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Source parameters, path attenuation and site effects from strong-motion recordings of the Wenchuan aftershocks (2008–2013) using a non-parametric generalized inversion technique

Source parameters, path attenuation and site effects from strong-motion recordings of the... Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Geophysical Journal International Geophys. J. Int. (2018) 212, 872–890 doi: 10.1093/gji/ggx447 Advance Access publication 2017 October 16 GJI Seismology Source parameters, path attenuation and site effects from strong-motion recordings of the Wenchuan aftershocks (2008–2013) using a non-parametric generalized inversion technique Hongwei Wang, Yefei Ren and Ruizhi Wen Key Laboratory of Earthquake Engineering and Engineering Vibration of China Earthquake Administration, Institute of Engineering Mechanics, China Earthquake Administration, No. 29 Xuefu Road, Harbin 150080, China. E-mail: renyefei@iem.net.cn Accepted 2017 October 14. Received 2017 August 14; in original form 2016 October 11 SUMMARY Secondary (S) wave amplitude spectra from 928 strong-motion recordings were collected to determine the source spectra, path attenuation and site responses using a non-parametric generalized inversion technique. The data sets were recorded at 43 permanent and temporary strong-motion stations in 132 earthquakes of M 3.2–6.5 from 2008 May 12 to 2013 December 31 occurring on or near the fault plane of the 2008 Wenchuan earthquake. Some source parameters were determined using the grid-searching method based on the omega-square 14 18 model. The seismic moment and corner frequency vary from 2.0 × 10 to 1.7 × 10 N · m and from 0.1 to 3.1 Hz, respectively. The S-wave energy-to-moment ratio is approximately −5 1.32 × 10 . It shows that the moment magnitude is systematically lower than the surface wave magnitude or local magnitude measured by the China Earthquake Network Center. The seismic moment is approximately inversely proportional to the cube of the corner frequency. The stress drop values mainly range from 0.1 to 1.0 MPa, and are lognormal distributed with a logarithmic mean of 0.52 MPa, significantly lower than the average level over global earthquake catalogues. The stress drop does not show significant dependence on the earthquake size and hypocentre depth, which implies self-similarity for earthquakes in this study. The ε indicator was used to determine the stress drop mechanism. The low stress drop characteristic of the Wenchuan aftershocks may be interpreted by the partial stress drop mechanism, which may result from remaining locked sections on the fault plane of the main shock. Furthermore, we compared the stress drop distribution of aftershocks and slip distribution on the fault plane of the main shock. We found that aftershocks with higher stress drop occurred at areas with smaller slip in the main shock. The inverted path attenuation shows that the geometrical spreading around the seismogenic region of Wenchuan earthquake sequence is weak and significantly dependent on frequency for hypocentre distances ranging from 30 to 150 km. The frequency-dependent 1.06 S-wave quality factor was regressed to 151.2f at frequencies ranging from 0.1 to 20 Hz. The inverted site responses provide reliable results for most stations. The site responses are obviously different at stations in a terrain array, higher at the hilltop and lower at the hillfoot, indicating that ground motion is significantly affected by local topography. Key words: Fourier analysis; Earthquake ground motions; Earthquake source observation; Seismic attenuation; Site effects. INTRODUCTION The M 7.9 Wenchuan earthquake on 2008 May 12 was the strongest earthquake ever recorded along the Longmenshan fault belt. It was also one of the most destructive earthquakes in China, which caused catastrophic damage and heavy casualties and affected a wide range of regions. This event generated a surface rupture zone of 240 km in length along the Beichuan fault and an additional 72 km along the Pengguan fault (Xu et al. 2009). Before the Wenchuan earthquake, the Longmenshan fault belt was not very active. In the past 100 yr, only two events of M ≥ 6.0 have been recorded. One was the 1958 M6.2 Beichuan earthquake, which occurred on the Beichuan fault. The other was the 1970 M6.2 Dayi earthquake, which occurred on the Pengguan fault (Chen et al. 1994). However, lots of fragmentary ruptures frequently occurred on The Authors 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 873 the Longmenshan fault belt, triggering a large number of small earthquakes with magnitudes ranging from 1.0 to 5.0 (Yang et al. 2005). Large ruptures occurred in recent years, including the 2008 M 7.9 Wenchuan earthquake and the 2013 M 6.6 Lushan earthquake, which w w implied that the Longmenshan fault belt was activated after a long silence. As a result, the design seismic accelerations for most areas in the Longmenshan region were substantially modified in the latest generation of seismic ground motion parameters zonation map of China, which was formally issued in 2015 (AQSIQ 2015). They were increased to 0.15 or 0.20g (g, gravitational acceleration) from 0.10 to 0.15g, respectively, in the previous version. Design seismic accelerations are divided into six levels in the zonation map of China, which gradually increase from 0.05 to 0.40g at an interval of 0.05 or 0.10g. The second, third and fourth levels are 0.10, 0.15 and 0.20g, respectively. This means that the seismic-proof demand was raised one level, or even two levels for most areas in the Longmenshan region, implying a current potential high seismic hazard in this region. The attenuation laws for ground motions, scaling relations of source parameters and site effects are directly related to the prediction and assessment of seismic hazard. They play essential roles in establishing ground motion prediction equations or simulating ground motion time histories. Therefore, it is very valuable to study the source, path and site characteristics of earthquakes occurring on the Longmenshan fault belt such as the Wenchuan earthquake sequence. In recent years, such studies have already been performed, for example, Ren et al.(2013), Yu and Li (2012)and Hua et al.(2009). Ren et al.(2013) analysed the site responses of permanent strong-motion stations and identified the soil non-linearity using strong-motion recordings from the Wenchuan aftershocks, based on the parametric generalized inversion technique (GIT). However, path and source characteristics were not considered. The source parameters and quality factor of the propagation medium were inverted by Yu and Li (2012) using the Levenberg–Marquardt algorithm. However, only 13 aftershocks of M > 5.0 were investigated, and few analyses regarding site effects were made in this study. More than 1000 aftershocks of M ≥ 3.0 were investigated by Hua et al.(2009) to study the segmentation features of the stress drop. However, other source parameters were not included, and site effects were neglected. There is not yet a study including systematic analyses on the source parameters, path attenuation and site effects of ground motions from the Wenchuan earthquake sequence. In this paper, a non-parametric generalized inversion of secondary (S) wave amplitude spectra of the strong-motion recordings from the Wenchuan earthquake sequence was performed to separate the source, propagation path and site effects simultaneously. Earthquakes considered in this study occurred on or near the fault plane of the Wenchuan earthquake from 2008 May 12 to 2013 December 31. We investigated the attenuation characteristics, mainly including geometrical spreading and anelastic attenuation. Some source parameters were estimated from the inverted source spectra and then used to study the source scaling relations of earthquakes in this region. Finally, we provided the site responses for stations considered in this study, and analysed preliminarily the local topographic effect on ground motions. DATA SET A total of seven issues (Issues 12–18) of uncorrected strong-motion acceleration recordings have been officially issued in China by the China Strong Motion Network Center since the China National Strong Motion Observation Network System (NSMONS) formally began operation in 2007. The analogue recordings in China before 2007 were published in Issues 1–11. Issue 12 covers recordings from the Wenchuan main shock. Issues 13 and 14 cover recordings from the Wenchuan aftershocks obtained by the permanent and temporary stations, respectively. Issues 15, 16 and 18 cover other recordings collected during 2007–2009, 2010–2011 and 2012–2013, respectively. Issue 17 covers recordings from the 2013 Lushan earthquake sequence. Strong-motion recordings in Issues 13–16 and 18 from earthquakes that occurred on or near the rupture fault of the Wenchuan earthquake are used as the data set in this study. It is composed of more than 2000 strong-motion recordings from 383 M (M ) 3.3–6.5 earthquakes from 2008 May 12 to September 30 recorded at 76 permanent stations s L of NSMONS in Gansu and Sichuan provinces (Issue 13), 2214 strong-motion recordings from 600 M (M ) 2.3–6.3 earthquakes from s L 2008 May 14 to October 10 recorded at 83 temporary stations (Issue 14, Wen et al. 2014), and 355 additional strong-motion recordings from 57 M (M ) 3.1–5.5 earthquakes from 2008 October 1 to 2013 December 31 recorded at 86 stations of NSMONS (Issues 15, s L 16 and 18). Deviations between the surface wave magnitude M and the local magnitude M for earthquakes in China and adjacent s L regions measured by the China Earthquake Network Center (CENC) were ignored (Zhang et al. 2008). In this paper, M was used to represent the measured magnitude by CENC. The baseline correction and a Butterworth bandpass filter between 0.1 and 30.0 Hz were performed. Fig. 1 shows the hypocentre distance (R) and geometric mean of the peak ground acceleration (PGA) for the two horizontal compo- nents (east–west and north–south) of the strong-motion recordings in this data set. PGAs of these strong-motion recordings mainly vary −2 from 2.0 to 100 cm s . Hypocentre distances of most recordings from Issues 13, 15, 16 and 18 generally range from 30 to 200 km. However, hypocentre distances for many recordings from Issue 14 are less than 30 km, with the minimum approaching 1.0 km. Recordings from Issue 14 were obtained by temporary stations deployed as close to the seismogenic fault as possible (Wen et al. 2014). Very few recordings from Issues 15, 16 and 18 were obtained from earthquakes of M > 5.0 because very few aftershocks with large magnitudes occurred in the seismogenic area of the Wenchuan earthquake during 2009–2013. We selected available recordings from this data set ac- −2 −2 cording to the following criteria proposed by Ren et al.(2013): (1) 30 km ≤ R ≤ 150 km; (2) 2 cm s ≤ PGA ≤ 100 cm s ; (3) each selected earthquake should be recorded by at least four stations, each of which should collect at least four recordings that match (1) and (2). Finally, we employed 928 strong-motion recordings from 132 earthquakes of M 3.2–6.5 at 43 strong-motion stations. Earthquake epicentres and strong-motion stations considered in this study are shown in Fig. 2. Most stations are located in the mountains, west of Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 874 H. Wang, Y. Ren and R. Wen Figure 1. Hypocentre distance and peak ground acceleration (PGA) of the data set used in this study. The dashed–dotted lines in the left-hand panel represent the hypocentre distance range for most data in the Issues 13, 15, 16 and 18 released by China Strong Motion Network Center. The dashed–dotted lines in the right-hand panel represent the PGA range for most recordings of the data set used in this study. Issues 13 and 14 cover recordings from the Wenchuan aftershocks obtained by the permanent and temporary stations, respectively. Issues 15, 16 and 18 cover other recordings collected during 2007–2009, 2010–2011 and 2012–2013, respectively. 102˚E 103˚E 104˚E 105˚E 106˚E 34˚N 34˚N 62SHW 62WUD 51JZY L2015 51JZG L2016 L2008 51JZW (62WIX,L2002,L2007,L2009) 33˚N L2004 33˚N L2005 L2010 L2001 L2006 51GYZ 51SPA 51GYQ L0020 L0021 Guangyuan L0022 51HSL 51HSD 51MXD 32˚N 32˚N 51HSS 51MXN 51CXQ 51AXY 51MXB 51LXM 51MZQ 51LXS 51LXT 51AXT Mianyang Perm. station 51XJB 51WCW Temp. station 31˚N 51SFB 31˚N 51XJD City Mainshock Ms 3.0−3.9 Chengdu Ms 4.0−4.9 51QLY Ms 5.0−5.9 51PJW 51PJD Ms 6.0−6.5 30˚N 30˚N 102˚E 103˚E 104˚E 105˚E 106˚E Figure 2. The locations of earthquakes (circle) and strong-motion stations (triangle and square) used in this study. The grey solid lines represent the surface traces of the Longmenshan fault belt. Insert in the top left corner shows the location of the study region in China. the Longmenshan fault belt. In contrast to data used by Ren et al.(2013), we added more earthquakes and strong-motion stations in this study. The S waves of the two horizontal components of the strong-motion recordings were extracted, according to studies of Husid (1967) and McCann (1979). A cosine taper was applied at the beginning and end of the S-wave window, and the length of each taper was set at 10 per cent of the total trace length (Hassani et al. 2011;Ren et al. 2013). The Fourier amplitude spectrum of the S wave was calculated and Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 875 Figure 3. Residuals of synthetic results produced by the inverted source spectra, site responses and path attenuation, computed as log10 (observation/synthetics), versus hypocentre distance at (a) 0.5 Hz, (b) 5.0 Hz and (c) 10.0 Hz. The average residuals (blue circles) and one standard deviations (error bars) for different distance bins were computed. (d) The average residuals at each frequency of 0.1–20 Hz for different distance bins. smoothed using the windowing function of Konno & Ohmachi (1998) with b = 20. The vector synthesis of the Fourier amplitude spectra from two horizontal components was used to represent the horizontal ground motion in frequency domain. METHODOLOGY We applied a two-step non-parametric GIT (Castro et al. 1990;Oth et al. 2008, 2009) to separate attenuation characteristics, source spectra and site response functions. In the first step, the dependence of the spectral amplitudes on the distance at frequency (f) can be expressed as: O f, R = M ( f ) · A f, R (1) ij ij i ij where O (f,R ) is the spectral amplitude observed at the jth station resulting from the ith earthquake, R is the hypocentre distance, M (f)is ij ij ij i a scale dependent on the size of the ith earthquake and A(f, R ) is a non-parametric function of distance and frequency accounting for the ij seismic attenuation (e.g. geometrical spreading, anelastic and scattering attenuation, refracted arrivals, etc.) along the path from source to site. A(f, R ) is not supposed to have any parametric functional form and is constrained to be a smooth function of distance with a value of 1 ij at reference distance R . Once A(f, R ) is determined, the spectral amplitudes can be corrected for the seismic attenuation effect. In the second step, the corrected ij spectra are divided into source spectra and site response functions: O f, R /A f, R = S ( f ) · G ( f ) (2) ij ij ij i j where G (f) is the site response function at the jth station and S (f) is the source spectrum of the ith earthquake. The trade-off between the site j i and source is resolved by selecting station 62WIX as a reference site, where the site responses are constrained to be 2.0 around all frequencies (Ren et al. 2013). Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 876 H. Wang, Y. Ren and R. Wen Figure 4. The inverted source spectra for four typical earthquakes representing four magnitude levels. The dark lines represent the inverted source spectra using the total recordings in this study. The grey lines represent the inverted source spectra from 100 bootstrap inversions. The name of the earthquake is composed of the date and time of this event. Eq. (1) can be turned into a linear problem by taking the natural logarithm and expressing it as a matrix formulation: ⎡ ⎤ lnA ( f, R ) ⎡ ⎤ 1 1000 ··· 010 ··· 0 ⎢ ⎥ ⎡ ⎤ ⎢ ⎥ lnA ( f, R ) ⎢ ⎥ lnO ( f, R ) 1 1 ⎢ ⎥ ⎢ ⎥ 0100 ··· 001 ··· 0 ⎢ ⎥ lnA ( f, R ) ⎢ ⎥ 3 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ lnO ( f, R ) ⎥ 2 2 ⎢ ⎥ . . . . . . . . . . ⎢ ⎥ lnA ( f, R ) ⎢ ⎥ . . . . . . . . . . ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ . . . . . . . . . . ⎢ ⎥ . ⎢ ⎥ . ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ . ⎥ ⎢ 0000 ··· 100 ··· 1⎥ ⎢ ⎥ ⎢ ⎥ lnO ( f, R ) ⎢ ⎥ ⎢ N N ⎥ · ⎢ ⎥ = (3) lnA ( f, R ) ⎢ ⎥ N ⎢ ⎥ ⎢ ⎥ ω 000 ··· 000 ··· 0 0 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ lnM ( f ) ⎥ ⎢ ⎥ ⎢ 0 ⎥ −ω /2 ω −ω /20 ··· 000 ··· 0 ⎢ ⎥ ⎢ 2 2 2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ lnM ( f ) 0 ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ 0 −ω /2 ω −ω /2 ··· 000 ··· 0 ⎢ ⎥ 2 2 2 ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ . ⎢ . ⎥ . . . . . . . . . . ⎣ ⎦ . . . . . . . . . . . . . . . . . . . . ( ) lnM f In eq. (3), the hypocentre distance ranges are divided into N bins with a 5 km width. R , R ..., R is a monotonically increasing 1 2 N sequence of hypocentre distance. The weighting factor ω is used to constrain A(f, R ) = 1 at reference distance R and ω is the factor 1 0 0 2 determining the degree of smoothness of the solution. The reference distance was set to 30 km, which is the smallest hypocentre distance considered in this study. We calculated the residuals between the observed data and the synthetic results from the product of the inverted source spectra, site responses and path attenuation, as shown in Fig. 3. The residuals were expressed as the logarithmic observed values minus logarithmic synthetic values. They vary around zero and have an average close to zero in the whole frequencies of 0.1–20 Hz. This shows that the residuals are independent on the hypocentre distance, indicating that the non-parametric inversion provides a good representation of the observed recordings considered in this study. SOURCE SPECTRA The bootstrap analysis proposed by Oth et al.(2008, 2011) was performed in this study to assess the stability of the inverted source spectra. 150 strong-motion recordings, accounting for approximately 16 per cent of the total recordings, were randomly removed from the data set, and the remaining ones were assembled as a new data set used in the inversion. We repeated this procedure 100 times to investigate the stability of the inverted source spectra. Fig. 4 shows the inverted source spectra resulting from 100 bootstrap inversions for four typical earthquakes representing four magnitude levels. The deviation from the source spectra obtained using the whole data set remains small, implying that the source spectra are stable. Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 877 Table 1. The basic information of a large earthquake and its four empirical Green’s function (EGF) events used to estimate the cumulative attenuation within the reference distance of 30 km. Large earthquakes Small earthquakes as EGF events ∗ ◦ ◦ ◦ ◦ Number Date and time M / M Long. ()Lat.()Depth(km) M /f Number Date and time M Long. ()Lat.()Depth(km) s w w c s 01 08 08 05 174 916 6.5/6.0 105.61 32.72 13 5.86/0.206 02 08 06 19 182 559 4.4 105.62 32.73 10 5.92/0.176 03 08 05 12 224 606 5.1 105.64 32.72 10 6.12/0.109 04 08 05 27 160 322 5.3 105.65 32.76 15 6.07/0.105 05 08 07 24 03 5443 5.7 105.63 32.72 10 M is derived from the Global Centroid-Moment-Tensor (CMT) catalogue. The cumulative attenuation within the reference distance is not included in the A(f,R) derived from the first-step inversion. The inverted source spectra from the second-step inversion absorb this cumulative attenuation when the trade-off between the site and source is solved using the known site response of the reference site. Therefore, the real source spectrum can be expressed as: S ( f ) = S ( f ) /ψ ( f ) (4) inverted where ψ(f) represents the cumulative attenuation within the reference distance and S (f) is the inverted source spectrum. If the real source inverted spectrum of an earthquake is known, the cumulative attenuation can be derived from eq. (4). Assuming that the source spectrum follows the omega-square source model (Brune 1970), R V M θ 0 S ( f ) = (2π f ) · · (5) 3 2 4πρ β s 1 + ( f / f ) s c where R is the average radiation pattern over a suitable range of azimuths and take-off angles set to 0.55. V = 1/ 2 accounts for the portion of total S-wave energy in the horizontal components. ρ and β are the density and S-wave velocity in the vicinity of the source set to 2700 kg s s −3 −1 m and 3.6 km s , respectively. M and f are the seismic moment and corner frequency. We used the relationship proposed by Hanks & 0 c −7 Kanamori (1979) to convert moment magnitude (M )to M (unit: dynecm = 10 N · m): w 0 logM = 1.5 × (M + 10.7) (6) 0 w If a small earthquake is regarded as the empirical Green’s function (EGF) event of a large earthquake, the differences of the path attenuation in the strong-motion recordings at the same station from large and small earthquakes can be neglected. Fourier amplitude spectral ratio O (f)/O (f) can be approximately expressed as the theoretical source spectral ratio S (f)/S (f), L S L S O ( f ) S ( f ) M 1 + ( f / f ) L L 0L cS ≈ = · (7) O ( f ) S ( f ) M ( ) S S 0S 1 + f / f cL where subscripts L and S represent the large and small earthquakes, respectively. According to eq. (7), the values of seismic moment and corner frequency for both large and small earthquakes could be achieved by minimizing the differences between the Fourier amplitude spectral ratio of the observed strong-motion recordings averaged over all stations triggered in both earthquakes and the theoretical source spectral ratio. In this study, an M 6.5 earthquake (No. 01) that occurred on 2008 August 5 at 17:49:16 (Beijing time) at the northeastern part of the Longmenshan fault was selected as a large event, and four other earthquakes (M 4.4, 5.1, 5.3 and 5.7) were selected as its EGF events. The basic information for these earthquakes is listed in Table 1, and their epicentres and the recorded strong-motion stations are shown in Fig. 5. The grid-searching method was adopted to determine the best-fit seismic moment and corner frequency in eq. (7). The best-fitting theoretical source spectral ratios between large and small earthquakes are in good agreement with the Fourier amplitude spectral ratios calculated using observed strong-motion recordings at frequencies of 0.1–20 Hz, as shown in Fig. 6. The obtained M values range from 5.86 to 6.12 and the f values range from 0.105 to 0.206 Hz for the M 6.5 earthquake, as shown in Table 1. The values of M are in good c s w agreement with the one from the Global Centroid-Moment-Tensor (CMT) catalogue, that is, 6.0. According to eq. (5), the theoretical source spectra of the M 6.5 earthquake were obtained, then the values of ψ(f) were calculated using eq. (4), as shown in Fig. 6. It shows that the ψ(f) is not strongly dependent on the selected EGF event, implying its stable estimation. In this study, we adopted the ψ(f) derived from the spectral ratio between the M 6.5 and the M 5.3 earthquakes (i.e. Nos. 01 and 04 in Table 1), which is approximately median of all four ψ(f). s s The source displacement spectra corrected using ψ(f) are shown in Fig. 7 for seven magnitude bins from 3.0 to 6.5 at an interval of 0.5 mag. −2 Source spectra at high frequencies are close to the ω decay. Note that for a proper quantification of the stability of ψ(f), it would be useful to consider additional pairs of collocated large events/EGFs, in particular in the southwestern part of the fault. Unfortunately, such pairs are not available. Because the hypocentres of large and small earthquakes are not close enough to remove the difference of path attenuation from their sources to sites, or the strong-motion recordings obtained in both earthquakes are not enough to calculate the reliable spectral ratio between them. Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 878 H. Wang, Y. Ren and R. Wen 104˚E 105˚E 106˚E 62WUD 51JZB 51JZY L2015 51JZG L2016 L2008 33˚N L2004 33˚N 62WIX (L2002,L2007,L2009) L2005 L2001 L2012 51SPC (L2013,L2014) L2006 L2011 51GYZ 51GYQ L0020 L0021 02 04 L0022 51GYS 32˚N 32˚N L0002 L0045 (L0048,L0049) L0004 51CXQ 01 05 03 104˚E 105˚E 106˚E Figure 5. The epicentre locations of a large and four small earthquakes listed in Table 1, and strong-motion stations operating during these earthquakes. Figure 6. (a) The averaged Fourier amplitude spectral ratio (solid line) of strong-motion recordings observed at the same stations between the large and small earthquakes listed in Table 1, and the best-fit theoretical source spectral ratio (dashed line). (b) The cumulative attenuation within the reference distance of 30 km. SOURCE PARAMETERS The grid-searching method was adopted to obtain the best-fit seismic moment and corner frequency for each earthquake, making the theoretical source spectrum expressed by eq. (5) closest to the attenuation-corrected source spectrum. It can be represented as: Nf S ( f ) / ( f ) i,inverted m m log = min. (8) S ( f ) i m m=1 M − 1.0 ≤ M ≤ M + 1.0, the corresponding searching ranges of M are derived from eq. (6). The values of stress drop ( σ)for s w s 0 small-to-moderate earthquakes generally vary from 0.1 to 100.0 MPa (Kanamori 1994). Following Brune (1970), the corner frequency is 6 1/3 expressed as f = 4.9 × 10 β ( σ/M ) . The searching ranges of f are estimated according to the possible variation ranges of σ. Fig. 7 c s 0 c Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 879 Figure 7. The attenuation-corrected source displacement spectra (left-hand panel), and the best-fitting theoretical source spectra to the inverted source spectra for four typical earthquakes representing four magnitude levels (right-hand panel). shows some examples of the best-fitting theoretical source spectra. Then, the seismic moment and corner frequency were used to determine the stress drop and the source radius r according to the Brune (1970) source model: 2.34β r = (9) 2π f 7M −13 σ = × 10 (10) 16r We also calculated the S-wave energy E in the frequency range from 0.01 to 30 Hz according to the relationship proposed by Vassiliou & Kanamori (1982): +∞ 2 1 1 M E = + 2π f d f (11) 5 5 2 15πρ α 10πρ β ( ) s s −∞ 1+ 1+ f / f s s c −1 where α = 6.1 km s represents the primary (P) wave velocity. The apparent stress σ was calculated by the following relationship: s a μE σ = (12) 10 −2 where μ = 3.5 × 10 Nm represents the rigidity modulus. All of these source parameters for earthquakes considered in this study are shown in Table 2. Seismic moment M and corner frequency f 0 c The M values determined in this study are in good agreement with those derived from the Global CMT catalogue, although they are slightly higher than measurements provided by Zheng et al.(2009), as shown in Fig. 8(a). We obtained the relationship between M and M measured w s by CENC by a least-squares regression analysis: M = (0.817 ± 0.024) M + (0.650 ± 0.111) (13) w s There are linear deviations between M and M measured by CENC. M is systematically lower than M for M = 3.5–6.5. This w s w s s overestimation of M is more severe in the case of larger earthquakes with the maximum close to 0.5. In fact, such phenomena have been commonly found in other studies, such as in the 2013 April 20 Lushan earthquake sequence (Lyu et al. 2013), large numbers of small-to- moderate earthquakes in mainland China (Zhao et al. 2011), some small earthquakes in the Tangshan area (Matsunami et al. 2003), and earthquakes with magnitude greater than 4.0 in the Sichuan–Yunnan region of China (Xu et al. 2010a). This deviation may result from the inaccurate calibration functions and the neglect of the base correction in the process of measuring magnitude by CENC (Zhao et al. 2011). Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 880 H. Wang, Y. Ren and R. Wen Table 2. List of source parameters including moment magnitude (M ), seismic moment (M ), corner frequency (f ), source radius (r), stress drop ( σ), w 0 c S-wave energy (E ) and apparent stress (σ ) determined in this study. s a ∗ 14 11 Earthquake M † M f (Hz) M (× 10 N·m) r (m) σ (MPa) E (× 10 J) σ (MPa) s w c 0 s a 08 051 214 4315 6.3 5.41 0.275 1462.177 4867.92 0.555 21.224 0.435 08 051 214 5417 5.8 5.68 0.114 3715.352 11 772.07 0.100 9.756 0.079 08 051 215 0134 5.5 5.37 0.333 1273.503 4029.34 0.852 28.319 0.667 08 051 215 1345 4.7 4.33 0.849 35.075 1579.38 0.390 0.349 0.298 08 051 215 3442 5.8 4.87 0.429 226.464 3122.31 0.325 1.917 0.254 08 051 215 4416 4.6 4.27 0.917 28.510 1461.39 0.400 0.290 0.305 08 051 215 4533 4.7 4.46 0.534 54.954 2510.81 0.152 0.216 0.118 08 051 215 5821 4.3 3.84 1.617 6.457 828.98 0.496 0.079 0.367 08 051 216 0258 4.7 4.05 1.204 13.335 1113.68 0.422 0.142 0.318 08 051 216 0806 4.3 4.17 1.218 20.184 1100.86 0.662 0.336 0.499 08 051 216 1057 5.5 4.86 0.403 218.776 3328.92 0.259 1.478 0.203 08 051 216 2140 5.5 4.99 0.462 342.768 2901.62 0.614 5.463 0.478 08 051 216 2612 5.1 4.97 0.388 319.890 3456.09 0.339 2.825 0.265 08 051 216 4030 4.2 3.92 1.544 8.511 868.36 0.569 0.120 0.422 08 051 216 5039 4.8 4.52 0.713 67.608 1880.37 0.445 0.772 0.343 08 051 217 0659 5.2 4.74 0.446 144.544 3005.29 0.233 0.875 0.182 08 051 217 3115 5.2 4.88 0.386 234.423 3472.56 0.245 1.496 0.191 08 051 217 4224 5.3 5.10 0.382 501.187 3509.10 0.507 6.626 0.397 08 051 217 4457 4.2 3.85 2.386 6.683 561.80 1.649 0.262 1.178 08 051 217 4746 4.4 4.01 1.899 11.614 706.04 1.444 0.408 1.055 08 051 218 1915 4.0 3.53 2.904 2.213 461.74 0.984 0.051 0.686 08 051 218 2339 5.0 4.44 0.865 51.286 1550.34 0.602 0.788 0.461 08 051 218 4312 4.6 4.10 0.852 15.849 1573.14 0.178 0.072 0.136 08 051 218 5922 4.1 3.88 1.615 7.413 830.33 0.567 0.104 0.419 08 051 219 1101 6.3 5.82 0.137 6025.596 9790.57 0.281 44.566 0.222 08 051 219 3320 5.0 4.47 0.769 56.885 1744.21 0.469 0.684 0.360 08 051 220 1159 4.3 4.15 1.083 18.836 1237.99 0.434 0.207 0.329 08 051 220 1348 4.3 4.12 1.686 16.982 795.08 1.478 0.617 1.091 08 051 220 1540 4.9 4.60 0.645 89.125 2078.93 0.434 0.996 0.335 08 051 220 2958 4.6 4.21 0.869 23.174 1543.31 0.276 0.163 0.211 08 051 220 3855 4.2 3.83 1.768 6.237 758.20 0.626 0.096 0.460 08 051 221 4053 5.2 4.78 0.421 165.959 3184.61 0.225 0.970 0.175 08 051 222 1024 4.6 4.22 1.032 