2. Pingtan Seismic Station, Earthquake Administration of Fujian Province, Pingtan 350400, Fujian, China
The magnitude of an earthquake is a basic parameter determined by a digital seismic network for describing an earthquake. The determination of earthquake magnitude is always an important research topic for seismologists. Usually, the magnitude of an earthquake is determined by measuring the amplitude of a certain seismic phase in seismic wave. Because the energy radiating in different directions is not uniform for earthquakes of different source types, seismic waves attenuate differently in different propagation paths and the site response differs among stations, all of which affect the amplitude of the recorded seismic waves. When calculating the magnitude, the attenuation of seismic wave in its propagation is compensated for mainly by a calibration function. Statistical regression on a large number of seismic events can eliminate the influence of the uneven distribution of energy due to different focal mechanisms and calculate the average magnitude deviation of each station, which reflects the station base difference in stations, and its value can be used as reference value for magnitude correction of a single station. Through statistical analysis of the average magnitude deviation and correction of a single station, Zhang Hongcai et al. (2010) used the earthquake magnitude of a single station (first station) to quickly estimate the final magnitude of the earthquake for early warning services. In addition, in recent years, many people inverted the site response of stations with the Moya et al.(2000) method, and then estimated the seismic source parameters for moderate and small earthquakes. The site response can reflect the condition of a station base. The output value of the two methods may reflect the influence of station base on the determination of magnitude. In this paper, the average magnitude deviation of each station is gained by regression statistics, the site response is obtained by the Moya inversion method, and then the magnitude deviation caused by the site response is estimated, and finally, by comparing the relationship between the average magnitude deviation and the site response of each station, the influence of the station base on the amplitude of seismic wave recorded by seismograph is analyzed.
1 MAGNITUDE DEVIATION STATISTICS OF THE STATION 1.1 Brief Introduction of Fujian Digital Seismic NetworkThe Fujian Digital Seismic Network consists of 88 seismic stations. In addition, the network can also access data from multiple stations of neighboring provinces for the purpose of data sharing (Fig. 1). In routine operation, the records of 13 stations of the neighboring provinces located within 30km from the provincial boundary line are also used in earthquake fast reporting and cataloging. In recent years, a wealth of seismic data within the province and the surrounding 30km are accumulated. In the 88 seismic stations of the Fujian Digital Seismic Network, three stations, namely YTFQ, PTAQ and ZPYF, are not included in the calculation because of their short running time and lower data accumulation.
The arithmetic mean of the single station's magnitude calculated from all the stations is determined as the magnitude of the seismic network. The deviation of the single station magnitude, the average magnitude of the network, the total average deviation and the total standard deviation are calculated, and these parameters can be used to evaluate the reliability of magnitude calculation of each station (Li Xueying et al., 2004). For a j earthquake, magnitude deviation of i station is: ΔM_{ij}=M_{ij}-
$ \Delta {\overline M _i} = \frac{1}{N}\sum\limits_{j = 1}^N {{M_{ij}}} $ | (1) |
And the standard deviation:
$ {\sigma _i} = \frac{{\sum\limits_{j = 1}^N {{{\left({\Delta {M_{ij}} - \Delta {M_i}} \right)}^2}} }}{{N - 1}} $ | (2) |
At present, the velocity record is simulated as a displacement record of the Wood-Anderson short-period seismograph to obtain the magnitude of earthquake. After simulation, the maximum amplitude and the corresponding period recorded on the horizontal displacement waveform are measured out, and the magnitude of M_{L} is calculated by the formula of the near earthquake magnitude, namely
$ {M_{\rm{L}}} = \lg \frac{{{A_{\mu {\rm{EW}}}} + {A_{\mu {\rm{NS}}}}}}{2} + R\left(\Delta \right) + C $ | (3) |
R (Δ) in formula (3) is for calibration function R_{1} (Δ) of a short-period seismograph, C for station base corrections, which are currently not available for the Fujian Digital Seismic Network. There are many factors influencing magnitude determination. Besides the influence of earthquake source radiation patterns, instruments, calibration functions, the station base also have influence on the magnitude deviation. Studies by Li Xueying et al. (2004) show that the type of instrument has some influence on the magnitude deviation, but the influence is not great. Zhang Hongcai et al. (2010) analyzed the influence of calibration function on the magnitude calculation, and considered that the effect was small and could be ignored. Xiang Yuewen et al. (2010), Chen Jifeng et al. (2013) calculated the average magnitude deviation according to the epicentral distance, found that the magnitude is smaller at stations with a shorter epicenter distance and larger at stations with a greater epicenter distance, and they used the negative magnitude deviation of each section as the calibration function. If there are a large number of earthquake samples in a wide range of epicentral distances, the magnitude deviation caused by different calibration functions due to the difference in epicenter distance can be eliminated, that is to say, it can be ideally assumed that the compensation of seismic wave attenuation in the propagation path by the calibration function is reasonable. Under the condition that the station is surrounded reasonably by many earthquake events, formula (1) can be used to eliminate the influence of the source radiation pattern. Thus, results obtained represent the influence of the station base on magnitude determination.
