2. Institute of Geophysics, China Earthquake Adninistration, Beijing 100081, China
With the popularization of broad frequency band digital seismic networks, the extraction of focal parameters such as seismic moment, stress drop and fracture radius of focal rupture from moderate and small earthquakes becomes basic work from seismic networks, which holds important significance for earthquake prediction and earthquake risk research. To precisely calculate focal parameters, it is necessary to get rid of the influence of propagation paths and monitoring sites upon the signals. It was found in previous research that some bed rock bases cannot completely avoid the magnification of the surface in the selection of reference stations, which leads to some deviations. Thus, the calculations of the inelastic attenuation in the research areas and the site response of each station can accurately remove the influence of propagation paths and monitoring sites on the signals, and obtain more accurate focal parameters.
After the completion of the fifteenth "Five-year Plan" projects, the Jiangsu Digital Seismic Network has 41 digital seismic stations (including 14 well stations and 1 island station). The stations are distributed evenly across the province. The distributions are dense in the south and north of the province, and less dense in the middle part and the coastal areas of the province with well stations as the staple because these areas have a loose sink base. In order to improve the monitoring ability of the edge earthquakes between the networks, we also use the real-time waveform data from 32 stations from Henan, Shandong, Anhui, Zhejiang and Shanghai within the SDH system of China Earthquake Networks. Up to now, the number of stations from which the Jiangsu Earthquake Monitoring Networks Center receives real time waveform data has reached 73.
This paper uses the S-wave data of the 49 earthquakes recorded by 73 digital seismic stations in Jiangsu and its neighboring areas, and obtains the average inelastic attenuation coefficients and geometric diffusion coefficients of the crust of the research region (115°-123°E, 29°-37°N) with Atkinson multi-station joint inversion, as well as site responses of the 63 stations with Moya calculation. We also discuss about the focal parameters of the M_{L} > 2.5 earthquakes recorded in the Jiangsu Seismic Networks from 2010 to 2015 on the basis of the Brune model.
1 DATA SELECTIONTo meet the needs of even distribution of earthquakes and stations, the SNR of seismic wave forms should be twice as large and there should be at least 3 stations recording an earthquake. Each station should have at least 3 earthquake records with the upper scale of M_{S}5.0. We selected 49 earthquakes of over M_{L}2.7 in Jiangsu and its neighboring regions recorded by the Jiangsu Digital Seismic Networks from January 2001 to April 2015 and 63 stations for the inversion calculation of inelastic attenuation and site response (Fig. 1). It is shown in Fig. 1 that the selected earthquakes cover Jiangsu and its neighboring areas and the coastal regions. The Q-values can represent the average inelastic attenuation coefficients of the province and the neighboring areas.
When instrument responses, noises and free surface effects are removed from the observation displacement spectrum, the SH component of the Fourier spectrum of the surface movement shear waves observed by any station in any earthquake can be expressed as (Hartzell, 1992):
$ {{A}_{ij}}\left(f \right)={{A}_{iO}}\left(f \right)\cdot G({{R}_{ij}})\cdot {{e}^{\frac{-\pi f{{R}_{ij}}}{Q\left(f \right)\beta }}}\cdot {{S}_{j}}\left(f \right) $ | (1) |
where A_{ij}(f) stands for the Fourier spectral amplitude of the S-wave observed by the jth station in the ith earthquake, A_{io}(f) is the focal spectral amplitude of the ith earthquake, G(R_{ij})is the geometric diffusion function, Q(f)is the quality factor of S waves, R_{ij} is the focal distance, β is the S-wave velocity, and S_{j}(f) is the site response of the jth station. The relationship between the inelastic coefficient and the medium quality factors is:
$ Q\left(f \right)=\frac{\text{lg}(\text{e})\text{ }\!\!\pi\!\!\text{ }f}{c\left(f \right)\beta } $ | (2) |
Substitute equation (2) for equation (1) and take the logarithm of both sides and the result is:
$ \text{lg}{{A}_{io}}\left(f \right)=\text{lg}{{A}_{ij}}\left(f \right)-\text{lg}G({{R}_{ij}})+c\left(f \right){{R}_{ij}}-\text{lg}{{S}_{j}}\left(f \right) $ | (3) |
where the three sectional attenuation model is taken:
$ {{G}_{ij}}=\left\{ \begin{align} &R_{ij}^{-{{b}_{1}}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {{R}_{ij}}\le {{R}_{1}} \\ &R_{1}^{-{{b}_{1}}}R_{1}^{{{b}_{2}}}R_{ij}^{-{{b}_{2}}}\ \ \ \ \ \ \ {{R}_{1}}\le {{R}_{ij}}\le {{R}_{2}} \\ &R_{1}^{-{{b}_{1}}}R_{1}^{{{b}_{2}}}R_{1}^{-{{b}_{2}}}R_{1}^{{{b}_{3}}}\ \ \ R_{ij}^{{{b}_{3}}}{{R}_{ij}}\ge {{R}_{2}} \\ \end{align} \right. $ | (4) |
where R is the focal distance, R_{1} and R_{2} are the focal distances from the turning points of Section 1 and Section 2 in the three sectional geometric diffusion, and R_{1}=1.5D and R_{2}=2.5D. D is the crust thickness of the research region and the average crust thickness in Jiangsu and its neighboring areas is 33km. b_{1}, b_{2} and b_{3} are 1, 0, 1/2 respectively.