23.988 1299.60 0.478 0.290 0.363 08 051 222 1527 4.6 4.57 0.679 80.353 1975.16 0.456 0.943 0.352 08 051 222 4606 5.1 5.27 0.343 901.571 3913.37 0.658 15.486 0.515 08 051 223 0530 5.2 4.94 0.357 288.403 3755.63 0.238 1.792 0.186 08 051 223 0536 5.1 4.91 0.396 260.016 3382.50 0.294 1.990 0.230 08 051 223 1658 4.6 4.19 1.063 21.627 1261.10 0.472 0.258 0.358 08 051 223 2852 5.1 4.87 0.339 226.464 3950.27 0.161 0.950 0.126 08 051 223 5212 3.7 3.85 1.496 6.683 895.92 0.407 0.067 0.303 08 051 301 0311 4.6 4.45 0.959 53.088 1397.53 0.851 1.148 0.649 08 051 301 2906 4.9 4.42 0.996 47.863 1346.31 0.858 1.042 0.653 08 051 301 5432 5.1 5.06 0.313 436.516 4289.76 0.242 2.760 0.190 08 051 302 2617 4.1 3.91 1.164 8.222 1151.85 0.235 0.049 0.178 08 051 304 0849 5.8 5.39 0.309 1364.583 4338.34 0.731 26.077 0.573 08 051 304 4531 5.2 5.12 0.247 537.032 5427.58 0.147 2.068 0.116 08 051 304 4855 4.1 3.79 2.023 5.433 662.59 0.817 0.107 0.594 08 051 304 5127 4.7 4.56 0.844 77.625 1589.44 0.846 1.677 0.648 08 051 305 0813 4.5 4.08 1.399 14.791 958.60 0.735 0.271 0.549 08 051 307 4618 5.4 5.09 0.315 484.172 4260.99 0.274 3.464 0.215 08 051 307 5446 5.2 4.95 0.364 298.538 3683.91 0.261 2.034 0.204 08 051 308 2217 4.4 4.06 1.025 13.804 1307.56 0.270 0.094 0.205 08 051 309 0759 3.8 3.65 3.029 3.350 442.63 1.690 0.131 1.171 08 051 310 1516 4.3 4.05 1.484 13.335 903.53 0.791 0.262 0.589 08 051 310 3338 4.3 3.97 1.826 10.116 734.38 1.117 0.276 0.819 08 051 311 0954 4.0 3.50 3.051 1.995 439.41 1.029 0.047 0.712 08 051 314 3819 4.2 4.08 1.189 14.791 1127.96 0.451 0.168 0.340 08 051 314 3951 4.2 3.92 1.304 8.511 1028.18 0.343 0.073 0.257 08 051 315 0708 6.1 5.59 0.186 2722.701 7195.41 0.320 22.874 0.252 08 051 315 1916 5.1 4.87 0.449 226.464 2983.36 0.373 2.195 0.291 08 051 315 5303 4.7 4.51 0.998 65.313 1343.38 1.179 1.952 0.897 08 051 316 2052 4.8 4.56 0.824 77.625 1628.04 0.787 1.561 0.603 08 051 318 3642 4.3 4.18 1.370 20.893 978.29 0.976 0.509 0.731 08 051 323 3038 3.8 3.94 2.084 9.120 643.25 1.499 0.330 1.086 08 051 401 0126 3.7 3.61 1.895 2.917 707.68 0.360 0.026 0.263 08 051 409 0920 4.2 4.03 1.301 12.445 1030.37 0.498 0.155 0.374 08 051 409 5641 4.4 4.13 1.548 17.579 865.86 1.185 0.515 0.880 Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 881 Table 2. (Continued.) ∗ 14 11 Earthquake M † M f (Hz) M (× 10 N·m) r (m) σ (MPa) E (× 10 J) σ (MPa) s w c 0 s a 08 051 410 5437 5.8 5.45 0.178 1678.804 7514.41 0.173 7.638 0.136 08 051 411 0748 4.3 3.99 1.587 10.839 844.78 0.787 0.211 0.583 08 051 413 5457 4.7 4.66 0.609 109.648 2203.14 0.449 1.269 0.347 08 051 415 3217 3.9 3.77 1.557 5.070 861.19 0.347 0.044 0.258 08 051 417 2643 5.1 5.01 0.396 367.282 3382.93 0.415 3.969 0.324 08 051 505 0106 4.8 4.65 0.613 105.925 2187.79 0.443 1.209 0.342 08 051 510 0523 3.8 3.92 1.084 8.511 1236.86 0.197 0.042 0.149 08 051 520 1024 4.2 4.17 1.168 20.184 1147.99 0.584 0.297 0.441 08 051 605 5547 4.5 4.26 1.574 27.542 851.73 1.950 1.328 1.446 08 051 611 3426 4.9 4.52 0.803 67.608 1669.62 0.636 1.099 0.488 08 051 613 2547 5.9 5.39 0.269 1364.583 4983.35 0.482 17.235 0.379 08 051 801 0824 6.1 5.88 0.170 7413.102 7864.85 0.667 129.940 0.526 08 051 912 0856 4.6 4.38 1.069 41.687 1254.49 0.924 0.974 0.701 08 052 001 5233 5.0 4.76 0.608 154.882 2203.43 0.633 2.531 0.490 08 052 123 2954 4.3 4.22 1.242 23.988 1079.80 0.834 0.502 0.627 08 052 400 3546 4.0 4.01 1.339 11.614 1001.34 0.506 0.147 0.379 08 052 401 5332 3.9 4.03 1.471 12.445 911.31 0.719 0.222 0.536 08 052 516 2147 6.4 5.92 0.236 8511.380 5671.41 2.041 455.520 1.606 08 052 704 4201 3.5 3.58 1.838 2.630 729.49 0.296 0.019 0.217 08 052 716 0322 5.3 5.25 0.347 841.395 3865.42 0.637 13.993 0.499 08 052 716 1206 3.7 3.72 2.188 4.266 612.85 0.811 0.083 0.585 08 052 716 3751 5.7 5.41 0.395 1462.177 3390.63 1.641 62.484 1.282 08 052 721 5934 4.7 4.83 0.333 197.242 4025.71 0.132 0.681 0.104 08 052 801 3510 4.7 4.69 0.816 121.619 1642.96 1.200 3.731 0.920 08 052 912 4845 4.5 4.31 1.031 32.734 1299.85 0.652 0.541 0.495 08 053 114 2242 4.3 4.09 1.540 15.311 870.38 1.016 0.385 0.754 08 060 311 0928 4.6 4.67 0.524 113.501 2557.02 0.297 0.873 0.231 08 060 501 2643 4.2 4.20 0.926 22.387 1448.04 0.323 0.184 0.246 08 060 512 4106 4.8 4.66 0.639 109.648 2099.63 0.518 1.464 0.401 08 060 714 2832 4.2 4.08 1.589 14.791 843.95 1.077 0.393 0.798 08 060 806 1428 4.7 4.59 0.629 86.099 2129.89 0.390 0.865 0.301 08 060 906 5536 3.2 3.74 1.103 4.571 1215.62 0.111 0.013 0.084 08 061 010 1504 3.6 3.68 2.249 3.715 596.16 0.767 0.068 0.552 08 061 100 2728 4.0 4.18 1.290 20.893 1038.94 0.815 0.426 0.612 08 061 713 5142 4.3 4.18 1.100 20.893 1218.32 0.505 0.267 0.383 08 061 721 4044 4.1 4.08 1.409 14.791 951.80 0.750 0.276 0.561 08 061 918 2559 4.4 4.32 1.095 33.884 1224.26 0.808 0.691 0.612 08 062 112 0303 3.9 4.06 1.105 13.804 1212.93 0.338 0.118 0.256 08 062 218 3734 4.2 4.06 1.385 13.804 967.78 0.666 0.229 0.498 08 062 305 3831 4.0 4.00 1.478 11.220 907.15 0.658 0.183 0.490 08 062 805 4210 4.5 4.32 1.045 33.884 1282.83 0.702 0.602 0.533 08 062 907 5519 4.2 4.05 1.164 13.335 1151.95 0.382 0.128 0.288 08 071 706 2053 3.6 4.03 0.761 12.445 1761.33 0.100 0.032 0.077 08 072 401 3018 3.9 3.77 1.607 5.070 834.39 0.382 0.048 0.283 08 072 403 5443 5.7 5.61 0.223 2917.427 6000.10 0.591 45.221 0.465 08 072 413 3009 4.9 4.81 0.410 184.077 3269.25 0.230 1.104 0.180 08 072 415 0928 6.0 5.83 0.186 6237.348 7214.77 0.727 119.080 0.573 08 080 116 3242 6.2 5.70 0.241 3981.072 5556.24 1.015 105.960 0.798 08 080 202 1217 5.0 4.66 0.719 109.648 1865.87 0.738 2.079 0.569 08 080 221 2546 4.0 4.13 1.098 17.579 1220.59 0.423 0.188 0.320 08 080 517 4916 6.5 6.12 0.109 16 982.437 12 342.09 0.395 176.920 0.313 08 080 611 4227 4.2 4.19 1.183 21.627 1133.19 0.650 0.354 0.491 08 080 612 4706 4.3 4.22 1.172 23.988 1144.31 0.700 0.423 0.529 08 080 716 1534 5.0 4.66 0.809 109.648 1658.18 1.052 2.951 0.807 08 080 920 1020 3.9 4.05 0.894 13.335 1499.91 0.173 0.059 0.132 08 081 305 0321 4.5 4.42 1.146 47.863 1170.07 1.307 1.577 0.988 08 081 316 4543 3.8 3.89 1.634 7.674 820.35 0.608 0.115 0.450 08 083 115 2451 3.6 3.83 2.188 6.237 612.68 1.187 0.178 0.855 110 323 080 308 3.9 3.74 2.113 4.571 634.54 0.783 0.086 0.566 110 506 184 815 4.1 3.70 1.973 3.981 679.53 0.555 0.054 0.404 110 507 082 112 3.9 3.71 2.340 4.121 572.89 0.959 0.094 0.686 110 605 132 145 4.2 4.00 1.258 11.220 1065.80 0.405 0.114 0.305 110 904 121 345 4.2 3.97 1.606 10.116 835.01 0.760 0.190 0.563 111 101 055 815 5.2 4.99 0.592 342.768 2264.50 1.291 11.428 1.000 111 226 004 652 4.7 4.44 0.875 51.286 1532.62 0.623 0.815 0.477 The earthquake number is composed of the data and time of this earthquake, for example, 08 051 214 4315 represent a earthquake occurred on 2008 May 12 at 14:43:15 (Beijing time). We ignore the deviation between the surface wave magnitude M and the local magnitude M measured by CENC. M is used to uniformly represent the M s L s s and M . L Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 882 H. Wang, Y. Ren and R. Wen Figure 8. (a) Moment magnitude M derived from this study versus M measured by CENC. The solid line represents the best least-squares fit. The dashed– w s dotted lines represent the relationship of M = M ,and M = M − 0.5. The triangles and crosses represent the M values determined by Global CMT and w s w s w Zheng et al.(2009), respectively. (b) Seismic moment M versus corner frequency f . The dashed lines represent the relationship between M and f for various 0 c 0 c constant stress drops as indicated on the top of each line. The triangles, crosses and stars represent the relation of M versus f derived from Ameri et al.(2011), 0 c Hassani et al.(2011)and Sivaram et al.(2013), respectively. Figure 9. (a) The distribution of stress drops and the fitted lognormal distribution (red line). (b) The stress drop versus the moment magnitude (left) and the hypocentre depth (right). The dashed lines represent the logarithmic average of the stress drop of aftershocks that occurred at the northeastern, southwestern and central fault segments, respectively. The solid line represents the logarithmic average of the stress drop over all aftershocks. Fig. 8(b) shows the plots of seismic moment versus corner frequency for the earthquakes considered in this study. These are also 14 18 compared with the constant stress drop relations corresponding to 0.1, 1 and 10 MPa. The M and f vary from 2.0 × 10 to 1.7 × 10 0 c N · m and from 0.1 to 3.1 Hz, respectively. Corner frequencies in our study are significantly lower than those obtained in the 2009 L’Aquila earthquake sequence (Ameri et al. 2011) and earthquakes in central-eastern Iran (Hassani et al. 2011), which implies the lower stress drop. Some much smaller earthquakes in Kumaon Himalaya, India also provide a similar distribution of M versus f with a low stress drop (Sivaram 0 c −3 et al. 2013). The seismic moment is approximately inversely proportional to the cube of the corner frequency in this study, that is, M ∝ f , 0 c and the data regression yields: log M = (15.459 ± 0.278) − 3.0log f (14) 0 c 3 15 −3 M f is equal to 2.87 × 10 N · m · s , which corresponds to a constant stress drop of 0.522 MPa according to the Brune (1970) model. 0 c Stress drop The stress drop values mainly vary from 0.1 to 1.0 MPa (Fig. 9), which are consistent with the results (≤1.0 MPa) given by Hua et al.(2009) for most of the Wenchuan aftershocks. They do not exhibit a significant dependence on the moment magnitude and hypocentre depth (Fig. 9), which indicates that the earthquakes considered in this study follow self-similarity with a constant stress drop. Studies from Allmann & Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 883 Shearer (2009), Oth et al.(2010), Zhao et al.(2011), etc. all confirmed the self-similarity of global earthquakes. However, some other studies obtained conflicting results, in which the self-similarity is broken down in some specific earthquake sequences (e.g. Tusa et al. 2006; Drouet et al. 2010; Mandal & Dutta 2011; Pacor et al. 2016). The stress drops are nearly lognormal distributed with a logarithmic mean of 0.52 MPa, which is dramatically lower than the median value of 3.31 MPa for interplate earthquakes (Allmann & Shearer 2009). The Wenchuan aftershocks have small stress drop values in comparison to other large earthquake sequences, such as the 2010–2011 Canterbury, New Zealand earthquake sequence with stress release of 1–20 MPa (Oth & Kaiser. 2014), the 1983 M 7.7 Japan sea earthquake sequence with stress release of 1–30 MPa (Iwate & Irikura 1988), etc. They JMA are also much smaller than the value of the main shock, which is approximately 1–3 MPa for different finite fault-slip models (Bjerrum et al. 2010). However, the Wenchuan main shock has a stress drop value similar to other earthquakes of the same magnitude, for example, the 2001 M 7.8 Kunlun, China earthquake and the 2002 M 7.7 Denali, Alaska earthquake (Shaw 2013). Therefore, the Wenchuan aftershocks are w w characterized by obvious low values of stress drop. This characteristic was also observed in some other earthquakes, such as the 2010 JiaSian, Taiwan earthquake (Hwang 2012), and for several smaller earthquakes in the Garhwal Himalaya region (Sharma & Wason 1994). Shaw et al.(2015) proposed a physical model that shows reduced stress drops for nearby aftershocks compared to similar magnitude main shocks, because they rerupture part of the fault ruptured by the main shock which may have been partially healed. This model was supported by ground motion observations, showing smaller ground motions generated by nearby aftershocks (e.g. Abrahamson et al. 2014). Smaller values of aftershock stress drops have been also observed using corner frequency analysis of seismic sequences (e.g. Drouet et al. 2011). In this study, an indicator ε proposed by Zuniga (1993) was used to investigate the stress drop mechanism of the Wenchuan earthquake sequence: ε = (15) σ + ε< 1.0 implies a partial stress drop mechanism where the final stress is greater than the dynamic frictional stress (Brune 1970; Brune et al. 1986), whereas ε> 1.0 indicates that frictional overshoot has occurred with the final stress lower than the dynamic frictional stress (Savage & Wood 1971). The well-known Orowan’s hypothesis is met when ε = 1.0 (Orowan 1960). In this study, ε equals 0.75–0.85, which indicates that the Wenchuan aftershocks can be interpreted by the partial stress drop mechanism. Sharma & Wason (1994) pointed out that such kind of aftershocks occur either when the fault locks (heals) itself soon after the rupture of the main shock passes, so the average dynamic frictional stress drops over the whole fault, or when the stress release is not uniform and not coherent over the whole fault plane, and behaves like a series of multiple events with parts of the fault remaining locked. The blank area of the seismic moment release in the ruptured area during the Wenchuan earthquake, as well as the absence of the larger aftershocks, indicates a possibility of fault lock at the unruptured areas on the fault plane (Chen et al. 2013). The low stress drop may be related to parts of the fault remaining locked on the fault plane. The apparent stress of M ≥ 3.0 earthquakes during 2000–2004 in the Sichuan province calculated by Cheng et al.(2006) is approximately proportional to 0.21 σ. This means that ε equals 1.4 (eq. 15), indicating frictional overshoot prevails over partial stress drop. The stress drop mechanism associated with earthquakes along the Longmenshan fault belt changed after the Wenchuan earthquake. The stress drop spatial distribution was obtained by assembling and interpolating the values of all 132 aftershocks, compared with the slip distribution on the fault plane of the main shock, which was determined by Fielding et al.(2013), as shown in Fig. 10. Aftershocks were mainly concentrated on the southwest and northeast segments of the Beichuan fault, and less on the central part. Stress drop contours were generated in three segments from southwest to northeast, respectively. The higher slips emerged on the southwestern segment close to Wenchuan County. In the main shock, the Pengguan Massif began to rupture, and a large amount of stress was released on this segment (Chen et al. 2009). As a result, smaller stress releases occurred for aftershocks here, with a logarithmic average of stress drop of 0.46 MPa. However, the logarithmic average of stress drop is higher, approximately 0.64 MPa for the northeastern segment near the Qingchuan County. This segment also consists of Precambrian quartzite or other stiff geological bodies. Slip on this segment is relatively smaller, and the released stress is lower. The logarithmic average of the stress drop on the central segment is close to 0.52 MPa, and the median slip value corresponds to the median stress drop. Therefore, we infer that the stress drop of the aftershocks may be related to the slip distribution on the fault plane of the main shock. Higher stress release for aftershocks occurred in areas with lower slip in the main shock. For further verifying the above inference, we investigated the magnitude and hypocentre depth distribution between northeastern and southwestern segments, as shown in Fig. 9. The results show that both segments have a homogeneous distribution of magnitude ranging from 3.5 to 6.0, and a homogeneous distribution of depth ranging from 8 to 25 km. Furthermore, the stiffness of crustal structure shows few changes over the whole ruptured area of the Wenchuan main shock according to the CRUST1.0 model (Laske et al. 2013). Therefore, the magnitude, hypocentre depth and crust stiffness could be excluded from the cause of inhomogeneous distribution of stress drop between two segments. Radiated energy and apparent stress Fig. 11 shows the S-wave energy E versus M . The relation between E and M was obtained assuming E ∝ M : s 0 s 0 s 0 logE = (−4.88 ± 0.27) + logM (16) s 0 Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 884 H. Wang, Y. Ren and R. Wen Figure 10. Slip distribution on the fault plane of the Wenchuan main shock determined by Fielding et al.