We selected the above six stations to measure the magnitude of 3069 earthquake events occurring from October 1, 2008 to December 31, 2015 in Fujian Province and its adjacent areas within 30km from the province border for the statistical study. According to formula (1), we calculate the average magnitude deviation of each station and count the number of samples used, taking HAHF station as an example (Fig. 2(a)). The period corresponding to the maximum amplitude used to measure the magnitude of each station is calculated, and the frequency of these periods are calculated, by taking HAHF station as an example (Fig. 2 (b)). We take the period which was measured most as the dominant period for the analysis of the corresponding site response. The output of each station is shown in the two figures in Fig. 2. Detailed results are shown in Table 1.
Using the Atkinson et al. (1992) method, the three-segment geometrical attenuation model and the joint inversion of multiple stations and multiple earthquakes, we calculated the average crustal inelastic attenuation in the Fujian area, and the site response of stations is calculated by the Moya method of multiple stations, multiple earthquakes joint inversion (Liu Jie et al., 2003; Hua Wei et al., 2009; Li Zuning et al., 2012). ISDP software, popularized by the Institute of Earthquake Science, CEA in the national seismic system, is applied for the calculation.
2.2 Data Selection and Calculation ResultsWhen calculating the inelastic attenuation and site response, according to the principle that an earthquake is recorded by at least three stations and one station shall record at least three earthquakes and the signal-to-noise ratio is larger than twice, 108 earthquakes with M_{L}≥2.0 which are relatively uniformly distributed and occurred in the period from September 2012 to April 2015 in Fujian Province and its adjacent areas within 30km, 98 seismic stations, and a total of 1996 ray paths are selected (Fig. 3). These earthquakes were used to calculate the inelastic attenuation by the Atkinson (1992) method in the Fujian area, which is Q(f)=452.4f^{0.3338}. Compared with the result of Q(f)=366.5f^{0.4282} by Li Zuning et al. (2012), the Q_{0} value is bigger, the attenuation coefficient is smaller. In the calculation, the neighboring provincial stations and earthquakes near the provincial boundary lines were taken into account, the radiation could basically cover the whole province, the Q-value should be able to objectively reflect the situation of the province. Compared with the results of the neighboring province, the results of Q(f)=437.5f^{0.3937} and Q(f)=423.6f^{0.3912} in Guangdong Province (Kang Ying, 2010), e.g. the result of Q(f)=361.0f^{0.458} in Zhejiang Province (Zou Zhenxuan, 2006), our Q_{0} value is close to that of Guangdong Province and the attenuation coefficient is smaller.
After obtaining the coefficient of the quality factor of the medium, the Moya method is used to calculate the site response curves of the 98 seismic stations (Fig. 4). In the 98 site responses of stations, the site responses of 62 stations generally fluctuate in the vicinity of 1 (Fig. 4(a-p)), the site responses of 12 stations fluctuate in the vicinity of 2 (Fig. 4(q-s)). The site responses curves of 24 stations change greatly, some of them showing large magnification or attenuation in the high frequencies (Fig. 4(t-y)). The site response of stations is quite different in the frequencies of 1-20Hz.
As shown in formula (3), the corresponding period of the measured maximum amplitude is not used when calculating the local magnitude M_{L}. The local magnitude M_{L} is obtained by measuring the amplitude of seismic waves with a period of 0.8s (Chen Yuntai et al., 2004), the period corresponding to the maximum amplitude measured in the actual records varies greatly, and the measured dominant periods of each station are shown in Table 1.
Site response is calculated by 98 equal interval frequency points in 1-20Hz, the site response values of the dominant period and the 0.8s period of each station are the mean of two adjacent frequency points in calculating the site response, and the results are shown in Table 1. The magnitude deviation of site response in the table is the logarithm of site response taken according to formula (3).
3 ANALYSIS OF THE RELATIONSHIP BETWEEN THE SITE RESPONSE AND THE MAGNITUDE DEVIATIONIn Table 1, 24-1532 earthquake samples are used in calculating the statistical average magnitude deviation of a single station, and there are 79 stations which used more than 150 earthquake samples, accounting for 81%; the average magnitude deviation is -0.31 to 0.68, in which stations with positive or negative values account for almost half, and compared with the values calculated by Zhang Hongcai et al. (2010) and Guo Yang (2014), most of the values differ by 0.1. The difference is great in the minority of stations, which might be related to the difference in the number of samples and stations. The standard deviation is 0.12-0.39, in which the number of stations with the value less than or equal to 0.25 is 83, accounting for 85% of the total number of stations.
