2. Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
The ground motion attenuation relationship is influenced by the source effect, path effect and site effect, which can be used to calculate the ground motion of an engineering site. It has been widely used in seismic zoning map compilation and seismic safety evaluation. It is also one of the important research directions of engineering seismology. The methods of ground motion estimation are divided into the empirical method and theoretical method (Jiang Hui, 2005). The empirical method has a direct statistical method and conversion method. The direct statistical method is statistical regression according to an attenuation relationship formula with the existing target strong motion records. We've considered both the source effect and path effect in this statistical relationship. The method is fit for the countries and regions which have a lot of strong ground motion records, such as Japan and the Western United States. The theoretical method is also called the mapping method, that is to say, we choose a region which has a lot of strong motion records and also has similar regional tectonic conditions as a reference area, then we assumed that any point in the reference area has a matching point in the research area. If the two same epicentral distance points have the same earthquake intensity, then they have the same ground motion parameters. Although the physical conception of this method is not clear, it is a way of dealing with a lack of strong motion records. The theoretical method uses the dislocation and rise time to describe the source, and uses the seismic wave theory to simulate shear wave propagation from the source to site in homogeneous semi-infinite space. The theoretical method includes the theoretical Greens function method, the experiential Greens function method and the numerical Greens function method. The theoretical Greens function method can obtain a theoretical vibration map based on mathematics and physics. This method is suitable for a horizontal stratified medium, and also needs accurate seismic wave propagation path information and local site three-dimensional shear wave velocity structure information. In fact, it is difficult to calculate the theoretical Greens function (Li Qicheng et al., 2010). The experiential Greens function method is a half-theoretical method, which regards large earthquakes as a series of small earthquakes with the same focal mechanism. The large earthquake ground motion time history can be obtained through superposition of the Greens function of small earthquakes. The result contains source effect, path effect and site effect as this method is based on small earthquake records, however the section of high frequency seismic waves is unstable, in which an artificial cycle exists.
McGuire et al.(1980), Hanks et al. (1981) used Parsevel theorem of random vibration theory and statistical property of maximum random process value based on the ω^{2} point source model to estimate the attenuation relationship between RMS of ground motion acceleration and peak ground motion acceleration. Boore (1983) compared the results between the random vibration method and point source method to synthesize the ground motion time history, and both methods have good consistency. Based on the limited duration, limited bandwidth white noise random vibration theory, Atkinson (1984) used Hanks' (Hanks T.C. et al., 1981) method to calculate the ground motion acceleration attenuation relationship in Eastern Canada, where there was a lack of strong motion records. Atkinson et al.(1992) used the regression and inverse method to research the ground motion attenuation relationship of Canada, and determined the geometric attenuation and inelastic attenuation. Boore (2002) combined the regional parameters, the geometric attenuation parameters and the crust structure study in North America to develop the procedure of the stochastic method. Wang Guoxin et al. (2001) used the two-step regression method to build the ground motion acceleration attenuation relationship of Northern China based on the improved source spectrum model. Tao Zhengru (2010) used the last 10 records from the Northeastern Japan F-net stations and selected the Fourier spectrum as the objective function to invert the stress drop Δσ, quality factors Q_{0} and η, using the results to build the peak ground motion acceleration attenuation relationship by the random vibration method. Cui Anping (2013) selected 147 records of 82 small earthquakes in Sichuan Province and 863 records of 154 small earthquakes in Yunnan Province and took the acceleration Fourier spectra as the objective function to invert the seismic source parameters and the crustal media parameters, such as stress drop Δσ, quality factors Q_{0} and η, geometric attenuation parameters R_{1} and R_{2}, building the peak ground motion acceleration attenuation relationship of the Yunan-Sichuan region with the results. The author (Li Wenqian, 2014) selected 592 records of 33 small earthquakes in Lanzhou region to invert the peak ground motion acceleration attenuation relationship of the Lanzhou region, and applied this attenuation relationship to the Lanzhou region zoning map and found that most of the regions are in good agreement, while some areas are lower. At the same time, the author used 1995 records of 28 small earthquakes in Northern China, and adopted Kappa filtering to invert the peak ground motion acceleration attenuation relationship.