(2013) and the stress drop contours for aftershocks employed in this study. The cross represents the epicentre of the aftershocks. In order to clearly compare the slip distribution and the stress drop of the aftershocks, the panel of the slip distribution is parallel moved upward. Figure 11. S-wave energy E versus seismic moment M . The regression line (solid) corresponding to constant apparent stress is shown within one standard s 0 deviation range (shaded area). −5 This relationship means that the S-wave energy-to-moment ratio is approximately equals to 1.32 × 10 , which is consistent with the −5 result of 1.2 × 10 for small earthquakes in Anchorage, Alaska derived by Dutta et al.(2003). As shown in Table 2, the apparent stress σ varies from 0.077 to 1.606 MPa, which is directly proportional to 0.74 σ with a correlation coefficient of 0.998. The apparent stress is independent of the earthquake size, since σ is independent of M , as mentioned above. ATTENUATION CHARACTERISTICS The attenuation curve A(f, R) can be described in terms of anelastic attenuation and other factors ( ) related to seismic attenuation: π f lnA ( f, R) − ln =− (R − R ) (17) Q ( f ) β s s Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 885 Figure 12. Geometrical spreading exponents (n) at frequencies ranging from 0.1 to 20 Hz. The solid and dashed lines represent the average n and one standard deviation range, respectively. where Q stands for the S-wave quality factor dependent on the frequency. must be greater than A(f, R). Suppose only contains the geometrical spreading in this study. In general, the geometrical spreading can be a linear, hinged bilinear, or hinged trilinear model of R.In this study, geometrical spreading is a simple model expressed as (R /R) ,where n is the geometrical spreading exponent. The greater the n value is, the stronger the geometrical spreading. According to the necessary condition of lnA(f,R) − ln(R /R) < 0, we seek out a maximum n to meet this condition for each frequency, indicating the strongest geometrical spreading. Then Q can be evaluated from the slope of a linear least-squares fit of eq. (17) at each frequency. In this study, both geometrical spreading and anelastic attenuation were considered frequency dependent in order to deal with the trade-off between them. This strategy was also used in the study of Bindi et al.(2004). The geometrical spreading exponents at frequencies of 0.5–20 Hz for R = 30–150 km are shown in Fig. 12. The values of n vary from 0.35 to 0.75, increasing with increased frequency from 0.1 to 0.4 Hz at first, then overall decreasing until a critical frequencyaround 3.5 Hz, and finally increasing up to 20 Hz, which indicates frequency-dependent geometrical spreading in this region. Frequency-dependent geometrical spreading was also observed in North America by Babaie Mahani & Atkinson (2013) through studying response spectral amplitudes and PGAs of ground motions. Geometrical spreading in the Northeast, central United States (CUS), and the Pacific Northwest/southwestern British Columbia (PNW/BC) has a tendency to decrease at first and then increase with the increased frequency, which is very similar to what we observed in this study. Based on the analyses of larger numbers of strong-motions recordings, previous studies have shown that n is not lower than 1.0 for local distances, while n is approximately equal to 0.5 for regional distances (Atkinson & Mereu 1992;Bora et al. 2015). The threshold for local and regional distance is related to the crustal thickness. Our study region is located at the southeast margin of the Tibetan Plateau where the crustal thickness is about 50 km. Therefore, we regard 75 km (i.e. 1.5 times of crustal thickness) as the boundary between the local 1.0 0.5 and regional distances (Atkinson & Mereu 1992). A general geometrical spreading model (R /R) for R < 75 km, and (R /75)(75/R) for 0 0 R ≥ 75 km is assumed. In this study, n is lower than 0.5 at frequencies ranging from 3 to 15 Hz, and 0.5–0.75 at frequencies lower than 3 Hz and greater than 15 Hz (Fig. 12). The average n value is 0.57 with a standard deviation of 0.11, obtained over frequencies ranging from 0.57 0.1 to 20 Hz. We compared the average geometrical spreading (R /R) with the general geometrical spreading mentioned above, as shown in Fig. 13. We also compared the geometrical spreading in Yunnan and southern Sichuan determined by Xu et al.(2010b), which reflects a weak attenuation of ground motion. The average geometrical spreading in this study is slightly stronger than the one given by Xu et al. (2010b), while much weaker than the general geometrical spreading. This result implies that regions near the ruptured fault of the Wenchuan earthquake show weak geometrical spreading. Boore et al.(2014) determined that the observed ground motions from China, mainly derived from the Wenchuan earthquake sequence, exhibit a weaker attenuation, which is ascribed to a ‘high Q’. This may also be related to the weak geometrical spreading inferred from our study. As shown in eq. (17), the path attenuation mainly consists of geometricalspreading and anelastic attenuation (represented by Q), a potential trade-off is inherent between them. The S-wave quality factor Q versus frequency from 0.1 to 20 Hz is shown in Fig. 14. Q (f)isregressedintheform of Q f , and the s s s0 1.06 least-squares solution is given by 151.2f . Other studies also provided the Q values for the adjacent region (Fig. 14). Hua et al.(2009) 0.423 0.836 obtained the Q for the western mountains (274.6f ) and eastern plains (206.7f ) in northern Sichuan, separated by the Longmenshan 0.59 fault belt. Zhao et al. (2011) also determined Q = 191.8f for western Sichuan. Compared with results from Hua et al.(2009)and Zhao et al. (2011), Q , representing the quality factor at 1.0 Hz, is lower in our study. However, the attenuation coefficient η is much greater than s0 that at the mountains but close to that at the plains. Q is closer to the results for the plains from Hua et al.(2009). The study region in this s Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 886 H. Wang, Y. Ren and R. Wen Figure 13. Comparison of the average geometrical spreading derived in this study with the general geometrical spreading, and results from Xu et al.(2010b). 0.57 The averaged results of this study represent (R /R) over the hypocentre distance from 30 to 150 km. Two dashed lines represent the plus or minus one 1.0 0.5 standard deviation of the average. The general results represent (R /R) for R < 75 km and (R /75)(75/R) for R ≥ 75 km. 0 0 paper is located on both sides of the Longmenshan fault belt, where the elevation suddenly drops from about 4500 m on the plateau to 500 m in the Sichuan Basin. The low Q and high η may be related to the propagation path passing through the highly heterogeneous active fault s0 belt. SITE RESPONSE The calculated site response functions of the 43 strong-motion stations are shown in Fig. 15. Site responses for most stations are generally in good agreement with those determined by Ren et al.(2013). Compared with the site responses derived from the horizontal-to-vertical spectral ratio (HVSR) method (Fig. 15), predominant frequencies are approximately identical, while site amplifications from the non-parametric GIT are significantly higher, except for some stations (51SFB, 51SPA, 51QLY and L0021). That is because the HVSR method can approximately evaluate the predominant site frequency but underestimates the site amplification (Castro et al. 2004; Hassani et al. 2011). Since many analyses related to site effects in the Wenchuan earthquake sequence have been made in the study of Ren et al.(2013), our study only focused on the performance of a terrain effect array in the Wenchuan aftershocks. Stations L2009, L2002 and L2007 compose a terrain effect array, which were installed on the top (altitude 969 m), middle (altitude 960 m) and foot (altitude 927 m) of a hill (Wen et al. 2014). Fig. 16(a) shows the locations of the three stations on the hill, which share similar geological conditions. The site response functions of the three stations determined by the non-parametric GIT and HVSR method are shown in Fig. 16(b). Site responses from non-parametric GIT have significant discrepancies among the three stations, especially at frequencies of 2.0–8.0 Hz. Site amplification increases with the Figure 14. Frequency-dependent S-wave quality factor Q derived from this study. The solid line represents the least-squares regression of this study in the 1.06 0.423 frequency range 0.1–20 Hz, that is, Q (f) = 151.2f . The dotted line and the dashed–dotted line represent Q (f) = 274.6f for the western mountains and s s 0.836 0.56 Q (f) = 206.7f for the eastern plains in the northern Sichuan from the study of Hua et al.(2009). The dashed line represents Q (f) = 191.8f for western s s Sichuan from Zhao et al.(2011). Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 887 Figure 15. Site response functions derived from the non-parametric GIT, HVSR method and Ren et al.(2013). The locations of these stations are clearly shown in Fig. 2. Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 888 H. Wang, Y. Ren and R. Wen Figure 16. (a) Location illustration of the terrain effect array; (b) site response functions determined by the non-parametric GIT (black) and HVSR method (red). increased elevation and is 1.5–2.0 times larger at L2009 than that at L2007. The site amplifications given by the HVSR method have no significant difference at the three stations, implying the HVSR method may not effectively reflect the local terrain effect. This result is in agreement with the conclusion from other studies (Parolai et al. 2004; Massa et al. 2013). CONCLUSIONS Nine hundred twenty-eight strong-motion recordings with hypocentre distances smaller than 150 km were used for separating the source spectra, path attenuation and site responses in the frequency domain using the two-step non-parametric GIT. These recordings were obtained at 43 permanent and temporary strong-motion stations during 132 earthquakes of M 3.2–6.5, which occurred on or near the fault plane of the 2008 Wenchuan earthquake from 2008 May 12 to 2013 December 31. We assumed that the path attenuation equals 1.0 at the reference distance of 30 km. As a result, the cumulative attenuation within this distance is transferred to the inverted source spectra when the trade-off between the source effect and site response is solved using a reference site. The cumulative attenuation was supposed as a ratio of the inverted source spectrum over the theoretical source spectrum for an M 6.5 earthquake. Its theoretical source spectrum was determined using the Fourier amplitude spectral ratio method. Then the inverted source spectra of all 132 earthquakes were corrected by the cumulative attenuation to obtain the real source spectra, which show approximately −2 close to ω decay at high frequencies. Furthermore, a grid-searching method was used to determine the best-fit seismic moment and corner frequency. Moreover, the stress drop, source radius, S-wave energy and apparent stress were successively calculated. We investigated the scaling properties of these source parameters, and draw the following conclusions: (1) Moment magnitude M has a linear deviation from the surface wave magnitude M measured by CENC. M is generally lower than w s w −3 3 15 −3 M , and is in agreement with previous studies. M is approximately proportional to the f ,and M f = 2.87 × 10 N · m · s . The average s 0 c 0 c −5 S-wave energy-to-moment ratio is close to 1.32 × 10 . The apparent stress σ is approximately equal to 0.74 σ, independent of the earthquake size. (2) The value of stress drop σ for individual earthquakes varies mainly from 0.1 to 1.0 MPa, following an approximately lognor- mal distribution with an average of 0.52 MPa. The value is significantly smaller than the median stress drop of interplate earthquakes (Allmann & Shearer 2009), and some other large earthquake sequences. It is also much smaller than the stress drop of the Wenchuan main shock which is similar to some other large earthquakes with similar magnitude (∼8.0). This characteristic with low stress drop of Wenchuan aftershocks was investigated using the ε indicator. The results show that ε is less than 1.0, ranging from 0.75 to 0.85, indicating that the low stress drop may be interpreted by the partial stress drop mechanism. Explanations of the low stress drop in aftershocks may be related to the remaining locked parts on the fault plane of the main shock. (3) The investigation shows that the stress drop σ has no significant dependence on the earthquake size and the hypocentre depth, indicating that the Wenchuan aftershocks follow self-similarity over the M range of our data. The stress drop of aftershocks may be correlated to the slip distribution on the fault plane of the Wenchuan main shock. A relatively larger stress drop appeared at areas with relatively smaller slip. The geometrical spreading is weak around the Wenchuan area within distances of R = 30–150 km, and is strongly dependent on the 1.06 frequency. The S-wave quality factor Q (f) is regressed by Q (f) = 151.2f . The quality factor shows strong dependence on frequency, which s s can be ascribed to the high heterogeneity of the crustal medium. Our study region is located on the southeast edge of the Tibet Plateau where the elevation suddenly drops from about 4500 m on the plateau to 500 m in the Sichuan Basin. Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 889 The inverted site responses of three stations from a terrain effect array show that the site amplification is strongest at the hilltop and smallest at the hillfoot, implying that the local topography considerably affects the ground motions. The site responses, calculated using the HVSR method, were not very different among the three stations. This suggests that the HVSR method may not be effectively used for analysing the local topography effect on ground motion. ACKNOWLEDGEMENTS This work is supported by the Science Foundation of Institute of Engineering Mechanics, China Earthquake Administration under grant no. 2016A04, Nonprofit Industry Research Project of China Earthquake Administration under grant no. 201508005 and National Natural Science Foundation of China under grant no. 51308515. 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Source parameters, path attenuation and site effects from strong-motion recordings of the Wenchuan aftershocks (2008–2013) using a non-parametric generalized inversion technique

