2. China Earthquake Networks Center, Beijing 100045, China;
3. Hainan Earthquake Agency, Haikou 570203, China
The Q value, reflecting the inelastic properties of the propagation medium, is a sensitive index for the crystal structure variation caused by temperature and phase change, which has important application value in understanding the inelastic properties of the Earth's interior medium and deducing its thermodynamic state (Hong Xuehai, 2003). According to the study by Chen Yong et al. (2009), seismic wave attenuation mainly depends on the microscopic nature of the rock, that is, the interaction between the density, distribution and structure of inner cracks of the rock and pore fluid. A physical mechanism study of seismic wave attenuation by Liu Jianhua et al. (2004a) finds that the main cause of seismic wave attenuation in the crust is that there are plentiful fractures in the Earth's crust, which are full of water, or partially contain water, and seismic wave propagation causes fluid motion in fractures, resulting in seismic wave attenuation. When a seismic wave passes through the active tectonic zone, the energy will be strongly attenuated and shown as a low Q value, while in some stable areas, attenuation is weak and the Q value is high. Therefore, with the study of the Q value of the crust, the characteristics, structure and change of the earth's interior medium can be understood more accurately.
At present, attenuation in the medium is studied by mainly using long-period surface waves and Lg coda waves, and a large number of research results have been obtained. Anderson D.L. et al. (1965) studied the average Q structure of the Earth by using long-period surface wave. Sato Y. (1958) studied the amplitude attenuation of surface wave using the Fourier transform. Solomon S. C. (1972) used the same method to determine the crust-mantle Q value between two network stations. Tsai Y.B. et al. (1969) established a method of single source-multiple stations to measure the average surface wave attenuation. Aki K. (1969) first proposed that coda wave of near earthquakes is caused by backscattering of seismic wave from countless discontinuity surfaces of the earth's crust and upper mantle distributed uniformly and randomly in an ellipse, and after that, Suteau A.M. et al. (1979) defined the scattering mechanism. Herrmann R. B. (1980) proposed a formula for measuring the Q value of the coda wave according to Aki's coda wave model and a scattering mechanism put forward by Suteau A.M. et al.(1979), and Xie J. et al.(1988) extended its application scope to the calculation of the Lg coda wave, and came up with the method of stack spectral ratio (SSR) to calculate the Q value; Cong Lianli et al. (2003) explored the distribution of Q of Lg waves in the Chinese mainland and its adjacent areas using the SSR method based on broadband vertical components of 785 shallow-focus earthquakes recorded by 10 seismic stations of the China Digital Seismograph Network and 5 seismic stations of the Global Seismic Network. Liu Jianhua et al.(2004b, 2004c) promoted the SSR method in the measurement of Q of Lg coda wave in small regions with epicentral distances less than 600km, and conducted tomography for the Q of coda waves in North China.
Current research on the Q value of the Tianshan area is focused mainly on the results of large regions or Chinese mainland and the average Q value obtained by joint inversion of multiple seismic stations and earthquakes, research of fine Q distribution has not been carried out. For instance, the results obtained by Wang Suyun et al. (2008) showed low attenuation in the west of Tarim Basin, with high attenuation in the east. Steinshouer D.W. et al. (1999) found that the west of the Tianshan Mountains presented high attenuation, while the eastern end of Tianshan Mountains presented low attenuation. The research results of the Q-value distribution of Lg coda waves in the Chinese mainland and its adjacent areas obtained by Cong Lianli et al. (2003) showed that the Q_{0} value of the Tarim platform was significantly higher, which was 350-425. Jiang Hui et al. (2007), by joint inversion using data from 52 earthquakes with M_{L}2.5-5.0 in the northern Tianshan Mountains, obtained a Q_{0} value of the region, which was 344, and Zhao Cuiping et al. (2011) updated the Q_{0} in the region to 460 in subsequent studies. With the establishment and improvement of the Xinjiang regional digital seismic network, a large amount of seismic waveform data has been accumulated, providing favorable conditions for the study of tomography for Q of the crustal medium. In this article, high-frequency attenuation data fitting of the S-wave displacement spectra is used for Q tomography in the mid-eastern section of the Tianshan area on a resolution of 0.5°×0.5°, and the characteristics of the Q distribution in the region are analyzed.
