Earthquake magnitude is the representation of earthquake intensity, which is one of the basic parameters describing an earthquake and one of the important parameters in earthquake prediction research (Chen Yuntai et al., 2000, 2004). Measuring an earthquake with the magnitude has the advantages of being simple and practical, but the biggest drawback to this is the magnitude saturation effect. The moment magnitude is a mechanical quantity that describes the absolute size of an earthquake, so it is the most ideal physical quantity to measure the magnitude of the earthquake, and there is no saturation problem (Gao Jingchun et al., 2011; Yang Jingqiong, 2013). In 1977, Kanamori defined the moment magnitude M_{W}, and put forward the relationships between the seismic moment, the moment magnitude and the seismic wave energy (Kanamori H., 1977). In 1981, Dziewonski et al. (1981) completed the moment tensor inversion of centroid moment tensor solution (Dziewonski et al., 1981, Sipkin, 1982), and achieved the rapid release of moment magnitude M_{W}. The United Stated Geological Survey, in its 2001"USGS", specifically requests that the moment magnitude shall be the preferred magnitude released to the government agencies and the public. M_{W} is able to connect with conventional surface wave magnitudes within a certain magnitude (Chen Yuntai et al., 2004). In the latest"Earthquake Magnitude Regulation" (GB17740-2017), the moment magnitude M_{W} is the preferred magnitude to be released. After the Wenchuan earthquake in 2008, the earthquake emergency work has imposed higher demands on the output of seismic network. After several years of development, it has become possible to incorporate the focal mechanism solution and moment magnitude into the traditional earthquake catalog (Kang Ying et al., 2015), and has laid a solid foundation for the daily output of moment magnitude.
The seismic structure is complex in the central and western regions of Inner Mongolia (104°-115°E, 36°-42°N), the difference of regional characteristics is very obvious, and moderately strong earthquakes occur frequently (Cao Gang, 2001). Since 1970, there have been a series of moderately strong earthquakes (Sun Jialin et al., 1998), such as the M_{S}6.3 earthquake in Horinger in 1976, the M_{S}6.2 earthquake in Bayinmuren, and the M_{S}6.0 earthquake in Wuyuan in 1979. So far, research on the moment magnitude of small and medium-sized earthquakes has not been carried out in Inner Mongolia. The near field digital seismic waveform data recorded by the Inner Mongolia Digital Seismic Network from 2008 to March, 2016 is used in this paper to calculate the source spectrum parameters of small and medium-sized earthquakes using the multi-station joint inversion method (Liu Fang et al., 2007; Yang Jingqiong et al., 2010). As a result, the seismic moment M_{0}, the moment magnitude M_{W} and the stress drop σ of these earthquakes are obtained. The linear regression method is used to study the relationships between the near earthquake magnitude M_{L} and M_{W}, M_{W} and σ, in order to provide a scientific reference for strong earthquake quick reporting, earthquake cataloging and related seismological studies.
1 DATA SELECTION AND DATA PROCESSINGSeismic waveform data of 202 earthquakes occurring in the central and western regions of Inner Mongolia are selected for "S window"data preprocessing to get the quality factor value Q(f) and station site response in this area. According to the principle of "signal to noise ratio greater than 2, and the recording station number for each earthquake N≥4"(Liu Lifang et al., 2010; Yang Jingqiong et al., 2013), seismic source parameters (seismic moment, moment magnitude and stress drop) of 182 earthquakes that met the requirements are finally obtained.
1.1 Data SelectionThere are 22 seismic stations in the central and western regions of Inner Mongolia (including eight in Inner Mongolia, one in Hebei, nine in Ningxia, and four in Shanxi), except for stations TLE and LWU of the Ningxia Digital Seismic Network whose stylobates are of clay, the stylobates of the remaining twenty stations are all of bedrock. The stations are equipped with five types of 24-bit data acquirers, namely, EDAS-24IP, EDAS-24GN6, EDAS-24L6, SMARRT-24R and CMG-DM24, and four types of seismometers; ground ultra-broadband, very broadband, borehole very broadband and broadband, with a ground motion velocity response frequency of 60s/50Hz. The effective seismometer dynamic range is more than 130dB, the sampling rate is 100 points per second, and the dynamic range of data acquisition is more than 130dB. Two hundred and two earthquake events with M_{L}≥2.8 occurring during 2009-March, 2016 are selected to measure the moment magnitude in this study (Fig. 1), it can be seen from Fig. 1 that the 202 earthquakes basically cover the central and western regions of Inner Mongolia, basically reflecting the characteristics of the geological structure of the region.