The Atkinson method (Atkinson et al., 1992) is used to calculate the inelastic attenuation coefficients c(f). This method assumes that the source spectra of the same earthquake recorded by different stations are the same, and the adjustment of c(f) value helps obtain the minimum residues of the focal spectral amplitudes of the same earthquake. The residue is defined as:
$ {{\delta }_{ij}}={{\left[ {{A}_{iO}}\left(f \right) \right]}_{j}}-\overline{\lg {{A}_{iO}}\left(f \right)} $ | (5) |
In equation (5),
$ \delta =\sum\limits_{i}{\sum\limits_{j}{{{\delta }_{ij}}}} $ | (6) |
The inelastic attenuation coefficients and geometric diffusion functions can be obtained by calculation of the minimum total residue with the help of heritage calculation.
See the references for the specific calculations (Liu Jie et al., 2003; Huang Yulong et al., 2003).
The Q values of the inelastic attenuation coefficient of Jiangsu and its neighboring areas are 1-20Hz (Fig. 2) Fig. 2 shows a good linear relation between Q and f. The relationship between Q(f) and the frequencies after the fitting is Q(f)=272.1·f^{0.5575}.
We use the Moya's method (Moya et al., 2000) for site response inversion. The method assumes that there is no connection between site responses and earthquakes. The focal spectrum parameters are first selected for each earthquake (Brune, 1970, 1971). Each focal spectrum parameter is used to calculate the site response at the recording station. Different focal spectrum parameters can be obtained by heritage calculation to get the minimum standard deviation of the site responses of the stations in different times and obtain the final site responses. The detailed steps are: first to rectify in terms of geometric diffusion and inelastic attenuation the S-wave Fourier spectral amplitude observed at the jth station in the ith earthquake, and three sectional linear regression is adopted for the geometric diffusion. Then for each earthquake, focal spectrum parameters such as zero frequency amplitude Ω_{0}and corner frequency f_{c} are selected and thus the theoretical focal spectrum of each earthquake can be obtained.
$ {{S}_{i}}\left(f \right)=\frac{{{\mathit{\Omega} }_{0i}}}{1+{{(f/{{f}_{ci}})}^{2}}} $ | (7) |
Therefore, the site response of the jth station for the ith earthquake at the k frequency is
$ {{G}_{ij}}({{f}_{k}})=\frac{O_{ij}^{\text{corr}}({{f}_{k}})}{{{S}_{i}}({{f}_{k}})} $ | (8) |
The residue of the standard deviation and average of the site response of the jth station for different earthquakes at the k frequency is defined as
$ {{\delta }_{jk}}=\frac{{{[{{G}_{ij}}({{f}_{k}})]}_{\text{std}}}}{{{[{{G}_{ij}}({{f}_{k}})]}_{\text{mean}}}} $ | (9) |
The heritage calculation is used to adjust the focal spectrum parameters of all earthquakes to minimize the following equation and obtain the site responses of all stations.
$ \delta =\sum\limits_{j}{\sum\limits_{k}{{{\delta }_{jk}}}} $ | (10) |
The above calculations help obtain the site responses of the 63 stations in Jiangsu and its neighboring areas as shown in Fig. 3. Fig. 3(a) displays the site responses of the 25 stations of surface bed rock types. Fig. 3(b) shows the site responses of the 14 well seismic instruments. Fig. 3(c) is the site responses of the 24 shared stations outside the province. The results show that most site response magnifications of the bed rock base within Jiangsu Province are around 1, i.e. without obvious magnifying effects. The exception is Sihong surface station in the northern province whose base is andesite and there is magnification of 3 to 4 times in the low frequency which attenuates to 0.1 in the high frequency. We used well seismic instruments in the middle part of the province because of the thick covering layer. There is a consistency of morphology curves of the site responses. At most stations, the low frequency is magnified 2 to 5 times and the high frequency attenuates to 0.1-0.8 times. This could be caused by the influence of the loose sediment bed bases and the sites. Here the well instruments in the middle part of the province are LAS, the bed base is quartzite, the site response curve is flat and the high frequency attenuation is not obvious. Fig. 3(c) shows that the curves of all site responses are flat but the values and selections of site response do not focus around 1 but between 0.3 to 4.