1 METHOD AND PRINCIPLEIn the frequency domain, the amplitude spectrum of the ith event observed at the jth station can be expressed as
$ {A_{ij}}\left(f \right) = {S_i}\left(f \right){I_j}\left(f \right){R_j}\left(f \right){G_{ij}}\left(f \right){B_{ij}}\left(f \right) $ | (1) |
where, f denotes frequency, S_{i}(f) source spectrum, I_{j}(f) instrument response function and R_{j}(f) the site response, which is used to describe the amplifying effect of the near-surface layer medium on seismic wave motion near seismic stations. G_{ij}(r) denotes the geometric spreading factor along path r, and B_{ij}(f) is attenuation spectrum.
Source spectrum can be described by the long-period spectrum Ω_{0} and corner frequency f_{c}, and its mathematical expression is as below (Brune J. N., 1970)
$ {S_i}\left(f \right) = {\mathit{\Omega }_0}/\left({1 + \left({{f^2}/f_{\rm{c}}^2} \right)} \right) $ | (2) |
According to research by Wong Yuklung et al. (2003) and Su Youjin et al. (2006), the geometric spreading factor can be represented by three coherent geometric attenuation functions put forward by Atkinson G.M. et al. (1992), as below,
$ {G_{ij}}\left(r \right) = \left\{ {\begin{array}{*{20}{l}} {{r^{ - {b_1}}}, }&{r \le {R_{01}}}\\ {R_{01}^{ - {b_1}}R_{01}^{ - b2}{r^{ - {b_2}}}, }&{{R_{01}} < r \le {R_{02}}}\\ {R_{01}^{ - {b_1}}R_{01}^{ - b2}R_{02}^{ - b2}R_{02}^{ - b3}{r^{ - {b_3}}}, }&{r > {R_{02}}} \end{array}} \right. $ | (3) |
In the geometric attenuation model, coefficients b_{1}, b_{2} and b_{3} are all considered to be independent of frequency. When r≤R_{01}, it corresponds to the geometric attenuation of the direct wave. When R_{01}≤r≤R_{02}, in the transition zone and within the range of hypocentral distance, reflected waves from discontinuity surfaces and Moho surface in the crust are added to the direct wave; when r>R_{02,} it corresponds to the S-wave attenuation after multiple reflection and refraction.
The attenuation spectrum along the entire ray path can be expressed by the following formula (Sanders C.O., 1993; Sherbaum F., 1990),
$ {B_{ij}}\left(f \right) = \exp \left({ - {\rm{ \mathsf{ π} }}f{t_{ij}}Q_{ij}^{ - 1}} \right) = \exp \left({ - {\rm{ \mathsf{ π} }}ft_{ij}^*} \right) $ | (4) |
where, t_{ij} denotes travel time along ray path, Q_{ij} dimensionless quality factor and t_{ij}^{*} the operator along the entire ray path (namely, attenuation operator t^{*}).
Instrument response can be directly deducted according to station parameters, and at this point the amplitude spectrum is expressed as A′_{ij}(f)=A_{ij}(f)/I_{j}(f). Moreover, since most regional stations are built on bedrock, its field response can be assumed to be approximately 1. Therefore, equation (1) can be written as,
$ A{'_{ij}}\left(f \right) = {\mathit{\Omega }_0}\frac{{f_c^0}}{{f_c^0 + {f^2}}}G\left(r \right)\exp \left({ - {\rm{ \mathsf{ π} }}ft_{ij}^*} \right) $ | (5) |
In addition, operator t_{ij}^{*} can be written as the projection of 1/(Q(S)v(S)) along the ray path from epicenter i to station j(Cormier V.F., 1982; Wittlinger G.H. et al., 1983), namely,
$ t_{ij}^* = \int {_{{\rm{path}}}} \frac{1}{{Q\left({\rm{S}} \right)\nu \left({\rm{S}} \right)}}{\rm{dS}} $ | (6) |
where, v denotes shear wave velocity, dS denotes ray path unit.