Before measuring the moment magnitude, the"S window" should be intercepted. The"S window" is defined as the time period from the initial S-wave to 90% of the total energy of S-wave. However, the"90% of total energy of S-wave"is only a theoretical concept, which is realized by human-computer combined"visual reading". Experienced analysts and permanent personnel are selected to read the arrival time of seismic phase and the"S window", so as to avoid reading errors to the maximum extent.
According to the above reading principles, the arrival time of the seismic phase and the closing times of the"S window"of the 182 earthquakes are defined, and the fitting relationship between the length of "S window"and Sg-Pg is also obtained (Fig. 2). From Fig. 2, the fitting relationship is the linear relationship, the root-mean-square is 0.11. The relationship between the length of the"S window"and Sg-Pg is as follows:
$ {T_{{\rm{se}}}} - {T_{{\rm{sf}}}} = 0.78({T_{{\rm{Sg}}}} - {T_{{\rm{Pg}}}}) + 16.3 $ | (1) |
Where, T_{se} is the closing time of "S window"; T_{Sf} is the arrival time of S_{f}, and T_{Pg} is the arrival time of Pg.
S_{f} is the first arrival time of S-wave phase: ① if the station records the arrival time of Sn, S_{f} is equal to the arrival time of Sn; ② if there is no Sn, S_{f} is equal to the arrival time of Sg.
1.2.2 The Determination of Q Value and the Site Response of the StationThe quality factor Q(f) in the research area and the site response of 22 stations should be determined before calculating the moment magnitude. The 46 seismic waveform data with relatively clear waveforms from 2009 to 2015 (3.0≤M_{L}≤4.7) are used for the inversion of quality factors Q(f). In the range of 1- 20Hz, the value of quality factor Q(f) has a good linear relation with its frequency (Fig. 3, formula (2)).
$ Q\left(f \right) = {Q_0}{f^n} $ | (2) |
Where, Q_{0}=556.3 is the Q value when the frequency is 1Hz, and 0.3775 is the absorption coefficient η of the medium.
$ Q\left(f \right) = 556.3{f^{0.3775}} $ | (3) |
The site responses of 22 stations are obtained according to the above quality factor Q(f). Among them, a total of 14 stations' site responses are near 1, namely, the stations of Baochang, Liangcheng, Horinger, Jining, Xishanzui, Kangbao, Niushoushan, Xiangshan, Zhongwei, Tongxin, Yanchi, Taole, Yinchuan and Shizuishan, where the change of site response is small along with the change of frequency. The site response of the Lingwu and Baoheshao stations has a slight amplification effect. It can be seen from the analysis that the amplification effect at Lingwu station is due to the relatively soft soil layer (Jin Chunhua et al., 2012), and the amplification effect of Baoheshaotai station is due to the thick surrounding coating. The site response at Baotou and Eelianhaote stations has a slight attenuation effect, it may be because that the base rock of the station is relatively hard or it is influenced by the geological environment of the station (Wang Xin et al., 2015). The site response of Datong and Zhenchuan stations shows a slight attenuation at low frequencies and amplification effect at high frequencies. The site response of Youyu and Pianguan stations is near 1 at low frequencies and the amplification effect is obvious at high frequencies. Fig. 4 only shows the site responses of HLG, JIN, LCH, XSZ, ZCH and SHZ stations.
In summary, the site responses of the 14 stations of the 22 stations are around 1, accounting for 63.6% of the total, site responses of 4 stations have slight amplification or attenuation effects, accounting for 18.2% of the total, the site responses of another 4 stations have amplification effects at high frequencies, accounting for 18.2% of the total. According to the analysis, the accuracy of the magnitude measurement is almost guaranteed by the change result of site responses of these 22 stations.
Based on the results of "S window"selection, quality factor and site response, the seismic source parameters of the 182 earthquakes that met the conditions are finally obtained, and the earthquakes and station rays are shown in Fig. 5.
"An earthquake is a bright lamp that illuminates the interior of the earth in a moment", extracting and analyzing the rich information carried by seismic waves is the most important way to overcome the"invisibility"of the earth's interior.The seismic wave recorded by seismograph contains the"effect of seismic source, effect of propagation path of seismic wave (geometric diffusion of medium, inelastic attenuation of medium), site response of station, instrument response and noise".The source spectrum can be obtained only by deducting the propagation path effect, station site response and instrument response, etc.