Pishan County (37.6°N, 78.2°E), located in the Hotan Region of Xinjiang Uygur Autonomous Region experienced the M_{S}6.5 earthquake on July 3, 2015. It is a kind of thrust type seismic event (Li Jin et al., 2016) occurred in the west Kunlun fault zone. By the end of July 27, 2015, the Xinjiang Strong Motion Network had recorded more than 120 records including 39 main shock records, and the Xinjiang Regional Digital Seismic Network had recorded 2, 173 aftershocks including 27 earthquakes above M_{S}4.0 and 1 earthquake greater than M_{S}5.0. In this paper, we used Pishan earthquake sequences waveform data, adopted micro-genetic algorithm to invert 5 medium parameters of the focal area. We use these parameters to calculate the Fourier spectrum and combine them with the random phase spectrum to get the ground motion time history, and build the strong ground motion acceleration attenuation relationship.It is a kind of half-experience and half-theoretical method, which considers the effects of source, path and site. At the same time, this method based on seismological small earthquake data can solve the current absence of strong motion records to some degree. It is also suitable for regions which have abundant small earthquake records but lack strong motion records. The purpose of this paper is to examine the applicability of this method in the Xinjiang region.
1 BUILDING THE GROUND MOTION ATTENUATION RELATIONSHIPWe assuming that the far field acceleration is an elastic half-space with finite duration and finite bandwidth white noise, we use seismological methods to build a point source Fourier spectrum equation. We use the source spectrum to express the source effect, use geometric attenuation and inelastic attenuation to express the path effect, and use surface amplitude amplification factor and high cutoff term to express the site effect. We can get the velocity Fourier spectrum by fast Fourier transform with small earthquake records, then choose the velocity Fourier spectrum as the target curve with the micro-genetic algorithm method to get the five medium parameters of the source region. We use these parameters to calculate the Fourier spectrum and combine them with the random phase spectrum to get the ground motion time history. In order to avoid the error caused by randomness, we took 50 times' peak ground motion accelerations to get the average value, and built the ground motion acceleration attenuation relationship.
The ground motion Fourier spectrum caused by point source can be expressed as (Boore D.M., 1983):
$ {\rm{FA}}({M_0}, f, R) = C \cdot S({M_0}, f) \cdot G\left(R \right) \cdot D\left({R, f} \right) \cdot A\left(f \right) \cdot P\left(f \right) \cdot I\left(f \right) $ | (1) |
In this equation, S(M_{0}, f) is source spectrum, G(R) and D(R, f) are propagation path effects, A(f) and P(f) are site condition effects, and I(f) is the spectrum type parameter. From equation (1), the ground motion Fourier spectrum caused by the point source is related to the seismic moment M_{0}, frequency f and distance R.
1.1 The SourceProportionality coefficient C can be expressed as (Boore D.M., 1983):
$ C = \frac{{{R_{\theta \phi }}FV}}{{4\pi {R_0}{\rho _{\rm{S}}}{\beta _{\rm{S}}}^3}} $ | (2) |
R_{θφ} reflects the source radiation pattern and station orientation effect, taken as 0.6 generally; F is the free surface amplification effect, taken as 2.0; V is the horizontal component coefficient of seismic energy, taken as
We choose Wang Guoxin's et al. (Wang Guoxin et al., 2001) point source spectrum model as our source spectrum S(M_{0}, f) which is based on the improved result of Brune's ω^{2} source spectrum model. It can express the change of corner frequency with the rupture area. It not only approaches the ω^{2} source spectrum in the high frequency but the characteristics of source spectrum amplitude will also not quickly increase with the magnitude increase in the low frequency. It is expressed by:
$ S\left({{M_0}, f} \right) = \frac{{{M_0}}}{{{{\left[ {1 + {{\left({f/{f_0}} \right)}^a}} \right]}^b}}} $ | (3) |
M_{0} is seismic moment, f is frequency, factors are a=3.05-0.33M_{W} and b=2.0/a, f_{0} is corner frequency, the relationship between f_{0} and Δσ expressed as:
$ {f_0} = 4.9 \times {10^6}{\beta _{\rm{S}}}{\left({\mathit{\Delta }\sigma \mathit{/}{\mathit{M}_0}} \right)^{1/3}} $ | (4) |
We adopt the viewpoint of some seismologists (Abercrombie R.E., 1995; Kanamori H. et al., 1975; Shearer P.M., 2009), they considered that the stress drop of small earthquakes is the same as large earthquakes which is basically constant, and therefore we take the stress drop as the source regional inversion parameter.
1.2 PathG(R) and D(R, f) are geometrical attenuation and inelastic attenuation. G(R) is related to the regional crustal velocity structure, and the seismic wave has different components at different distances. The main ingredients of the seismic wave are the shear wave in the near field, and the surface wave in the middle field. The geometrical attenuation is expressed by the three-stage geometric attenuation model (Boore D.M., 1983):
$ G\left(R \right) = \left\{ {\begin{array}{*{20}{l}} {\frac{1}{R}}&{1 < R < {R_1}}\\ {\frac{1}{{{R_1}}}}&{{R_1} \le R \le {R_2}}\\ {\frac{1}{{{R_1}}}\sqrt {\frac{{{R_2}}}{R}} }&{R > {R_2}} \end{array}} \right. $ | (5) |
In this equation, R is epicentral distance, expressed as
$ D\left({R, F} \right) = \exp \left({ - \frac{{\pi fR}}{{Q{\beta _{\rm{S}}}}}} \right) $ | (6) |
Q is the quality factor, the high-frequency of the ground motion is attenuated lower than the part of the low-frequency in the same situation. Q value becomes larger, the attenuation will be slower when distance R and frequency f are determined. The quality factor shows the regional characteristic from a great deal of studies (Boore D.M. et al., 1984; Chen P.S. et al., 1984), different areas have different Q values. Q=Q_{0}f^{η}, Q_{0} and η are regional parameters, Q_{0} is the quality factor when f=1Hz. We take Q_{0} and η as source regional inversion parameters.