As shown in equation (5), there are 3 unknown variables in the equation, namely, Ω_{0}, f_{c} and t_{ij}^{*}. According to equation (5), path attenuation t_{ij}^{*} from the seismic source to each station can be determined by the inversion of displacement spectrum of waveform. Then, according to equation (6), the attenuation tomography is performed with the same method as the travel time tomography to determine Q.
1.1 Pretreatment of Observation DataWaveforms selected in this study are from 25 digital seismic stations in mid-eastern section of the Tianshan area, and the locations of stations are shown in Fig. 1. Firstly, two horizontal components of waveform records are corrected with band-pass filtering, and then the S-wave window and noise window are taken. The time period (T_{se}-T_{sn}) from the start of S-wave to 90% energy of the S-wave is defined as the S-wave window. At near-source distances, S-wave window contains only a direct S-wave, while at greater distances, it incorporates reflected waves from discontinuity surfaces and the Moho surface in the crust, and at a further distance, it contains the seismic phase Sn and Lg. For the same earthquake, because of the difference in epicentral distance or (Sg-Pg), the S-wave window length also varies, and the two are generally proportional to each other. For the mid-eastern section of the Tianshan area, Liu Jianming et al. (2014) gave results obtained after fitting, which were y=0.793x+14.09, in which, y denotes the S-wave window, x denotes (Sg-Pg).
256 sampling points before the first motion of the P-wave are taken as the noise window (Rietbrock A., 2001; Hansen S. et al., 2004). The selection of the S-wave window and noise window is shown in Fig. 2. Fast Fourier transform is performed to deal with the intercepted S-wave window and noise window by the translational window spectrum method to convert the S-wave window waveform record and noise window noise record into the observed amplitude spectrum and noise spectrum respectively. Since all seismic station seismometers are velocimeters, the velocity amplitude spectrum should be converted into the displacement amplitude spectrum. After the above treatment for the two respective S-wave horizontal components, the synthetic displacement spectrum of the S-wave horizontal component is obtained (Su Youjin et al., 2006). In order to acquire a reliable signal-to-noise ratio, a frequency within 1-15Hz is selected and the amplitude spectrum is at least 3 times that of the noise spectrum. Fig. 1(a) shows waveforms of two horizontal components of the M_{S}3.2 earthquake recorded by Urumqi seismic station (WMQ) on June 24, 2011 and the observed displacement spectrum and fitting spectrum at WMQ, STZ, GAZ, KMS and SCH station after geometric diffusion correction.
According to formula (5), the principle of multi-station, multi-spectrum data joint inversion method (Zhou Longquan et al., 2009) is to assume that an earthquake is recorded by N stations, and that N+2 unknown variables need to be inverted, namely Ω_{0}, f_{c}, t_{1}^{*}, t_{2}^{*}…, t_{N}^{*}, 2N-2 variables are reduced compared with the single-station observation spectrum inversion method, thereby reducing the non-uniqueness of solutions. Given M frequency points, the value of observed spectrum of the ith station at the jth frequency point can be expressed as A_{i}^{obs}(f_{j}), and theoretical amplitude spectrum is A_{i}^{cal}(f_{j}). Multi-station observation spectrum inversion is the search of the unknown variable value which will generate the minimum residual
After obtaining attenuation operator t^{*}, the Q_{S} value can be obtained by using the attenuation tomography method. First, the qualified attenuation operator t^{*} is picked out, appropriate grid size is determined according to the average number of rays for resolution test of detecting board, and according to the test results of resolution of detecting board, grid size is repeatedly adjusted, and eventually proper resolution is determined. Then, by calculating the average Q_{S} of the crust as the initial input model and adopting the pseudo-bending ray tracing method, 10 iterative computations are carried out to obtain the Q_{S} value. To remove the influence of focal depth, focal distance is used to replace epicentral distance in the process of inversion of Q_{S} with t^{*}.