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Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Geophysical Journal International Geophys. J. Int. (2018) 212, 872–890 doi: 10.1093/gji/ggx447 Advance Access publication 2017 October 16 GJI Seismology Source parameters, path attenuation and site effects from strong-motion recordings of the Wenchuan aftershocks (2008–2013) using a non-parametric generalized inversion technique Hongwei Wang, Yefei Ren and Ruizhi Wen Key Laboratory of Earthquake Engineering and Engineering Vibration of China Earthquake Administration, Institute of Engineering Mechanics, China Earthquake Administration, No. 29 Xuefu Road, Harbin 150080, China. E-mail: renyefei@iem.net.cn Accepted 2017 October 14. Received 2017 August 14; in original form 2016 October 11 SUMMARY Secondary (S) wave amplitude spectra from 928 strong-motion recordings were collected to determine the source spectra, path attenuation and site responses using a non-parametric generalized inversion technique. The data sets were recorded at 43 permanent and temporary strong-motion stations in 132 earthquakes of M 3.2–6.5 from 2008 May 12 to 2013 December 31 occurring on or near the fault plane of the 2008 Wenchuan earthquake. Some source parameters were determined using the grid-searching method based on the omega-square 14 18 model. The seismic moment and corner frequency vary from 2.0 × 10 to 1.7 × 10 N · m and from 0.1 to 3.1 Hz, respectively. The S-wave energy-to-moment ratio is approximately −5 1.32 × 10 . It shows that the moment magnitude is systematically lower than the surface wave magnitude or local magnitude measured by the China Earthquake Network Center. The seismic moment is approximately inversely proportional to the cube of the corner frequency. The stress drop values mainly range from 0.1 to 1.0 MPa, and are lognormal distributed with a logarithmic mean of 0.52 MPa, significantly lower than the average level over global earthquake catalogues. The stress drop does not show significant dependence on the earthquake size and hypocentre depth, which implies self-similarity for earthquakes in this study. The ε indicator was used to determine the stress drop mechanism. The low stress drop characteristic of the Wenchuan aftershocks may be interpreted by the partial stress drop mechanism, which may result from remaining locked sections on the fault plane of the main shock. Furthermore, we compared the stress drop distribution of aftershocks and slip distribution on the fault plane of the main shock. We found that aftershocks with higher stress drop occurred at areas with smaller slip in the main shock. The inverted path attenuation shows that the geometrical spreading around the seismogenic region of Wenchuan earthquake sequence is weak and significantly dependent on frequency for hypocentre distances ranging from 30 to 150 km. The frequency-dependent 1.06 S-wave quality factor was regressed to 151.2f at frequencies ranging from 0.1 to 20 Hz. The inverted site responses provide reliable results for most stations. The site responses are obviously different at stations in a terrain array, higher at the hilltop and lower at the hillfoot, indicating that ground motion is significantly affected by local topography. Key words: Fourier analysis; Earthquake ground motions; Earthquake source observation; Seismic attenuation; Site effects. INTRODUCTION The M 7.9 Wenchuan earthquake on 2008 May 12 was the strongest earthquake ever recorded along the Longmenshan fault belt. It was also one of the most destructive earthquakes in China, which caused catastrophic damage and heavy casualties and affected a wide range of regions. This event generated a surface rupture zone of 240 km in length along the Beichuan fault and an additional 72 km along the Pengguan fault (Xu et al. 2009). Before the Wenchuan earthquake, the Longmenshan fault belt was not very active. In the past 100 yr, only two events of M ≥ 6.0 have been recorded. One was the 1958 M6.2 Beichuan earthquake, which occurred on the Beichuan fault. The other was the 1970 M6.2 Dayi earthquake, which occurred on the Pengguan fault (Chen et al. 1994). However, lots of fragmentary ruptures frequently occurred on The Authors 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 873 the Longmenshan fault belt, triggering a large number of small earthquakes with magnitudes ranging from 1.0 to 5.0 (Yang et al. 2005). Large ruptures occurred in recent years, including the 2008 M 7.9 Wenchuan earthquake and the 2013 M 6.6 Lushan earthquake, which w w implied that the Longmenshan fault belt was activated after a long silence. As a result, the design seismic accelerations for most areas in the Longmenshan region were substantially modified in the latest generation of seismic ground motion parameters zonation map of China, which was formally issued in 2015 (AQSIQ 2015). They were increased to 0.15 or 0.20g (g, gravitational acceleration) from 0.10 to 0.15g, respectively, in the previous version. Design seismic accelerations are divided into six levels in the zonation map of China, which gradually increase from 0.05 to 0.40g at an interval of 0.05 or 0.10g. The second, third and fourth levels are 0.10, 0.15 and 0.20g, respectively. This means that the seismic-proof demand was raised one level, or even two levels for most areas in the Longmenshan region, implying a current potential high seismic hazard in this region. The attenuation laws for ground motions, scaling relations of source parameters and site effects are directly related to the prediction and assessment of seismic hazard. They play essential roles in establishing ground motion prediction equations or simulating ground motion time histories. Therefore, it is very valuable to study the source, path and site characteristics of earthquakes occurring on the Longmenshan fault belt such as the Wenchuan earthquake sequence. In recent years, such studies have already been performed, for example, Ren et al.(2013), Yu and Li (2012)and Hua et al.(2009). Ren et al.(2013) analysed the site responses of permanent strong-motion stations and identified the soil non-linearity using strong-motion recordings from the Wenchuan aftershocks, based on the parametric generalized inversion technique (GIT). However, path and source characteristics were not considered. The source parameters and quality factor of the propagation medium were inverted by Yu and Li (2012) using the Levenberg–Marquardt algorithm. However, only 13 aftershocks of M > 5.0 were investigated, and few analyses regarding site effects were made in this study. More than 1000 aftershocks of M ≥ 3.0 were investigated by Hua et al.(2009) to study the segmentation features of the stress drop. However, other source parameters were not included, and site effects were neglected. There is not yet a study including systematic analyses on the source parameters, path attenuation and site effects of ground motions from the Wenchuan earthquake sequence. In this paper, a non-parametric generalized inversion of secondary (S) wave amplitude spectra of the strong-motion recordings from the Wenchuan earthquake sequence was performed to separate the source, propagation path and site effects simultaneously. Earthquakes considered in this study occurred on or near the fault plane of the Wenchuan earthquake from 2008 May 12 to 2013 December 31. We investigated the attenuation characteristics, mainly including geometrical spreading and anelastic attenuation. Some source parameters were estimated from the inverted source spectra and then used to study the source scaling relations of earthquakes in this region. Finally, we provided the site responses for stations considered in this study, and analysed preliminarily the local topographic effect on ground motions. DATA SET A total of seven issues (Issues 12–18) of uncorrected strong-motion acceleration recordings have been officially issued in China by the China Strong Motion Network Center since the China National Strong Motion Observation Network System (NSMONS) formally began operation in 2007. The analogue recordings in China before 2007 were published in Issues 1–11. Issue 12 covers recordings from the Wenchuan main shock. Issues 13 and 14 cover recordings from the Wenchuan aftershocks obtained by the permanent and temporary stations, respectively. Issues 15, 16 and 18 cover other recordings collected during 2007–2009, 2010–2011 and 2012–2013, respectively. Issue 17 covers recordings from the 2013 Lushan earthquake sequence. Strong-motion recordings in Issues 13–16 and 18 from earthquakes that occurred on or near the rupture fault of the Wenchuan earthquake are used as the data set in this study. It is composed of more than 2000 strong-motion recordings from 383 M (M ) 3.3–6.5 earthquakes from 2008 May 12 to September 30 recorded at 76 permanent stations s L of NSMONS in Gansu and Sichuan provinces (Issue 13), 2214 strong-motion recordings from 600 M (M ) 2.3–6.3 earthquakes from s L 2008 May 14 to October 10 recorded at 83 temporary stations (Issue 14, Wen et al. 2014), and 355 additional strong-motion recordings from 57 M (M ) 3.1–5.5 earthquakes from 2008 October 1 to 2013 December 31 recorded at 86 stations of NSMONS (Issues 15, s L 16 and 18). Deviations between the surface wave magnitude M and the local magnitude M for earthquakes in China and adjacent s L regions measured by the China Earthquake Network Center (CENC) were ignored (Zhang et al. 2008). In this paper, M was used to represent the measured magnitude by CENC. The baseline correction and a Butterworth bandpass filter between 0.1 and 30.0 Hz were performed. Fig. 1 shows the hypocentre distance (R) and geometric mean of the peak ground acceleration (PGA) for the two horizontal compo- nents (east–west and north–south) of the strong-motion recordings in this data set. PGAs of these strong-motion recordings mainly vary −2 from 2.0 to 100 cm s . Hypocentre distances of most recordings from Issues 13, 15, 16 and 18 generally range from 30 to 200 km. However, hypocentre distances for many recordings from Issue 14 are less than 30 km, with the minimum approaching 1.0 km. Recordings from Issue 14 were obtained by temporary stations deployed as close to the seismogenic fault as possible (Wen et al. 2014). Very few recordings from Issues 15, 16 and 18 were obtained from earthquakes of M > 5.0 because very few aftershocks with large magnitudes occurred in the seismogenic area of the Wenchuan earthquake during 2009–2013. We selected available recordings from this data set ac- −2 −2 cording to the following criteria proposed by Ren et al.(2013): (1) 30 km ≤ R ≤ 150 km; (2) 2 cm s ≤ PGA ≤ 100 cm s ; (3) each selected earthquake should be recorded by at least four stations, each of which should collect at least four recordings that match (1) and (2). Finally, we employed 928 strong-motion recordings from 132 earthquakes of M 3.2–6.5 at 43 strong-motion stations. Earthquake epicentres and strong-motion stations considered in this study are shown in Fig. 2. Most stations are located in the mountains, west of Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 874 H. Wang, Y. Ren and R. Wen Figure 1. Hypocentre distance and peak ground acceleration (PGA) of the data set used in this study. The dashed–dotted lines in the left-hand panel represent the hypocentre distance range for most data in the Issues 13, 15, 16 and 18 released by China Strong Motion Network Center. The dashed–dotted lines in the right-hand panel represent the PGA range for most recordings of the data set used in this study. Issues 13 and 14 cover recordings from the Wenchuan aftershocks obtained by the permanent and temporary stations, respectively. Issues 15, 16 and 18 cover other recordings collected during 2007–2009, 2010–2011 and 2012–2013, respectively. 102˚E 103˚E 104˚E 105˚E 106˚E 34˚N 34˚N 62SHW 62WUD 51JZY L2015 51JZG L2016 L2008 51JZW (62WIX,L2002,L2007,L2009) 33˚N L2004 33˚N L2005 L2010 L2001 L2006 51GYZ 51SPA 51GYQ L0020 L0021 Guangyuan L0022 51HSL 51HSD 51MXD 32˚N 32˚N 51HSS 51MXN 51CXQ 51AXY 51MXB 51LXM 51MZQ 51LXS 51LXT 51AXT Mianyang Perm. station 51XJB 51WCW Temp. station 31˚N 51SFB 31˚N 51XJD City Mainshock Ms 3.0−3.9 Chengdu Ms 4.0−4.9 51QLY Ms 5.0−5.9 51PJW 51PJD Ms 6.0−6.5 30˚N 30˚N 102˚E 103˚E 104˚E 105˚E 106˚E Figure 2. The locations of earthquakes (circle) and strong-motion stations (triangle and square) used in this study. The grey solid lines represent the surface traces of the Longmenshan fault belt. Insert in the top left corner shows the location of the study region in China. the Longmenshan fault belt. In contrast to data used by Ren et al.(2013), we added more earthquakes and strong-motion stations in this study. The S waves of the two horizontal components of the strong-motion recordings were extracted, according to studies of Husid (1967) and McCann (1979). A cosine taper was applied at the beginning and end of the S-wave window, and the length of each taper was set at 10 per cent of the total trace length (Hassani et al. 2011;Ren et al. 2013). The Fourier amplitude spectrum of the S wave was calculated and Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 875 Figure 3. Residuals of synthetic results produced by the inverted source spectra, site responses and path attenuation, computed as log10 (observation/synthetics), versus hypocentre distance at (a) 0.5 Hz, (b) 5.0 Hz and (c) 10.0 Hz. The average residuals (blue circles) and one standard deviations (error bars) for different distance bins were computed. (d) The average residuals at each frequency of 0.1–20 Hz for different distance bins. smoothed using the windowing function of Konno & Ohmachi (1998) with b = 20. The vector synthesis of the Fourier amplitude spectra from two horizontal components was used to represent the horizontal ground motion in frequency domain. METHODOLOGY We applied a two-step non-parametric GIT (Castro et al. 1990;Oth et al. 2008, 2009) to separate attenuation characteristics, source spectra and site response functions. In the first step, the dependence of the spectral amplitudes on the distance at frequency (f) can be expressed as: O f, R = M ( f ) · A f, R (1) ij ij i ij where O (f,R ) is the spectral amplitude observed at the jth station resulting from the ith earthquake, R is the hypocentre distance, M (f)is ij ij ij i a scale dependent on the size of the ith earthquake and A(f, R ) is a non-parametric function of distance and frequency accounting for the ij seismic attenuation (e.g. geometrical spreading, anelastic and scattering attenuation, refracted arrivals, etc.) along the path from source to site. A(f, R ) is not supposed to have any parametric functional form and is constrained to be a smooth function of distance with a value of 1 ij at reference distance R . Once A(f, R ) is determined, the spectral amplitudes can be corrected for the seismic attenuation effect. In the second step, the corrected ij spectra are divided into source spectra and site response functions: O f, R /A f, R = S ( f ) · G ( f ) (2) ij ij ij i j where G (f) is the site response function at the jth station and S (f) is the source spectrum of the ith earthquake. The trade-off between the site j i and source is resolved by selecting station 62WIX as a reference site, where the site responses are constrained to be 2.0 around all frequencies (Ren et al. 2013). Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 876 H. Wang, Y. Ren and R. Wen Figure 4. The inverted source spectra for four typical earthquakes representing four magnitude levels. The dark lines represent the inverted source spectra using the total recordings in this study. The grey lines represent the inverted source spectra from 100 bootstrap inversions. The name of the earthquake is composed of the date and time of this event. Eq. (1) can be turned into a linear problem by taking the natural logarithm and expressing it as a matrix formulation: ⎡ ⎤ lnA ( f, R ) ⎡ ⎤ 1 1000 ··· 010 ··· 0 ⎢ ⎥ ⎡ ⎤ ⎢ ⎥ lnA ( f, R ) ⎢ ⎥ lnO ( f, R ) 1 1 ⎢ ⎥ ⎢ ⎥ 0100 ··· 001 ··· 0 ⎢ ⎥ lnA ( f, R ) ⎢ ⎥ 3 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ lnO ( f, R ) ⎥ 2 2 ⎢ ⎥ . . . . . . . . . . ⎢ ⎥ lnA ( f, R ) ⎢ ⎥ . . . . . . . . . . ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ . . . . . . . . . . ⎢ ⎥ . ⎢ ⎥ . ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ . ⎥ ⎢ 0000 ··· 100 ··· 1⎥ ⎢ ⎥ ⎢ ⎥ lnO ( f, R ) ⎢ ⎥ ⎢ N N ⎥ · ⎢ ⎥ = (3) lnA ( f, R ) ⎢ ⎥ N ⎢ ⎥ ⎢ ⎥ ω 000 ··· 000 ··· 0 0 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ lnM ( f ) ⎥ ⎢ ⎥ ⎢ 0 ⎥ −ω /2 ω −ω /20 ··· 000 ··· 0 ⎢ ⎥ ⎢ 2 2 2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ lnM ( f ) 0 ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ 0 −ω /2 ω −ω /2 ··· 000 ··· 0 ⎢ ⎥ 2 2 2 ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ . ⎢ . ⎥ . . . . . . . . . . ⎣ ⎦ . . . . . . . . . . . . . . . . . . . . ( ) lnM f In eq. (3), the hypocentre distance ranges are divided into N bins with a 5 km width. R , R ..., R is a monotonically increasing 1 2 N sequence of hypocentre distance. The weighting factor ω is used to constrain A(f, R ) = 1 at reference distance R and ω is the factor 1 0 0 2 determining the degree of smoothness of the solution. The reference distance was set to 30 km, which is the smallest hypocentre distance considered in this study. We calculated the residuals between the observed data and the synthetic results from the product of the inverted source spectra, site responses and path attenuation, as shown in Fig. 3. The residuals were expressed as the logarithmic observed values minus logarithmic synthetic values. They vary around zero and have an average close to zero in the whole frequencies of 0.1–20 Hz. This shows that the residuals are independent on the hypocentre distance, indicating that the non-parametric inversion provides a good representation of the observed recordings considered in this study. SOURCE SPECTRA The bootstrap analysis proposed by Oth et al.(2008, 2011) was performed in this study to assess the stability of the inverted source spectra. 150 strong-motion recordings, accounting for approximately 16 per cent of the total recordings, were randomly removed from the data set, and the remaining ones were assembled as a new data set used in the inversion. We repeated this procedure 100 times to investigate the stability of the inverted source spectra. Fig. 4 shows the inverted source spectra resulting from 100 bootstrap inversions for four typical earthquakes representing four magnitude levels. The deviation from the source spectra obtained using the whole data set remains small, implying that the source spectra are stable. Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 877 Table 1. The basic information of a large earthquake and its four empirical Green’s function (EGF) events used to estimate the cumulative attenuation within the reference distance of 30 km. Large earthquakes Small earthquakes as EGF events ∗ ◦ ◦ ◦ ◦ Number Date and time M / M Long. ()Lat.()Depth(km) M /f Number Date and time M Long. ()Lat.()Depth(km) s w w c s 01 08 08 05 174 916 6.5/6.0 105.61 32.72 13 5.86/0.206 02 08 06 19 182 559 4.4 105.62 32.73 10 5.92/0.176 03 08 05 12 224 606 5.1 105.64 32.72 10 6.12/0.109 04 08 05 27 160 322 5.3 105.65 32.76 15 6.07/0.105 05 08 07 24 03 5443 5.7 105.63 32.72 10 M is derived from the Global Centroid-Moment-Tensor (CMT) catalogue. The cumulative attenuation within the reference distance is not included in the A(f,R) derived from the first-step inversion. The inverted source spectra from the second-step inversion absorb this cumulative attenuation when the trade-off between the site and source is solved using the known site response of the reference site. Therefore, the real source spectrum can be expressed as: S ( f ) = S ( f ) /ψ ( f ) (4) inverted where ψ(f) represents the cumulative attenuation within the reference distance and S (f) is the inverted source spectrum. If the real source inverted spectrum of an earthquake is known, the cumulative attenuation can be derived from eq. (4). Assuming that the source spectrum follows the omega-square source model (Brune 1970), R V M θ 0 S ( f ) = (2π f ) · · (5) 3 2 4πρ β s 1 + ( f / f ) s c where R is the average radiation pattern over a suitable range of azimuths and take-off angles set to 0.55. V = 1/ 2 accounts for the portion of total S-wave energy in the horizontal components. ρ and β are the density and S-wave velocity in the vicinity of the source set to 2700 kg s s −3 −1 m and 3.6 km s , respectively. M and f are the seismic moment and corner frequency. We used the relationship proposed by Hanks & 0 c −7 Kanamori (1979) to convert moment magnitude (M )to M (unit: dynecm = 10 N · m): w 0 logM = 1.5 × (M + 10.7) (6) 0 w If a small earthquake is regarded as the empirical Green’s function (EGF) event of a large earthquake, the differences of the path attenuation in the strong-motion recordings at the same station from large and small earthquakes can be neglected. Fourier amplitude spectral ratio O (f)/O (f) can be approximately expressed as the theoretical source spectral ratio S (f)/S (f), L S L S O ( f ) S ( f ) M 1 + ( f / f ) L L 0L cS ≈ = · (7) O ( f ) S ( f ) M ( ) S S 0S 1 + f / f cL where subscripts L and S represent the large and small earthquakes, respectively. According to eq. (7), the values of seismic moment and corner frequency for both large and small earthquakes could be achieved by minimizing the differences between the Fourier amplitude spectral ratio of the observed strong-motion recordings averaged over all stations triggered in both earthquakes and the theoretical source spectral ratio. In this study, an M 6.5 earthquake (No. 01) that occurred on 2008 August 5 at 17:49:16 (Beijing time) at the northeastern part of the Longmenshan fault was selected as a large event, and four other earthquakes (M 4.4, 5.1, 5.3 and 5.7) were selected as its EGF events. The basic information for these earthquakes is listed in Table 1, and their epicentres and the recorded strong-motion stations are shown in Fig. 5. The grid-searching method was adopted to determine the best-fit seismic moment and corner frequency in eq. (7). The best-fitting theoretical source spectral ratios between large and small earthquakes are in good agreement with the Fourier amplitude spectral ratios calculated using observed strong-motion recordings at frequencies of 0.1–20 Hz, as shown in Fig. 6. The obtained M values range from 5.86 to 6.12 and the f values range from 0.105 to 0.206 Hz for the M 6.5 earthquake, as shown in Table 1. The values of M are in good c s w agreement with the one from the Global Centroid-Moment-Tensor (CMT) catalogue, that is, 6.0. According to eq. (5), the theoretical source spectra of the M 6.5 earthquake were obtained, then the values of ψ(f) were calculated using eq. (4), as shown in Fig. 6. It shows that the ψ(f) is not strongly dependent on the selected EGF event, implying its stable estimation. In this study, we adopted the ψ(f) derived from the spectral ratio between the M 6.5 and the M 5.3 earthquakes (i.e. Nos. 01 and 04 in Table 1), which is approximately median of all four ψ(f). s s The source displacement spectra corrected using ψ(f) are shown in Fig. 7 for seven magnitude bins from 3.0 to 6.5 at an interval of 0.5 mag. −2 Source spectra at high frequencies are close to the ω decay. Note that for a proper quantification of the stability of ψ(f), it would be useful to consider additional pairs of collocated large events/EGFs, in particular in the southwestern part of the fault. Unfortunately, such pairs are not available. Because the hypocentres of large and small earthquakes are not close enough to remove the difference of path attenuation from their sources to sites, or the strong-motion recordings obtained in both earthquakes are not enough to calculate the reliable spectral ratio between them. Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 878 H. Wang, Y. Ren and R. Wen 104˚E 105˚E 106˚E 62WUD 51JZB 51JZY L2015 51JZG L2016 L2008 33˚N L2004 33˚N 62WIX (L2002,L2007,L2009) L2005 L2001 L2012 51SPC (L2013,L2014) L2006 L2011 51GYZ 51GYQ L0020 L0021 02 04 L0022 51GYS 32˚N 32˚N L0002 L0045 (L0048,L0049) L0004 51CXQ 01 05 03 104˚E 105˚E 106˚E Figure 5. The epicentre locations of a large and four small earthquakes listed in Table 1, and strong-motion stations operating during these earthquakes. Figure 6. (a) The averaged Fourier amplitude spectral ratio (solid line) of strong-motion recordings observed at the same stations between the large and small earthquakes listed in Table 1, and the best-fit theoretical source spectral ratio (dashed line). (b) The cumulative attenuation within the reference distance of 30 km. SOURCE PARAMETERS The grid-searching method was adopted to obtain the best-fit seismic moment and corner frequency for each earthquake, making the theoretical source spectrum expressed by eq. (5) closest to the attenuation-corrected source spectrum. It can be represented as: Nf S ( f ) / ( f ) i,inverted m m log = min. (8) S ( f ) i m m=1 M − 1.0 ≤ M ≤ M + 1.0, the corresponding searching ranges of M are derived from eq. (6). The values of stress drop ( σ)for s w s 0 small-to-moderate earthquakes generally vary from 0.1 to 100.0 MPa (Kanamori 1994). Following Brune (1970), the corner frequency is 6 1/3 expressed as f = 4.9 × 10 β ( σ/M ) . The searching ranges of f are estimated according to the possible variation ranges of σ. Fig. 7 c s 0 c Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 879 Figure 7. The attenuation-corrected source displacement spectra (left-hand panel), and the best-fitting theoretical source spectra to the inverted source spectra for four typical earthquakes representing four magnitude levels (right-hand panel). shows some examples of the best-fitting theoretical source spectra. Then, the seismic moment and corner frequency were used to determine the stress drop and the source radius r according to the Brune (1970) source model: 2.34β r = (9) 2π f 7M −13 σ = × 10 (10) 16r We also calculated the S-wave energy E in the frequency range from 0.01 to 30 Hz according to the relationship proposed by Vassiliou & Kanamori (1982): +∞ 2 1 1 M E = + 2π f d f (11) 5 5 2 15πρ α 10πρ β ( ) s s −∞ 1+ 1+ f / f s s c −1 where α = 6.1 km s represents the primary (P) wave velocity. The apparent stress σ was calculated by the following relationship: s a μE σ = (12) 10 −2 where μ = 3.5 × 10 Nm represents the rigidity modulus. All of these source parameters for earthquakes considered in this study are shown in Table 2. Seismic moment M and corner frequency f 0 c The M values determined in this study are in good agreement with those derived from the Global CMT catalogue, although they are slightly higher than measurements provided by Zheng et al.(2009), as shown in Fig. 8(a). We obtained the relationship between M and M measured w s by CENC by a least-squares regression analysis: M = (0.817 ± 0.024) M + (0.650 ± 0.111) (13) w s There are linear deviations between M and M measured by CENC. M is systematically lower than M for M = 3.5–6.5. This w s w s s overestimation of M is more severe in the case of larger earthquakes with the maximum close to 0.5. In fact, such phenomena have been commonly found in other studies, such as in the 2013 April 20 Lushan earthquake sequence (Lyu et al. 2013), large numbers of small-to- moderate earthquakes in mainland China (Zhao et al. 2011), some small earthquakes in the Tangshan area (Matsunami et al. 2003), and earthquakes with magnitude greater than 4.0 in the Sichuan–Yunnan region of China (Xu et al. 2010a). This deviation may result from the inaccurate calibration functions and the neglect of the base correction in the process of measuring magnitude by CENC (Zhao et al. 2011). Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 880 H. Wang, Y. Ren and R. Wen Table 2. List of source parameters including moment magnitude (M ), seismic moment (M ), corner frequency (f ), source radius (r), stress drop ( σ), w 0 c S-wave energy (E ) and apparent stress (σ ) determined in this study. s a ∗ 14 11 Earthquake M † M f (Hz) M (× 10 N·m) r (m) σ (MPa) E (× 10 J) σ (MPa) s w c 0 s a 08 051 214 4315 6.3 5.41 0.275 1462.177 4867.92 0.555 21.224 0.435 08 051 214 5417 5.8 5.68 0.114 3715.352 11 772.07 0.100 9.756 0.079 08 051 215 0134 5.5 5.37 0.333 1273.503 4029.34 0.852 28.319 0.667 08 051 215 1345 4.7 4.33 0.849 35.075 1579.38 0.390 0.349 0.298 08 051 215 3442 5.8 4.87 0.429 226.464 3122.31 0.325 1.917 0.254 08 051 215 4416 4.6 4.27 0.917 28.510 1461.39 0.400 0.290 0.305 08 051 215 4533 4.7 4.46 0.534 54.954 2510.81 0.152 0.216 0.118 08 051 215 5821 4.3 3.84 1.617 6.457 828.98 0.496 0.079 0.367 08 051 216 0258 4.7 4.05 1.204 13.335 1113.68 0.422 0.142 0.318 08 051 216 0806 4.3 4.17 1.218 20.184 1100.86 0.662 0.336 0.499 08 051 216 1057 5.5 4.86 0.403 218.776 3328.92 0.259 1.478 0.203 08 051 216 2140 5.5 4.99 0.462 342.768 2901.62 0.614 5.463 0.478 08 051 216 2612 5.1 4.97 0.388 319.890 3456.09 0.339 2.825 0.265 08 051 216 4030 4.2 3.92 1.544 8.511 868.36 0.569 0.120 0.422 08 051 216 5039 4.8 4.52 0.713 67.608 1880.37 0.445 0.772 0.343 08 051 217 0659 5.2 4.74 0.446 144.544 3005.29 0.233 0.875 0.182 08 051 217 3115 5.2 4.88 0.386 234.423 3472.56 0.245 1.496 0.191 08 051 217 4224 5.3 5.10 0.382 501.187 3509.10 0.507 6.626 0.397 08 051 217 4457 4.2 3.85 2.386 6.683 561.80 1.649 0.262 1.178 08 051 217 4746 4.4 4.01 1.899 11.614 706.04 1.444 0.408 1.055 08 051 218 1915 4.0 3.53 2.904 2.213 461.74 0.984 0.051 0.686 08 051 218 2339 5.0 4.44 0.865 51.286 1550.34 0.602 0.788 0.461 08 051 218 4312 4.6 4.10 0.852 15.849 1573.14 0.178 0.072 0.136 08 051 218 5922 4.1 3.88 1.615 7.413 830.33 0.567 0.104 0.419 08 051 219 1101 6.3 5.82 0.137 6025.596 9790.57 0.281 44.566 0.222 08 051 219 3320 5.0 4.47 0.769 56.885 1744.21 0.469 0.684 0.360 08 051 220 1159 4.3 4.15 1.083 18.836 1237.99 0.434 0.207 0.329 08 051 220 1348 4.3 4.12 1.686 16.982 795.08 1.478 0.617 1.091 08 051 220 1540 4.9 4.60 0.645 89.125 2078.93 0.434 0.996 0.335 08 051 220 2958 4.6 4.21 0.869 23.174 1543.31 0.276 0.163 0.211 08 051 220 3855 4.2 3.83 1.768 6.237 758.20 0.626 0.096 0.460 08 051 221 4053 5.2 4.78 0.421 165.959 3184.61 0.225 0.970 0.175 08 051 222 1024 4.6 4.22 1.032 23.988 1299.60 0.478 0.290 0.363 08 051 222 1527 4.6 4.57 0.679 80.353 1975.16 0.456 0.943 0.352 