According to Brune's findings (1970) the relationship between seismic moments, stress drops and focal radius is defined as
$ {{M}_{0}}=\frac{4\pi \rho v_{\text{S}}^{3}{{\mathit{\Omega} }_{0}}}{2{{R}_{\theta \varphi }}} $ | (11) |
$ \Delta \sigma =\frac{7{{M}_{0}}}{16{{r}^{3}}} $ | (12) |
$ r=\frac{2.34{{v}_{\text{S}}}}{2\pi {{f}_{c}}} $ | (13) |
where ρ is the density, v_{S} is the S velocity, R_{θφ} is radiation pattern coefficients, Ω_{0} is the zero frequency value, and f_{c} is the corner frequency. Equations 11 -13 are used to calculate 149 earthquakes of M_{L}≥2.5 from October 2010 to May 2015 and the focal spectrum parameters and focal parameters are obtained about 58 earthquakes (Table 1).
We analyze the relationships between the seismic moments, focal scales, corner frequencies, stress drops and near earthquake magnititude (M_{L}) as is shown in Figs. 4(a), 4(b), 4(c), and 4(d). The increased closeness of r^{2}in figures to 1 shows the increased closeness of its relationship with near earthquake scales. It can be seen in the figures that the fitting relationship between the seismic moment and near earthquake magnititude (M_{L}) is best with r^{2} reaching 0.9254. There is an increase of the focal scales corresponding to the increase of the scales with relativity of 0.5623. The corner frequencies become smaller as the scales become larger with relativity of 0.5623. The stress drops have a weak relativity of 0.247 with the scales.
The Q values of this paper are lower than those in the study of southern Jiangsu by Liu Honggui et al. (2004). It is generally believed that Q values are higher in the more stable tectonic activity areas and lower in strong tectonic activity areas (Signh et al., 1983; Li Baiji et al., 2004). The present research includes the whole Jiangsu region. The northern Jiangsu and the coastal areas of the province have a large chasmic basin, north-south Yellow Sea basin and a number of faults, and the Jiangsu-Anhui bordering area has the southern section of the Tanlu (Tancheng-Lujiang) fault, which is a deep and large fault in the eastern Chinese mainland. Modern earthquake activities are not very strong, but the geological structures are very complicated (Gu Qinping et al., 2016). The strongest earthquake in Eastern China occurred on this fault belt on July 25, 1668 in Tancheng, Shandong. Compared with the previous studies, the tectonic activities in the present study region are stronger than those in southern Jiangsu, and the Q-value is lower. In our calculation, the medium quality factor of the Jiangsu region is Q(f)=272.1·f^{0.5575}, similar to that of Shen Xiaoqi et al. (2005) study. This indicates that the average Q-value of Jiangsu and its neighboring areas is consistent with that of the Anhui region.
It can be seen from the inversion result of the site responses of the 63 digital seismic stations in Jiangsu and its neighboring areas that in the middle part of Jiangsu and coastal area with loose sediments, all other 11 well seismometers have site responses of the magnification of low frequency and the rapid attenuation of high frequency, except for the site response of the LAS station which is stable and close to 1. Most of the surface seismometers in Jiangsu have site response magnitudes close to 1. The site responses of the stations in the neighboring provinces, compared with those of the stations in Anhui and Shandong Digital Seismic Networks, show consistent curves between them, but the magnification factor at some stations are different, which could be related to site selection.
The calculation of the focal parameters of 58 earthquakes with M_{L} > 2.5 shows that the seismic moment has the best fitting with near earthquake magnitudes and the focal scale increases in some way with the increase of the magnitude. The corner frequency tends to decrease with the magnitude and the relationship of the stress drop with the magnitude is not clear.
ACKNOWLEDGEMENT: The software used in the research comes from the Institute of Earthquake Science, CEA and the graphs in the paper are drawn with GMT and Matlab. Research Professors Zhao Cuiping, Liu Jie, Hua Wei, and Wang Qincai offered us valuable advice and aids. We owe our greatest gratitude to all of them.
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