2 TOMOGRAPHY FOR Q OF S-WAVE IN THE MID-EASTERN SECTION OF THE TIANSHAN AREA 2.1 Stability Analysis of Data and SolutionsData used in this article incorporates 5, 076 localizable M_{L}2.0-5.4 seismic events recorded by 25 digital seismic stations in mid-eastern section of the Tianshan area during January 1, 2009-December 31, 2014 (Fig. 1). According to formula (5), a data set of 44, 599 t^{*} is obtained by inversion using the genetic algorithm. Because of large Q error, the data needs to be further screened, and 19, 140 t^{*} values with error less than one time mean-square deviation are selected, and corresponding ray distribution is shown in Fig. 1. Using selected t^{*} data, the crust of mid-eastern section of the Tianshan area (40.5°-45.5°N, 79°-90.5°E) is horizontally divided into a uniform grid of 0.5°×0.5° for Q_{S} inversion, and the average number of rays in the grid is 342, which is helpful to reduce the non-uniqueness of solutions.
Before the inversion, the initial average velocity of S-wave in the mid-eastern section of the Tianshan area is 3.406km/s by calculation. Assuming that the initial Q value of the region is uniform, according to equation (6), when Q is uniform, t^{*} has a linear relationship with epicenter distance. The linear least square method is used for linear fitting of t^{*} data (Fig. 3), and the average Q_{0} of the crust in the mid-eastern section of the Tianshan area is obtained, which is 520, slightly higher than that given by Zhao Cuiping et al.(2005, 2011). The obtained Q_{0} and initial average velocity are used as initial value for inversion and are input into the model. After 10 iterative inversions, the root mean square (RMS) residual of t^{*} is reduced from 0.0255 before the inversion to 0.0226, and the distribution of residuals with epicentral distance before and after the inversion is shown in Fig. 4.
To determine whether the inversion results of 0.5°×0.5° grid are reliable, the detecting board resolution test is performed (Fig. 5), and the results show that the study area is densely covered with rays, with good resolution effect, only in some marginal areas, due to station and earthquake distribution, the ray coverage is sparse, indicating that the inversion results are reliable in most areas.
The crust of mid-eastern section of the Tianshan area (40.5°-45.5°N, 79°-90.5°E) is horizontally divided into a uniform grid of 0.5°×0.5°, and after 10 iterative inversions, the image of Q_{S} distribution of S-wave in mid-eastern section of the Tianshan area is obtained (6). The results show that Q_{S} of the mid-eastern section of the Tianshan area is between 380-790, with an average Q_{0} value of 520, slightly higher than that given by Zhao Cuiping et al. (2011), which is 460. Fig.(6) displays significant lateral variation of S-wave attenuation in mid-eastern section of the Tianshan area, which manifests the attenuation distribution of seismic energy in the earth's crust, and its size is closely related to the sedimentary layer thickness, tectonic activity intensity and crustal medium properties (Sun Lian et al., 2012). On the whole, the Q_{S} distribution and the attenuation variation characteristics it reveals are obviously related to the surface structure of the study area. For instance, the area between the Boluokenu and Beiluntai faults has a relatively higher Q_{S} of about 650-750, which happens to be the main area of the Tianshan Mountains. Low Q_{S} areas are mainly concentrated in the north and south sides of the Tianshan Mountains, that is, the intersection between the Tianshan Mountains and the Junggar Basin and the Tarim Basin, with Q_{S} generally under 550. Physical properties of the medium have changed in these areas, transitioning gradually from hard rocks in mountainous areas to sedimentary layers of basins. Low value areas mainly include the east of Ili River Valley, the north of Jinghe, Wusu, Shihezi, Urumqi, Kumux, Korla, Kuqa and Luntai regions. The relationship between Q_{S} and temperature is mainly manifested in the relation between regional Q_{S} and distribution of regional terrestrial heat flow. Terrestrial heat flow is the most direct display of thermal state and thermal structure of the Earth's interior on the Earth's surface. According to the Compilation of Heat Flow Data in the China Continental Area (3rd edition) published by Hu Shengbiao et al. (2001), data of 24 heat flow points within the scope of the study area (40.5°-45.5°N, 79°-90.5°E) are given in this paper. It can be seen from Fig.(6) that the Q_{S} distribution of the medium quality factor in mid-eastern section of the Tianshan area obtained from inversions has a certain relationship with the distribution of terrestrial heat flow. For instance, high heat flow points in the region are mostly distributed in low Q_{S} areas in the south and north sides of the Tianshan Mountains.