1.3 SiteA(f) and P(f) are the amplification factor and attenuation factor. A(f) shows different frequency amplitude variation near the surface caused by difference of crustal velocity gradient. It can be approximately determined by the quarter-wave method according to the regional crustal velocity structure transfer function (Boore D.M. et al., 1997). P(f) is high cut-off frequency item. Papageorgiou et al. (1983) suggested that high frequency attenuation is caused by the source effect, and Hanks T.C., (1982) considered that it is the result of the site effect, or the combined action of the source effect and the site effect. We adopted the f_{max} filter, expressed as (Hanks T.C., 1982):
$ P\left(f \right) = {\left[ {1 + {{\left({\frac{f}{{{f_{\max }}}}} \right)}^8}} \right]^{1/2}} $ | (7) |
where f_{max} is high cut-off frequency, taken as 5-10Hz in general.
2 THE GROUND MOTION ACCELERATION ATTENUATION RELATIONSHIP OF THE PISHAN AREAWe selected 63 small earthquakes in the earthquake sequence. The magnitudes of those small events were between M_{W}3.0 and M_{W}3.5 from July 3, 2015 to July 17, 2015 and the focal depths distributed in 0-11km. The 23 digital seismic stations recorded 63 earthquakes (1, 179 records in total) within the scope of an epicentral distance of about 300km. We used these small earthquake records to calculate the Pishan area strong ground motion attenuation. We also collected 39 peak ground motion accelerations which are the larger between the EW component and NS components of the main shock to comparatively analyze and calculate the result. These strong ground motion stations are soil sites mostly distributed in the northwest of the epicenter. Fig. 1 shows the distribution of the epicenter and the stations. All the records with the epicentral distance from 188km to 432km are distributed in the Kashi-Wuqia intersection area as the Hotan region has no strong ground motion station. Selibuya station was the closest station which recorded 30.4gal of the peak acceleration with an epicenter 191.8km, and the Qiongkuerqiake station recorded 62.5gal of the peak acceleration with the epicenter 192km, which was the largest peak acceleration of this earthquake. The strong ground motion stations which obtained the records are both soil sites except for Wuheshalu station, which is a rock site. The information of the strong motion stations and the seismological stations is listed in Tables 1 and 2.
The magnitude-epicenter distance distribution and the magnitude-focal depth distribution of the records were shown in the Fig. 2 and Fig. 3. In the magnitude-epicenter distance distribution, the magnitudes of the seismic sequence we adopted were between M_{W}3.0 and M_{W}3.3 except for several earthquakes for which the magnitudes were larger than M_{W}3.3. Most of the epicenter distances were between 20km to 120km or 150km to 300km. Epicenter distances from 130km to 150km only have several records. The focal depths were from 6km to 10km.
We selected 30 seconds of waveform data which includes the S-wave to take the Fourier transform, thus we could get the Fourier spectral envelope scattering through envelope discretization. We adopted the micro-genetic algorithm to invert the regional parameters. Combined with original genetic method, this method canceled the mutation, and at the same time took the best individual preservation strategy. We used the known magnitude, the known epicentral distance and scattering of the Fourier spectral envelope to invert the stress drop Δσ, quality factors (Q_{0}, η) and geometric attenuation parameters (R_{1,} R_{2}). The range of the inversion parameters were summarized from the Xinjiang regional seismological research (Meng Lingyuan et al., 2014; Zhou Yunhao et al., 2004; Zhao Cuiping et al., 2011; Li Zhihai et al., 2010; Ayixiangu·Maimaiti et al., 2015; Pan Zhensheng et al., 2010; Wang Ji et al., 2010), and the inversion results are listed in Table 3.