08 051 222 4606 5.1 5.27 0.343 901.571 3913.37 0.658 15.486 0.515 08 051 223 0530 5.2 4.94 0.357 288.403 3755.63 0.238 1.792 0.186 08 051 223 0536 5.1 4.91 0.396 260.016 3382.50 0.294 1.990 0.230 08 051 223 1658 4.6 4.19 1.063 21.627 1261.10 0.472 0.258 0.358 08 051 223 2852 5.1 4.87 0.339 226.464 3950.27 0.161 0.950 0.126 08 051 223 5212 3.7 3.85 1.496 6.683 895.92 0.407 0.067 0.303 08 051 301 0311 4.6 4.45 0.959 53.088 1397.53 0.851 1.148 0.649 08 051 301 2906 4.9 4.42 0.996 47.863 1346.31 0.858 1.042 0.653 08 051 301 5432 5.1 5.06 0.313 436.516 4289.76 0.242 2.760 0.190 08 051 302 2617 4.1 3.91 1.164 8.222 1151.85 0.235 0.049 0.178 08 051 304 0849 5.8 5.39 0.309 1364.583 4338.34 0.731 26.077 0.573 08 051 304 4531 5.2 5.12 0.247 537.032 5427.58 0.147 2.068 0.116 08 051 304 4855 4.1 3.79 2.023 5.433 662.59 0.817 0.107 0.594 08 051 304 5127 4.7 4.56 0.844 77.625 1589.44 0.846 1.677 0.648 08 051 305 0813 4.5 4.08 1.399 14.791 958.60 0.735 0.271 0.549 08 051 307 4618 5.4 5.09 0.315 484.172 4260.99 0.274 3.464 0.215 08 051 307 5446 5.2 4.95 0.364 298.538 3683.91 0.261 2.034 0.204 08 051 308 2217 4.4 4.06 1.025 13.804 1307.56 0.270 0.094 0.205 08 051 309 0759 3.8 3.65 3.029 3.350 442.63 1.690 0.131 1.171 08 051 310 1516 4.3 4.05 1.484 13.335 903.53 0.791 0.262 0.589 08 051 310 3338 4.3 3.97 1.826 10.116 734.38 1.117 0.276 0.819 08 051 311 0954 4.0 3.50 3.051 1.995 439.41 1.029 0.047 0.712 08 051 314 3819 4.2 4.08 1.189 14.791 1127.96 0.451 0.168 0.340 08 051 314 3951 4.2 3.92 1.304 8.511 1028.18 0.343 0.073 0.257 08 051 315 0708 6.1 5.59 0.186 2722.701 7195.41 0.320 22.874 0.252 08 051 315 1916 5.1 4.87 0.449 226.464 2983.36 0.373 2.195 0.291 08 051 315 5303 4.7 4.51 0.998 65.313 1343.38 1.179 1.952 0.897 08 051 316 2052 4.8 4.56 0.824 77.625 1628.04 0.787 1.561 0.603 08 051 318 3642 4.3 4.18 1.370 20.893 978.29 0.976 0.509 0.731 08 051 323 3038 3.8 3.94 2.084 9.120 643.25 1.499 0.330 1.086 08 051 401 0126 3.7 3.61 1.895 2.917 707.68 0.360 0.026 0.263 08 051 409 0920 4.2 4.03 1.301 12.445 1030.37 0.498 0.155 0.374 08 051 409 5641 4.4 4.13 1.548 17.579 865.86 1.185 0.515 0.880 Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 881 Table 2. (Continued.) ∗ 14 11 Earthquake M † M f (Hz) M (× 10 N·m) r (m) σ (MPa) E (× 10 J) σ (MPa) s w c 0 s a 08 051 410 5437 5.8 5.45 0.178 1678.804 7514.41 0.173 7.638 0.136 08 051 411 0748 4.3 3.99 1.587 10.839 844.78 0.787 0.211 0.583 08 051 413 5457 4.7 4.66 0.609 109.648 2203.14 0.449 1.269 0.347 08 051 415 3217 3.9 3.77 1.557 5.070 861.19 0.347 0.044 0.258 08 051 417 2643 5.1 5.01 0.396 367.282 3382.93 0.415 3.969 0.324 08 051 505 0106 4.8 4.65 0.613 105.925 2187.79 0.443 1.209 0.342 08 051 510 0523 3.8 3.92 1.084 8.511 1236.86 0.197 0.042 0.149 08 051 520 1024 4.2 4.17 1.168 20.184 1147.99 0.584 0.297 0.441 08 051 605 5547 4.5 4.26 1.574 27.542 851.73 1.950 1.328 1.446 08 051 611 3426 4.9 4.52 0.803 67.608 1669.62 0.636 1.099 0.488 08 051 613 2547 5.9 5.39 0.269 1364.583 4983.35 0.482 17.235 0.379 08 051 801 0824 6.1 5.88 0.170 7413.102 7864.85 0.667 129.940 0.526 08 051 912 0856 4.6 4.38 1.069 41.687 1254.49 0.924 0.974 0.701 08 052 001 5233 5.0 4.76 0.608 154.882 2203.43 0.633 2.531 0.490 08 052 123 2954 4.3 4.22 1.242 23.988 1079.80 0.834 0.502 0.627 08 052 400 3546 4.0 4.01 1.339 11.614 1001.34 0.506 0.147 0.379 08 052 401 5332 3.9 4.03 1.471 12.445 911.31 0.719 0.222 0.536 08 052 516 2147 6.4 5.92 0.236 8511.380 5671.41 2.041 455.520 1.606 08 052 704 4201 3.5 3.58 1.838 2.630 729.49 0.296 0.019 0.217 08 052 716 0322 5.3 5.25 0.347 841.395 3865.42 0.637 13.993 0.499 08 052 716 1206 3.7 3.72 2.188 4.266 612.85 0.811 0.083 0.585 08 052 716 3751 5.7 5.41 0.395 1462.177 3390.63 1.641 62.484 1.282 08 052 721 5934 4.7 4.83 0.333 197.242 4025.71 0.132 0.681 0.104 08 052 801 3510 4.7 4.69 0.816 121.619 1642.96 1.200 3.731 0.920 08 052 912 4845 4.5 4.31 1.031 32.734 1299.85 0.652 0.541 0.495 08 053 114 2242 4.3 4.09 1.540 15.311 870.38 1.016 0.385 0.754 08 060 311 0928 4.6 4.67 0.524 113.501 2557.02 0.297 0.873 0.231 08 060 501 2643 4.2 4.20 0.926 22.387 1448.04 0.323 0.184 0.246 08 060 512 4106 4.8 4.66 0.639 109.648 2099.63 0.518 1.464 0.401 08 060 714 2832 4.2 4.08 1.589 14.791 843.95 1.077 0.393 0.798 08 060 806 1428 4.7 4.59 0.629 86.099 2129.89 0.390 0.865 0.301 08 060 906 5536 3.2 3.74 1.103 4.571 1215.62 0.111 0.013 0.084 08 061 010 1504 3.6 3.68 2.249 3.715 596.16 0.767 0.068 0.552 08 061 100 2728 4.0 4.18 1.290 20.893 1038.94 0.815 0.426 0.612 08 061 713 5142 4.3 4.18 1.100 20.893 1218.32 0.505 0.267 0.383 08 061 721 4044 4.1 4.08 1.409 14.791 951.80 0.750 0.276 0.561 08 061 918 2559 4.4 4.32 1.095 33.884 1224.26 0.808 0.691 0.612 08 062 112 0303 3.9 4.06 1.105 13.804 1212.93 0.338 0.118 0.256 08 062 218 3734 4.2 4.06 1.385 13.804 967.78 0.666 0.229 0.498 08 062 305 3831 4.0 4.00 1.478 11.220 907.15 0.658 0.183 0.490 08 062 805 4210 4.5 4.32 1.045 33.884 1282.83 0.702 0.602 0.533 08 062 907 5519 4.2 4.05 1.164 13.335 1151.95 0.382 0.128 0.288 08 071 706 2053 3.6 4.03 0.761 12.445 1761.33 0.100 0.032 0.077 08 072 401 3018 3.9 3.77 1.607 5.070 834.39 0.382 0.048 0.283 08 072 403 5443 5.7 5.61 0.223 2917.427 6000.10 0.591 45.221 0.465 08 072 413 3009 4.9 4.81 0.410 184.077 3269.25 0.230 1.104 0.180 08 072 415 0928 6.0 5.83 0.186 6237.348 7214.77 0.727 119.080 0.573 08 080 116 3242 6.2 5.70 0.241 3981.072 5556.24 1.015 105.960 0.798 08 080 202 1217 5.0 4.66 0.719 109.648 1865.87 0.738 2.079 0.569 08 080 221 2546 4.0 4.13 1.098 17.579 1220.59 0.423 0.188 0.320 08 080 517 4916 6.5 6.12 0.109 16 982.437 12 342.09 0.395 176.920 0.313 08 080 611 4227 4.2 4.19 1.183 21.627 1133.19 0.650 0.354 0.491 08 080 612 4706 4.3 4.22 1.172 23.988 1144.31 0.700 0.423 0.529 08 080 716 1534 5.0 4.66 0.809 109.648 1658.18 1.052 2.951 0.807 08 080 920 1020 3.9 4.05 0.894 13.335 1499.91 0.173 0.059 0.132 08 081 305 0321 4.5 4.42 1.146 47.863 1170.07 1.307 1.577 0.988 08 081 316 4543 3.8 3.89 1.634 7.674 820.35 0.608 0.115 0.450 08 083 115 2451 3.6 3.83 2.188 6.237 612.68 1.187 0.178 0.855 110 323 080 308 3.9 3.74 2.113 4.571 634.54 0.783 0.086 0.566 110 506 184 815 4.1 3.70 1.973 3.981 679.53 0.555 0.054 0.404 110 507 082 112 3.9 3.71 2.340 4.121 572.89 0.959 0.094 0.686 110 605 132 145 4.2 4.00 1.258 11.220 1065.80 0.405 0.114 0.305 110 904 121 345 4.2 3.97 1.606 10.116 835.01 0.760 0.190 0.563 111 101 055 815 5.2 4.99 0.592 342.768 2264.50 1.291 11.428 1.000 111 226 004 652 4.7 4.44 0.875 51.286 1532.62 0.623 0.815 0.477 The earthquake number is composed of the data and time of this earthquake, for example, 08 051 214 4315 represent a earthquake occurred on 2008 May 12 at 14:43:15 (Beijing time). We ignore the deviation between the surface wave magnitude M and the local magnitude M measured by CENC. M is used to uniformly represent the M s L s s and M . L Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 882 H. Wang, Y. Ren and R. Wen Figure 8. (a) Moment magnitude M derived from this study versus M measured by CENC. The solid line represents the best least-squares fit. The dashed– w s dotted lines represent the relationship of M = M ,and M = M − 0.5. The triangles and crosses represent the M values determined by Global CMT and w s w s w Zheng et al.(2009), respectively. (b) Seismic moment M versus corner frequency f . The dashed lines represent the relationship between M and f for various 0 c 0 c constant stress drops as indicated on the top of each line. The triangles, crosses and stars represent the relation of M versus f derived from Ameri et al.(2011), 0 c Hassani et al.(2011)and Sivaram et al.(2013), respectively. Figure 9. (a) The distribution of stress drops and the fitted lognormal distribution (red line). (b) The stress drop versus the moment magnitude (left) and the hypocentre depth (right). The dashed lines represent the logarithmic average of the stress drop of aftershocks that occurred at the northeastern, southwestern and central fault segments, respectively. The solid line represents the logarithmic average of the stress drop over all aftershocks. Fig. 8(b) shows the plots of seismic moment versus corner frequency for the earthquakes considered in this study. These are also 14 18 compared with the constant stress drop relations corresponding to 0.1, 1 and 10 MPa. The M and f vary from 2.0 × 10 to 1.7 × 10 0 c N · m and from 0.1 to 3.1 Hz, respectively. Corner frequencies in our study are significantly lower than those obtained in the 2009 L’Aquila earthquake sequence (Ameri et al. 2011) and earthquakes in central-eastern Iran (Hassani et al. 2011), which implies the lower stress drop. Some much smaller earthquakes in Kumaon Himalaya, India also provide a similar distribution of M versus f with a low stress drop (Sivaram 0 c −3 et al. 2013). The seismic moment is approximately inversely proportional to the cube of the corner frequency in this study, that is, M ∝ f , 0 c and the data regression yields: log M = (15.459 ± 0.278) − 3.0log f (14) 0 c 3 15 −3 M f is equal to 2.87 × 10 N · m · s , which corresponds to a constant stress drop of 0.522 MPa according to the Brune (1970) model. 0 c Stress drop The stress drop values mainly vary from 0.1 to 1.0 MPa (Fig. 9), which are consistent with the results (≤1.0 MPa) given by Hua et al.(2009) for most of the Wenchuan aftershocks. They do not exhibit a significant dependence on the moment magnitude and hypocentre depth (Fig. 9), which indicates that the earthquakes considered in this study follow self-similarity with a constant stress drop. Studies from Allmann & Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 883 Shearer (2009), Oth et al.(2010), Zhao et al.(2011), etc. all confirmed the self-similarity of global earthquakes. However, some other studies obtained conflicting results, in which the self-similarity is broken down in some specific earthquake sequences (e.g. Tusa et al. 2006; Drouet et al. 2010; Mandal & Dutta 2011; Pacor et al. 2016). The stress drops are nearly lognormal distributed with a logarithmic mean of 0.52 MPa, which is dramatically lower than the median value of 3.31 MPa for interplate earthquakes (Allmann & Shearer 2009). The Wenchuan aftershocks have small stress drop values in comparison to other large earthquake sequences, such as the 2010–2011 Canterbury, New Zealand earthquake sequence with stress release of 1–20 MPa (Oth & Kaiser. 2014), the 1983 M 7.7 Japan sea earthquake sequence with stress release of 1–30 MPa (Iwate & Irikura 1988), etc. They JMA are also much smaller than the value of the main shock, which is approximately 1–3 MPa for different finite fault-slip models (Bjerrum et al. 2010). However, the Wenchuan main shock has a stress drop value similar to other earthquakes of the same magnitude, for example, the 2001 M 7.8 Kunlun, China earthquake and the 2002 M 7.7 Denali, Alaska earthquake (Shaw 2013). Therefore, the Wenchuan aftershocks are w w characterized by obvious low values of stress drop. This characteristic was also observed in some other earthquakes, such as the 2010 JiaSian, Taiwan earthquake (Hwang 2012), and for several smaller earthquakes in the Garhwal Himalaya region (Sharma & Wason 1994). Shaw et al.(2015) proposed a physical model that shows reduced stress drops for nearby aftershocks compared to similar magnitude main shocks, because they rerupture part of the fault ruptured by the main shock which may have been partially healed. This model was supported by ground motion observations, showing smaller ground motions generated by nearby aftershocks (e.g. Abrahamson et al. 2014). Smaller values of aftershock stress drops have been also observed using corner frequency analysis of seismic sequences (e.g. Drouet et al. 2011). In this study, an indicator ε proposed by Zuniga (1993) was used to investigate the stress drop mechanism of the Wenchuan earthquake sequence: ε = (15) σ + ε< 1.0 implies a partial stress drop mechanism where the final stress is greater than the dynamic frictional stress (Brune 1970; Brune et al. 1986), whereas ε> 1.0 indicates that frictional overshoot has occurred with the final stress lower than the dynamic frictional stress (Savage & Wood 1971). The well-known Orowan’s hypothesis is met when ε = 1.0 (Orowan 1960). In this study, ε equals 0.75–0.85, which indicates that the Wenchuan aftershocks can be interpreted by the partial stress drop mechanism. Sharma & Wason (1994) pointed out that such kind of aftershocks occur either when the fault locks (heals) itself soon after the rupture of the main shock passes, so the average dynamic frictional stress drops over the whole fault, or when the stress release is not uniform and not coherent over the whole fault plane, and behaves like a series of multiple events with parts of the fault remaining locked. The blank area of the seismic moment release in the ruptured area during the Wenchuan earthquake, as well as the absence of the larger aftershocks, indicates a possibility of fault lock at the unruptured areas on the fault plane (Chen et al. 2013). The low stress drop may be related to parts of the fault remaining locked on the fault plane. The apparent stress of M ≥ 3.0 earthquakes during 2000–2004 in the Sichuan province calculated by Cheng et al.(2006) is approximately proportional to 0.21 σ. This means that ε equals 1.4 (eq. 15), indicating frictional overshoot prevails over partial stress drop. The stress drop mechanism associated with earthquakes along the Longmenshan fault belt changed after the Wenchuan earthquake. The stress drop spatial distribution was obtained by assembling and interpolating the values of all 132 aftershocks, compared with the slip distribution on the fault plane of the main shock, which was determined by Fielding et al.(2013), as shown in Fig. 10. Aftershocks were mainly concentrated on the southwest and northeast segments of the Beichuan fault, and less on the central part. Stress drop contours were generated in three segments from southwest to northeast, respectively. The higher slips emerged on the southwestern segment close to Wenchuan County. In the main shock, the Pengguan Massif began to rupture, and a large amount of stress was released on this segment (Chen et al. 2009). As a result, smaller stress releases occurred for aftershocks here, with a logarithmic average of stress drop of 0.46 MPa. However, the logarithmic average of stress drop is higher, approximately 0.64 MPa for the northeastern segment near the Qingchuan County. This segment also consists of Precambrian quartzite or other stiff geological bodies. Slip on this segment is relatively smaller, and the released stress is lower. The logarithmic average of the stress drop on the central segment is close to 0.52 MPa, and the median slip value corresponds to the median stress drop. Therefore, we infer that the stress drop of the aftershocks may be related to the slip distribution on the fault plane of the main shock. Higher stress release for aftershocks occurred in areas with lower slip in the main shock. For further verifying the above inference, we investigated the magnitude and hypocentre depth distribution between northeastern and southwestern segments, as shown in Fig. 9. The results show that both segments have a homogeneous distribution of magnitude ranging from 3.5 to 6.0, and a homogeneous distribution of depth ranging from 8 to 25 km. Furthermore, the stiffness of crustal structure shows few changes over the whole ruptured area of the Wenchuan main shock according to the CRUST1.0 model (Laske et al. 2013). Therefore, the magnitude, hypocentre depth and crust stiffness could be excluded from the cause of inhomogeneous distribution of stress drop between two segments. Radiated energy and apparent stress Fig. 11 shows the S-wave energy E versus M . The relation between E and M was obtained assuming E ∝ M : s 0 s 0 s 0 logE = (−4.88 ± 0.27) + logM (16) s 0 Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 884 H. Wang, Y. Ren and R. Wen Figure 10. Slip distribution on the fault plane of the Wenchuan main shock determined by Fielding et al.