The Fourier spectrum of the i seismic ground motion recorded by seismograph at the station j is:
$ {A_{ij}}\left(f \right) = {A_{i0}}\left(f \right) \cdot G\left({{R_{ij}}} \right) \cdot {S_j}\left(f \right) \cdot {I_j}\left(f \right) \cdot {{\rm{e}}^{ - \frac{{\pi {R_{ij}}f}}{{Q\left(f \right)\beta }}}} $ | (4) |
where, A_{ij}(f) stands for the Fourier amplitude spectrum (observed spectrum) of the i earthquake observed at the j site, A_{i0}(f) is the amplitude spectrum of seismic source (source spectrum) of the i earthquake, R_{ij} is the hypocentral distance (the i earthquake to the j station), G(R_{ij}) is the function of geometric attenuation, Q(f) is the frequency-dependent quality factor, β is the velocity of seismic wave (S-wave only here), S_{j}(f) is the site response term of the j station, I_{j}(f) is the instrument response term of the j station, and f is the frequency.
Within the frequency domain, the seismic source spectrum A_{i0}(f) is obtained after correction of the geometrical attenuation, inelastic attenuation, site response and instrument response of the observed displacement spectrum A_{ij}(f). In this paper, the influence of the propagation path is calculated by using the models of three-section geometric attenuation (Atkinson G.M., Mereu R.F., 1992; Wong Yuklung et al., 2003), the site response of the station can be calculated using the joint inversion of multiple stations and multiple earthquakes (Moya et al., 2000), and the instrument response can be calibrated through instrument calibration.
When calculating the seismic source spectrum of the station, it is necessary to deduct the transmission path effect, the site response of the station and the instrument response. The most critical is the medium quality factor Q of the medium of the quality factor, it is an important physical parameter of earth medium to describe the characteristics caused by the imperfect elasticity of medium, the attenuation of seismic wave in the process of propagation in the medium, or the energy dissipation defined as:
$ \frac{1}{Q} = \frac{1}{{2\pi }}\frac{{\Delta E}}{E} $ | (5) |
where, E stands for the accumulated energy in the movement of a certain volume of earth medium in a seismic wave period T (or a wave length λ), and ΔE the wasted energy in the movement of the same volume of medium in a seismic wave period T (or a wave length λ). It can be seen from formula (5), when the seismic wave propagates in a medium with larger Q value, the energy dissipation is smaller and the wave attenuation is slower.
Using the source spectrum model ω^{2} of Brune's quadratic attenuation as the theoretical source spectrum A_{the0}(f), the minimal residual source spectrum parameter Ω_{0}(zero frequency amplitude) and the corner frequency (Brune, 1970) defined by A_{0}(f) and A_{the0}(f) are calculated by using the genetic algorithm. The source parameters, i.e. seismic moment M_{0} and stress drop Δσ, are calculated by using the obtained source spectrum parameters.
$ {M_0} = \frac{{4{\rm{ \mathsf{ π} }}\rho {\beta ^3}{\mathit{\Omega }_0}}}{{2{R_{\theta \varphi }}}} $ | (6) |
where, density ρ is set as 2.7g/cm^{3}, β is the velocity of S-wave, R_{θφ} is the source radiation pattern coefficient, so:
$ \Delta \sigma = \frac{7}{{16}}\frac{{{M_0}}}{{{r^3}}} = \frac{{\rho {{\left({2\pi {f_c}} \right)}^3}{\mathit{\Omega }_0}}}{{2.34{R_{\theta f}}}} $ | (7) |
In the formula, density ρ is set as 2.9g/cm^{3}, β is the S-wave velocity (set as 3.5km/s), r is the source characteristic scale, R is the radiation pattern coefficient.
Moment magnitude M_{W} is calculated from the seismic moment M_{0} (Kanamori H., 1977a, 1977b; Hanks T.C. et al., 1979), as:
$ {M_{\rm{W}}} = \frac{2}{3}\left({\lg {M_0} - 9.1} \right) $ | (8) |
According to the above principle, the value of parameters of the seismic source (seismic moment, moment magnitude and stress drop) are obtained for the 182 M_{L}≥2.8 earthquakes, and the calculation results of seismic source parameters for 19 M_{L}≥3.8 earthquakes are listed in Table 1.