In this article, based on the waveform data of 5, 076 local earthquakes recorded at 25 digital seismic stations in mid-eastern section of the Tianshan area during the period from 2009-2014, tomography for the Q of mid-eastern section of the Tianshan area is performed at a resolution of 0.5°×0.5°, and the Q distribution characteristics in this region are analyzed. The main conclusions are as follows:
(1) Q_{S} value shows significant lateral variation in the mid-eastern section of the Tianshan area, and attenuation variation characteristics reflected by the Q_{S} value has an obvious correlation with the surface structure of this region, which is mainly manifested as such: ① Regions that happen to be the main area of the Tianshan Mountains have relatively higher Q_{S} value, about 650-750. ② Q_{S} value is lower in the intersection between the Tianshan Mountains and the Junggar Basin and the Tarim Basin which are located on the north and south sides of the Tianshan Mountains, and the farther from the mountainous areas, the lower the Q_{S} is, basically below 550, reflecting the gradual thickness of sedimentary layers during the transition from mountains to plains and basins.
(2) Since 1900, most M≥6.0 earthquakes (Fig. 6) have been located in low Q_{S} areas, such as the Boluokenu fault, the Qiulitag fault and Shihezi and Changji on the north slope of the Tianshan Mountains. Moreover, according to the Compilation of Heat Flow Data in the China Continental Area (3rd edition) published by Hu Shengbiao et al. (2001), 24 high heat flow points in mid-eastern section of the Tianshan area (40.5°-45.5°N, 79°-90.5°E) are basically located in low Q_{S} areas on the south and north sides of the Tianshan Mountains described above (Fig. 6), that is, the heat flow value is negatively correlated with attenuation value.
(3) Research on the velocity structure in mid-eastern section of the Tianshan area shows that north Tianshan and middle Tianshan area are uplifted regions with high P-wave velocity, and the Turpan Basin, the Kuqa depression and the south edge of the Junggar Basin constitute the piedmont low velocity zone on the north and south sides of the Tianshan Mountains (Xu Yi et al., 1994; Guo Biao et al., 2006; Qian Hui et al., 2011; Wang Zaihua et al., 2008). The research on S-wave velocity shows that there are many distinct S-wave low-velocity layers in the upper and middle crust of the Tianshan Mountains, which are located respectively at the intersection of basins and mountains on both sides of the Tianshan Mountains and the junction of different blocks of the Tianshan Mountains (Li Yu et al., 2007). The phase velocity images of a short period of 10s-20s show obvious low velocity anomaly areas in the Tarim Basin and the Junggar Basin, and the Tianshan Orogenic belt shows high velocity anomalies in the tomographic imaging of periods of 10s-16s, contrary to the low velocity anomalies of sedimentary rocks in the Tarim Basin and the Junggar Basin (Tang Xiaoyong et al., 2011). The research on the velocity structure of the mid-eastern section of the Tianshan area also shows that the velocity structure of this region is positively correlated with its attenuation structure, which proves that the two-dimensional attenuation structure is consistent with the velocity structure and two-dimensional density structure (Burtman V.S. et al., 1993). The primary cause of the lateral inhomogeneity of attenuation in the mid-eastern section of the Tianshan area is the uneven distribution of the medium. (Velocity structure and attenuation structure are two different things).
(4) The Q_{S} value inverted in this paper is frequency independent, and the initial average Q_{S} is slightly higher than the frequency-related inversion results (Zhao Cuiping et al., 2005, 2011). Although the frequency-independent assumption will affect the size of Q_{S}, its distribution will not change. Therefore, it still can be used to analyze the characteristics of physical property distribution of the medium (Zhou Longquan et al., 2009; Wang Huilin et al., 2012; Eberhart-Phillips D. et al., 2002).
ACKNOWLEDGEMENT
We are grateful to research professor Jiang Haikun for his guidance over the years. Assistant research professor Chen Xiangjun and Bao Cuiling, and assistant engineers Zhang Zhibin, Liu Shengmei and Wu Ni'er from the Earthquake Agency of Xinjiang Uygur Autonomous Region provided assistance in data sorting and other aspects. During the writing of this thesis, assistant research prefessor Liu Jianming and Dr.Ji Zhanbo provided much help and beneficial discussions, and to them we hereby express our sincere gratitude.
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