ,w r a) )( ,zw r a


Table 4 Values of parameters of similarity between epicentral distance and PGA orders

for the considered signals triplets

Event occurrence time Similarity between epicentral distanceand measured PGA orders

Similarity between epicentral distance

and reduced PGA orders Data Origin time h m s

Source energy [J]

ρp(r,a) Wp(r,a) ρz(r,a) Wz(r,a)

22 Jan 2000 21:30:34 2.10×108 0.5 4 –1 0 19 Feb 2000 21:40:50 1.1×105 0.866 4 –1 0 22 Feb 2000 13:01:08 2.4×105 0.5 4 –1 0 09 Mar 2000 01:56:19 2×106 –0.5 2 –1 0 25 Mar 2000 21:52:40 4.5×107 1 4 –0.5 2 23 Apr 2000 00:16:07 5.7×106 0.5 4 –1 0 02 May 2000 20:05:14 9.6×107 1 4 –0.5 2 03 May 2000 22:48:10 2×106 –1 0 –1 0 20 Jun 2000 18:31:09 7.9×107 0.5 4 –1 0 15 Nov 2000 06:28:56 3.3×107 –1 0 –1 0 27 Jan 2001 12:19:58 4.3×107 –0.5 2 –1 0 28 Mar 2001 23:25:09 2.3×107 –1 0 –1 0 03 Apr 2001 13:05:48 6.2×107 –0.5 2 –1 0 21 Jun 2001 02:58:43 3.5×107 –1 0 –1 0 13 Jul 2001 21:14:25 1.4×107 –1 0 –1 0 05 Aug 2001 19:18:15 4.0×106 –0.5 2 –1 0

–1 0 –1 0 17 Aug 2001 18:47:36 3.1×107

–1 0 –1 0 30 Aug 2001 03:10:42 1.6×107 –1 0 –1 0

–1 0 –1 0 08 Sep 2001 23:15:28 5.0×106

–1 0 –1 0 –1 0 –1 0 11 Oct 2001 14:21:44 2.9×106

–1 0 –1 0 0.5 4 –0.5 2 12 Oct 2001 11:46:13 7.5×107

–1 0 –1 0 19 Oct 2001 16:44:14 1.7×108 –1 0 –1 0 31 Oct 2001 05:55:40 4.4×106 –1 0 –1 0 21 Nov 2001 03:03:57 6.4×107 –1 0 –1 0 22 Jan 2002 12:33:53 7.2×105 –1 0 –1 0 25 Jan 2002 10:09:41 1.3×107 0.5 4 –0.5 2 16 Feb 2002 16:25:43 4.5×108 –0.5 2 –0.5 2


316

Table 4 (continuation)

19 Feb 2002 21:33:39 2.0×106 –1 0 –1 0 20 Feb 2002 12:46:53 1.0×106 –1 0 –1 0

–1 0 –1 0 18 Mar 2002 07:34:51 1.1×106

–1 0 –1 0

1 4 –1 0 20 Mar 2002 09:24:06 1.6×108

–0.5 2 0.5 4

–1 0 –1 0 23 Mar 2002 18:42:18 7.8×106

–1 0 –1 0

26 Apr 2002 21:19:01 5.2×106 –1 0 –1 0 02 Dec 2002 17:38:18 7.9×107 0.5 4 1 4 24 Jan 2003 05:11:30 4.7×108 0.5 4 –0.5 4

If reducing PGA with amplification factor estimates improved the orders agree-

ment, then both null hypotheses would be false. Furthermore, ( )0 ,w r a median would be greatest than median. ( ,zw r a)

The first hypothesis was tested with Student’s t-test. The test statistic was t = 2.729 with 82 degrees of freedom which led to estimated significance of this hy-pothesis, p = 0.008. The second hypothesis was tested with the Wilcoxon pair test. The test statistic was Z = 3.124 and, thus, the estimated significance of this hypothe-sis p = 0.0017. The median of ( )0 ,w r a was equal to 2 and the median of was equal to 0. The significances of both hypotheses were small, which, together with the relation between and

( ),zw r a

(0 ,w r a) ( ),zw r a medians, evidenced that after reducing the observed PGA-s with the estimated amplification factor the agreement between the epicentral distance and PGA orders had improved. Such a result indicated indirectly that the amplification factor values obtained from the Nakamura method were, at least approximately, correct.

6. DISSCUSION AND CONCLUSIONS

The horizontal to vertical spectral ratio (HVSR) method, know also as the Nakamura method, is a convenient and reliable tool used in earthquake regions for estimating ground motion amplification of the surface layer. Here the HVSR method was applied to study site effects on the ground motion caused by seismic events induced by min-ing. Such sources cause that the initial assumptions of the method are not perfectly preserved. In place of the S-wave signal which was not identifiable we evaluated spec-tra from the whole traces. As a result, the HVSR values for higher frequencies tended


to increase because of the influence of surface waves and noise contents in the traces. Due to higher frequencies of mining seismic sources, the surface layer could change vertical components of ground motion, whose effect is not accounted for in the HVSR method. The fact that the recording station sensors were not mounted directly in the ground could also distort the measured signals.

In spite of the above-mentioned disadvantages, the obtained results are encourag-ing. HVSR curves for induced seismicity are qualitatively similar to the typical HVSR-s for earthquakes. Concerning the HVSR peak, which is used to estimate site amplification, the studies of selected signals groups showed that neither its location nor amplitude depends on source parameters, signal frequency and epicentral distance. To the contrary, the shape of HVSR does depend on a sensor location, which means that HVSR is directly linked to subsurface geology at the site. The estimated amplifi-cation factors, when used to reduce observed PGA to the bedrock, lead to a statically significant improvement of orders agreement between the PGA values and epicentral distances. This indicates indirectly that the estimates obtained by the HVSR method are, at least approximately, correct.

A c k n o w l e d g e m e n t s . This work was performed as a research project No. 11.11.140.06 of the Faculty of Geology, Geophysics and Environmental Protec-tion of the AGH University of Science and Technology, Kraków, funded by the Polish State Committee for Scientific Research.

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Received 12 February 2004 Accepted 26 April 2004

the work presents an attempt of application of the hvsr...

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