The moment magnitude is a magnitude scale determined completely by the seismic moment. The moment magnitude is defined originally by the consistency principle of the determination results (Liu Ruifeng et al., 2015). The moment magnitude reflects the size of deformation scale, it is the best physical quantity to measure the earthquake magnitude, and will not cause the problem of magnitude saturation.
First of all, a comparative analysis is made between the measured near earthquake magnitudes M_{L} and the moment magnitude M_{W} (Fig. 6), and the linear relationship between M_{L} and M_{W} can be seen from Fig. 6. Most earthquakes in this study are below magnitude 4.5, their hypocenters are basically point sources, the dominant period of the seismic wave is about 1.0s, and the size of the earthquake can be indicated well by the near earthquake magnitude M_{L}. However, the moment magnitude M_{W} is a homogeneous magnitude scale, and can represent all sizes of earthquakes no matter whether it is a large earthquake or a small earthquake, a bathyseism or a shallow earthquake.
The M_{L} and M_{W} of the 182 earthquakes are analyzed using the linear regression method (Fig. 6, Table 2). From Fig. 6, the near earthquake magnitude M_{L} changes in the range of 2.8-5.0, the moment magnitude M_{W} changes in the range of 2.5-4.2, there is a good linear relationship between M_{L} and M_{W}, the correlation coefficient R=0.9302, indicating that with the increase of M_{L}, the moment magnitude M_{W} also increases. The regression relationship between M_{L} and M_{W} is as follows:
$ {M_{\rm{W}}} = 0.72{M_{\rm{L}}} + 0.66 $ | (9) |
Analyzing the fitting relationship finds that: when M_{L}=2.35, M_{L} and M_{W} are equal; when M_{L} is smaller than 2.35, M_{L}>M_{W}; when M_{L}>2.35, M_{L} < M_{W}.
3.3 The Relationship between Moment Magnitude and Stress DropBased on the linear regression method, a regression analysis is performed on the moment magnitude M_{W} and the stress drop Δσ of the 182 earthquakes (Fig. 7). As it can be seen from Fig. 7, M_{W} and lgΔσ have a weak positive correlation, basically, lgΔσ increases with the increase of M_{W}. When M_{W} < 2.5, the linear relationship is not obvious; When M_{W}>2.5, the relationship is significant. The distribution range of the moment magnitude is between 2.5 and 5.4, and the distribution range of lgΔσ is 10^{-1}-10^{4}, and the dominant distribution is in 1-10^{2}, indicating that M_{W} has a weak dependence on lgΔσ.
Through the study of moment magnitude of moderate and small earthquakes in the central and western regions of Inner Mongolia, it can be seen that incorporating the moment tensor solution that describes the source physical properties into the quick report and official report of the earthquake catalogue can not only avoid the problem of magnitude saturation, but also can integrate with international seismic data. At the same time, it can enrich the content of earthquake observation report to provide better service for earthquake emergency response and earthquake research.
(1) The moment magnitude is a uniform magnitude scale, suitable for statistics of a wide range of magnitudes, there will be no phenomenon of magnitude saturation, it can be used to measure not only a major earthquake, small seism, micro earthquake and even a minimal vibration, but also shallow earthquake and plutonic earthquakes. Studies suggest that, within a certain magnitude range, the moment magnitude can be connected with the conventional surface wave magnitude, and it is feasible to measure the moment magnitude of small and medium earthquakes in the local seismometry network.
(2) There is a good positive correlation relationship between the near earthquake magnitude M_{L} and the moment magnitude M_{W}. With the increase of M_{L}, the moment magnitude M_{W} also increases. The regression relationship between M_{L} and M_{W} is M_{W}=0.72 M_{L} +0.66.
(3) There is a basically weak linear relation between the moment magnitude M_{W} and the logarithm of stress drop lgΔσ, indicating that M_{W} has weak dependence on lgΔσ.
(4) In view of the time period studied in this paper, the number of earthquakes (M_{L}≥2.8) is small in the central and western regions of Inner Mongolia, and the earthquake distribution is not uniform, the relationships established between near earthquake magnitude and moment magnitude, moment magnitude and stress drop are yet to be continuously improved in the future, in order to make it more in line with the scaling relationships of statics parameters in the Inner Mongolia region.
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