We can get the acceleration Fourier amplitude spectrum with equation 1 by giving a pair of magnitude and distance according to the source parameters which we inverted. The calculated Fourier spectrum is combined with random phase spectrum to get the ground motion time history. We picked the peak ground motion acceleration of each time history and built the strong ground motion acceleration attenuation relationship. We added the earthquakes within epicenter 300km, the range of magnitude of (6.5±0.5), including the Wuqia M_{S}6.9 earthquake on October 5, 2008 (26 records), the Akto M_{S}6.2 earthquake on October 6, 2008 (3 records) and the Lop M_{S}6.0 earthquake on March 9, 2012 (23 records), as most epicentral distance of the Pishan earthquake records are far less than 200km. Because the Kunlun Mountains and Altun Mountains have few strong ground motion stations, the location of the recorded stations of those three earthquakes were in accord with the Pishan earthquake recorded stations. We compared the calculated result and empirical attenuation relationships (Zhang Zhenbin et al., 2010; Yu Yanxiang et al., 2013) with strong motion records in Fig. 4.
The calculation result is expressed by a series of scatter points which were applied to the mid-far field as the adoption point source spectrum model, and epicentral distance is from 10km to 300km in order to consider engineering significance. The result is similar to a straight line because we use three-stage geometry attenuation in 70km-130km. From Fig. 4 we can see the epicentral distance of Wuqia earthquake is distributed in 40km-300km, and the epicentral distance of the Lop earthquake is distributed in 200km-300km. The short axis results of Yu Yanxiang et al. (2013) indicates that it goes through the Wuqia earthquake records preferable but lower than the Lop and Pishan earthquake records; the result of Zhang Zhenbin et al. (2010) is consistent with the Wuqia and Lop earthquake records within the epicentral distance of 200km-300km, and is higher than the Wuqia earthquake records and lower than the Pishan earthquake records within 40km-200km. The result was higher than the Wuqia earthquake records and lower than the Pishan earthquake records, but can go through the Lop earthquake records. Pishan earthquake records are higher than the result of calculation and empirical attenuation relationships due to the Pishan earthquake occurring in the Hotan region of the Kunlun fault zone, and most of the strong ground motion stations which recorded records are distributed in the Wuqia area, where the intersecting area of western part of southern Tianshan Mountains and Kunlun Mountains is. The Pishan earthquake records have the geological characteristics of the Tianshan Mountains region. The seismic wave energy has different dissipation due to passing through two different crustal media in the propagation process, and finally expressed by the Pishan earthquake records higher than the calculate result and empirical attenuation relationships. We can indicate that the attenuation of Hotan region is partly faster than the Wuqia region. At the same time, most of the observation peak ground accelerations are soil site conditions, while empirical attenuation relationships are established by the rock site. The Lop earthquake records have similar characteristics to the Pishan earthquake records as Lop County is located 166km east of Pishan, so the Lop earthquake records are higher than the empirical attenuation relationships as well. Wuqia earthquake records are lower than the calculated result which is mainly caused by inversion parameter selection. There are differences in the quality factor parameters, because we used the seismological small earthquakes records to calculate the ground motion attenuation relationship, but adopted the parameters' scope of the South Tianshan Mountain fault (Kashi-Wuqia intersection area) to inversion. Meanwhile, even though we added three earthquakes to conduct comparison, but have only 91 records distributed 100km away. It reflects the lack of strong motion records and also indicates that verifying the empirical attenuation relationships by using the limited strong motion data is unreliable.
3 CONCLUSION AND DISCUSSIONWe took the Pishan M_{S}6.5 earthquake as the research object, used the seismic wave data with magnitudes between 3.0 and 3.5 recorded by the broadband digital seismic network. We could get 5 medium parameters using the micro genetic algorithm. After many Fourier transforms with the time function, we can get the peak ground motion acceleration attenuation relationship. We compared the calculated result and empirical results with the strong motion records including the Pishan M_{S}6.5 earthquake on July 3, 2015, Wuqia M_{S}6.9 earthquake on October 5, 2008, the Akto M_{S}6.2 earthquake on October 6, 2008 and the Lop M_{S}6.0 earthquake on March 9, 2012. The Pishan and Lop earthquakes occurred in the Hotan region of Kunlun Fault Zone, and most of the strong ground motion stations which recorded records are distributed in the Wuqia area which is the intersecting area of the western part of the Southern Tianshan Mountains and Kunlun Moutains. The seismic wave energy has different dissipation as it passes through two different crustal media in the propagation process. The records have the geological characteristics of the Tianshan Mountains region, and finally expressed by the Pishan and Lop earthquake records being higher than the calculated result and empirical attenuation relationships. To a certain extent, the attenuation of the Hotan region is faster than the Wuqia region. The Wuqia earthquake and Akto earthquake records did not show this characteristic, while it is lower than the calculated result.
ACKNOWLEDGEMENT
The seismographic records were acquired from the Monitoring Center of the Earthquake Agency of Xinjiang Uygur Autonomous Region. Thanks to assistant researcher Li Jin, and specially thanks for the guidance of research professors Tao Xiaxin and Tao Zhengru.
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