(2013) and the stress drop contours for aftershocks employed in this study. The cross represents the epicentre of the aftershocks. In order to clearly compare the slip distribution and the stress drop of the aftershocks, the panel of the slip distribution is parallel moved upward. Figure 11. S-wave energy E versus seismic moment M . The regression line (solid) corresponding to constant apparent stress is shown within one standard s 0 deviation range (shaded area). −5 This relationship means that the S-wave energy-to-moment ratio is approximately equals to 1.32 × 10 , which is consistent with the −5 result of 1.2 × 10 for small earthquakes in Anchorage, Alaska derived by Dutta et al.(2003). As shown in Table 2, the apparent stress σ varies from 0.077 to 1.606 MPa, which is directly proportional to 0.74 σ with a correlation coefficient of 0.998. The apparent stress is independent of the earthquake size, since σ is independent of M , as mentioned above. ATTENUATION CHARACTERISTICS The attenuation curve A(f, R) can be described in terms of anelastic attenuation and other factors ( ) related to seismic attenuation: π f lnA ( f, R) − ln =− (R − R ) (17) Q ( f ) β s s Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 885 Figure 12. Geometrical spreading exponents (n) at frequencies ranging from 0.1 to 20 Hz. The solid and dashed lines represent the average n and one standard deviation range, respectively. where Q stands for the S-wave quality factor dependent on the frequency. must be greater than A(f, R). Suppose only contains the geometrical spreading in this study. In general, the geometrical spreading can be a linear, hinged bilinear, or hinged trilinear model of R.In this study, geometrical spreading is a simple model expressed as (R /R) ,where n is the geometrical spreading exponent. The greater the n value is, the stronger the geometrical spreading. According to the necessary condition of lnA(f,R) − ln(R /R) < 0, we seek out a maximum n to meet this condition for each frequency, indicating the strongest geometrical spreading. Then Q can be evaluated from the slope of a linear least-squares fit of eq. (17) at each frequency. In this study, both geometrical spreading and anelastic attenuation were considered frequency dependent in order to deal with the trade-off between them. This strategy was also used in the study of Bindi et al.(2004). The geometrical spreading exponents at frequencies of 0.5–20 Hz for R = 30–150 km are shown in Fig. 12. The values of n vary from 0.35 to 0.75, increasing with increased frequency from 0.1 to 0.4 Hz at first, then overall decreasing until a critical frequencyaround 3.5 Hz, and finally increasing up to 20 Hz, which indicates frequency-dependent geometrical spreading in this region. Frequency-dependent geometrical spreading was also observed in North America by Babaie Mahani & Atkinson (2013) through studying response spectral amplitudes and PGAs of ground motions. Geometrical spreading in the Northeast, central United States (CUS), and the Pacific Northwest/southwestern British Columbia (PNW/BC) has a tendency to decrease at first and then increase with the increased frequency, which is very similar to what we observed in this study. Based on the analyses of larger numbers of strong-motions recordings, previous studies have shown that n is not lower than 1.0 for local distances, while n is approximately equal to 0.5 for regional distances (Atkinson & Mereu 1992;Bora et al. 2015). The threshold for local and regional distance is related to the crustal thickness. Our study region is located at the southeast margin of the Tibetan Plateau where the crustal thickness is about 50 km. Therefore, we regard 75 km (i.e. 1.5 times of crustal thickness) as the boundary between the local 1.0 0.5 and regional distances (Atkinson & Mereu 1992). A general geometrical spreading model (R /R) for R < 75 km, and (R /75)(75/R) for 0 0 R ≥ 75 km is assumed. In this study, n is lower than 0.5 at frequencies ranging from 3 to 15 Hz, and 0.5–0.75 at frequencies lower than 3 Hz and greater than 15 Hz (Fig. 12). The average n value is 0.57 with a standard deviation of 0.11, obtained over frequencies ranging from 0.57 0.1 to 20 Hz. We compared the average geometrical spreading (R /R) with the general geometrical spreading mentioned above, as shown in Fig. 13. We also compared the geometrical spreading in Yunnan and southern Sichuan determined by Xu et al.(2010b), which reflects a weak attenuation of ground motion. The average geometrical spreading in this study is slightly stronger than the one given by Xu et al. (2010b), while much weaker than the general geometrical spreading. This result implies that regions near the ruptured fault of the Wenchuan earthquake show weak geometrical spreading. Boore et al.(2014) determined that the observed ground motions from China, mainly derived from the Wenchuan earthquake sequence, exhibit a weaker attenuation, which is ascribed to a ‘high Q’. This may also be related to the weak geometrical spreading inferred from our study. As shown in eq. (17), the path attenuation mainly consists of geometricalspreading and anelastic attenuation (represented by Q), a potential trade-off is inherent between them. The S-wave quality factor Q versus frequency from 0.1 to 20 Hz is shown in Fig. 14. Q (f)isregressedintheform of Q f , and the s s s0 1.06 least-squares solution is given by 151.2f . Other studies also provided the Q values for the adjacent region (Fig. 14). Hua et al.(2009) 0.423 0.836 obtained the Q for the western mountains (274.6f ) and eastern plains (206.7f ) in northern Sichuan, separated by the Longmenshan 0.59 fault belt. Zhao et al. (2011) also determined Q = 191.8f for western Sichuan. Compared with results from Hua et al.(2009)and Zhao et al. (2011), Q , representing the quality factor at 1.0 Hz, is lower in our study. However, the attenuation coefficient η is much greater than s0 that at the mountains but close to that at the plains. Q is closer to the results for the plains from Hua et al.(2009). The study region in this s Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 886 H. Wang, Y. Ren and R. Wen Figure 13. Comparison of the average geometrical spreading derived in this study with the general geometrical spreading, and results from Xu et al.(2010b). 0.57 The averaged results of this study represent (R /R) over the hypocentre distance from 30 to 150 km. Two dashed lines represent the plus or minus one 1.0 0.5 standard deviation of the average. The general results represent (R /R) for R < 75 km and (R /75)(75/R) for R ≥ 75 km. 0 0 paper is located on both sides of the Longmenshan fault belt, where the elevation suddenly drops from about 4500 m on the plateau to 500 m in the Sichuan Basin. The low Q and high η may be related to the propagation path passing through the highly heterogeneous active fault s0 belt. SITE RESPONSE The calculated site response functions of the 43 strong-motion stations are shown in Fig. 15. Site responses for most stations are generally in good agreement with those determined by Ren et al.(2013). Compared with the site responses derived from the horizontal-to-vertical spectral ratio (HVSR) method (Fig. 15), predominant frequencies are approximately identical, while site amplifications from the non-parametric GIT are significantly higher, except for some stations (51SFB, 51SPA, 51QLY and L0021). That is because the HVSR method can approximately evaluate the predominant site frequency but underestimates the site amplification (Castro et al. 2004; Hassani et al. 2011). Since many analyses related to site effects in the Wenchuan earthquake sequence have been made in the study of Ren et al.(2013), our study only focused on the performance of a terrain effect array in the Wenchuan aftershocks. Stations L2009, L2002 and L2007 compose a terrain effect array, which were installed on the top (altitude 969 m), middle (altitude 960 m) and foot (altitude 927 m) of a hill (Wen et al. 2014). Fig. 16(a) shows the locations of the three stations on the hill, which share similar geological conditions. The site response functions of the three stations determined by the non-parametric GIT and HVSR method are shown in Fig. 16(b). Site responses from non-parametric GIT have significant discrepancies among the three stations, especially at frequencies of 2.0–8.0 Hz. Site amplification increases with the Figure 14. Frequency-dependent S-wave quality factor Q derived from this study. The solid line represents the least-squares regression of this study in the 1.06 0.423 frequency range 0.1–20 Hz, that is, Q (f) = 151.2f . The dotted line and the dashed–dotted line represent Q (f) = 274.6f for the western mountains and s s 0.836 0.56 Q (f) = 206.7f for the eastern plains in the northern Sichuan from the study of Hua et al.(2009). The dashed line represents Q (f) = 191.8f for western s s Sichuan from Zhao et al.(2011). Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 887 Figure 15. Site response functions derived from the non-parametric GIT, HVSR method and Ren et al.(2013). The locations of these stations are clearly shown in Fig. 2. Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 888 H. Wang, Y. Ren and R. Wen Figure 16. (a) Location illustration of the terrain effect array; (b) site response functions determined by the non-parametric GIT (black) and HVSR method (red). increased elevation and is 1.5–2.0 times larger at L2009 than that at L2007. The site amplifications given by the HVSR method have no significant difference at the three stations, implying the HVSR method may not effectively reflect the local terrain effect. This result is in agreement with the conclusion from other studies (Parolai et al. 2004; Massa et al. 2013). CONCLUSIONS Nine hundred twenty-eight strong-motion recordings with hypocentre distances smaller than 150 km were used for separating the source spectra, path attenuation and site responses in the frequency domain using the two-step non-parametric GIT. These recordings were obtained at 43 permanent and temporary strong-motion stations during 132 earthquakes of M 3.2–6.5, which occurred on or near the fault plane of the 2008 Wenchuan earthquake from 2008 May 12 to 2013 December 31. We assumed that the path attenuation equals 1.0 at the reference distance of 30 km. As a result, the cumulative attenuation within this distance is transferred to the inverted source spectra when the trade-off between the source effect and site response is solved using a reference site. The cumulative attenuation was supposed as a ratio of the inverted source spectrum over the theoretical source spectrum for an M 6.5 earthquake. Its theoretical source spectrum was determined using the Fourier amplitude spectral ratio method. Then the inverted source spectra of all 132 earthquakes were corrected by the cumulative attenuation to obtain the real source spectra, which show approximately −2 close to ω decay at high frequencies. Furthermore, a grid-searching method was used to determine the best-fit seismic moment and corner frequency. Moreover, the stress drop, source radius, S-wave energy and apparent stress were successively calculated. We investigated the scaling properties of these source parameters, and draw the following conclusions: (1) Moment magnitude M has a linear deviation from the surface wave magnitude M measured by CENC. M is generally lower than w s w −3 3 15 −3 M , and is in agreement with previous studies. M is approximately proportional to the f ,and M f = 2.87 × 10 N · m · s . The average s 0 c 0 c −5 S-wave energy-to-moment ratio is close to 1.32 × 10 . The apparent stress σ is approximately equal to 0.74 σ, independent of the earthquake size. (2) The value of stress drop σ for individual earthquakes varies mainly from 0.1 to 1.0 MPa, following an approximately lognor- mal distribution with an average of 0.52 MPa. The value is significantly smaller than the median stress drop of interplate earthquakes (Allmann & Shearer 2009), and some other large earthquake sequences. It is also much smaller than the stress drop of the Wenchuan main shock which is similar to some other large earthquakes with similar magnitude (∼8.0). This characteristic with low stress drop of Wenchuan aftershocks was investigated using the ε indicator. The results show that ε is less than 1.0, ranging from 0.75 to 0.85, indicating that the low stress drop may be interpreted by the partial stress drop mechanism. Explanations of the low stress drop in aftershocks may be related to the remaining locked parts on the fault plane of the main shock. (3) The investigation shows that the stress drop σ has no significant dependence on the earthquake size and the hypocentre depth, indicating that the Wenchuan aftershocks follow self-similarity over the M range of our data. The stress drop of aftershocks may be correlated to the slip distribution on the fault plane of the Wenchuan main shock. A relatively larger stress drop appeared at areas with relatively smaller slip. The geometrical spreading is weak around the Wenchuan area within distances of R = 30–150 km, and is strongly dependent on the 1.06 frequency. The S-wave quality factor Q (f) is regressed by Q (f) = 151.2f . The quality factor shows strong dependence on frequency, which s s can be ascribed to the high heterogeneity of the crustal medium. Our study region is located on the southeast edge of the Tibet Plateau where the elevation suddenly drops from about 4500 m on the plateau to 500 m in the Sichuan Basin. Downloaded from https://academic.oup.com/gji/article/212/2/872/4554834 by DeepDyve user on 12 July 2022 Spectral inversions in Wenchuan aftershocks 889 The inverted site responses of three stations from a terrain effect array show that the site amplification is strongest at the hilltop and smallest at the hillfoot, implying that the local topography considerably affects the ground motions. The site responses, calculated using the HVSR method, were not very different among the three stations. This suggests that the HVSR method may not be effectively used for analysing the local topography effect on ground motion. ACKNOWLEDGEMENTS This work is supported by the Science Foundation of Institute of Engineering Mechanics, China Earthquake Administration under grant no. 2016A04, Nonprofit Industry Research Project of China Earthquake Administration under grant no. 201508005 and National Natural Science Foundation of China under grant no. 51308515. 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