The site response value corresponding to the 0.8s period of each station is 0.92-3.41, in which there are 95 stations with the value greater than 1, and the deviations are from -0.04 to 0.53. In taking the statistics of a dominant period of each station, the number of the measured periods used is 48-3053, with 88 stations using more than 200 periods. The statistical dominant period is 0.06-0.38s; the site response value ranges from 0.45 to 5.80, in which 76 stations have a value greater than 1, the deviation of the site response value is from -0.35 to 0.76, which is close to part of the site response deviations calculated by Zhang Hongcai et al. (2015) with the noise spectrum ratio method. Some might vary greatly, which might be associated with different methods of calculating the site response. By drawing the plot of the statistical average magnitude deviation versus the magnitude deviations influenced by the site response corresponding to the period of 0.8s and the dominant period, the statistical average magnitude deviation and the magnitude deviation corresponding to a site response of the 0.8s period is concentrated into clusters (Fig. 5(a)), which does not show a good relationship, but the statistical average magnitude deviation and the magnitude deviation corresponding to the site response of the dominant period show a good linear relationship (Fig. 5(b)), as ΔM_{r}=0.94×ΔM_{S}+0.13±0.25, the site response has greater impact on determination of M_{L} magnitude. The site response especially differs in different frequencies, which leads to different magnitude deviations caused by site response with different periods. Furthermore, it is considered that the magnitude deviation of a single station is related to the site response of the corresponding period of the measured maximum amplitude.
There are many factors that influence the determination of magnitude of an earthquake, through averaging of a large number of the sample to eliminate as far as possible the impact on seismic radiation pattern and on the calibration function from different epicentral distance. Without considering the same number of earthquake samples and weight in each station in every direction, the average magnitude deviation of each station obtained to reflect the response of a station base should have a certain bias. The inversion of the site response by the Moya method will be affected by the distribution of earthquake epicenters and stations. Some stations participating in the inversion with small number of samples and single direction cannot reflect the overall site response, nor the magnitude deviations that influence site response. The analysis of the relationship between the two deviations might also be a comprehensive relationship of various factors.
4 CONCLUSION AND DISCUSSIONThis article applies the 3, 069 regional earthquake events recorded by the Fujian Digital Seismic Network from October 2008 to December 2015 to the statistical analysis on the magnitude deviation of the single station and the average magnitude deviation of the network, obtains the average magnitude deviation of each station, and by counting the corresponding periods through measuring the maximum amplitude in the records, the dominant periods are gained. By inverting the site response of each station with the Moya method, we obtain the site response of 98 stations in the 1-20Hz bands, which shows that the site response has an amplifying or suppressing effect on certain frequency band signals; the site response corresponding to the inherent 0.8s period of the Wood-Anderson pendulum seismograph and that corresponding to the dominant period, as well as their relationships with the average magnitude deviation of each station are compared. Through the study, the following conclusions are drawn:
(1) The total average magnitude deviation of 98 stations in the Fujian Digital Seismic Network and its adjacent neighboring areas is in the range of -0.31-0.68; the periods corresponding to maximum amplitude measured out in the records are counted in determining the magnitude, the dominant period is in the range of 0.06s-0.38s.
(2) The site responses of 98 stations in the 1-20Hz band inverted by Moya method are quite different. Some stations are in the vicinity of 1, some are in the vicinity of 2, and the overall curve of some stations changes remarkably, indicating that the effect of site response on the signals differs greatly in different frequency bands in the stations.
(3) The corresponding effect of the magnitude deviation calculated by the site response to the inherent 0.8s period of the Wood-Anderson Standard Seismograph and the single station total average magnitude deviation is not good; the corresponding magnitude deviation calculated by the site response to the dominant period and the single station total average magnitude deviation presents a close relationship, with the linear relationship as ΔM_{r}=0.94×ΔM_{S}+0.13±0.25, i.e., the statistic magnitude deviation of each station reflects the influence of site response corresponding to the period of maximum amplitude measured out in determining the magnitude.
(4) During the statistics of the total average magnitude deviation of each station, we only eliminate the influential factors through a large number of earthquake samples. Without considering the reasonable distribution, the samples' weight, as the obtained value may contain the influence of many factors. The site response calculated by the Moya method is affected by the calculated seismic data and the layout of the stations, so the results of some stations may not reflect the real site response. If we can build a model and choose sample data more scientifically and reasonably and eliminate the influence of various factors, we may be able to get a more objective and reasonable relationship between the magnitude deviation influenced by the site response and the average magnitude deviation of each station.
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2. 福建省地震局平潭地震台，福建平潭 350400