# Stochastic finite-fault simulation of the 2017 Jiuzhaigou earthquake in China

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## Abstract

## Keywords

Stochastic finite-fault model Strong ground-motion simulation Site amplification Jiuzhaigou earthquake## Introduction

On August 8, 2017 at 13:19 (local time), an earthquake with magnitude *Ms*7.0 occurred in Jiuzhaigou County of Sichuan Province at the eastern margin of the Tibetan Plateau. According to the China Earthquake Networks Center (CENC 2017), the epicenter was located at 33.20°N, 103.82°E and had a focal depth of 20 km. This powerful earthquake significantly impacted society and the natural environment. It was reported that the earthquake caused 25 deaths and injured more than 500 people. The seismic intensity from the field survey in the magistoseismic area reached IX, and the affected area with seismic intensity greater than VI was approximately 18,295 km^{2}.

The Jiuzhaigou earthquake was located in the region between the eastern Kunlun fault system and the Longmen Shan fault system. This region is tectonically complex with high seismicity, which is related to the extrusion of the Indian Plate to the Eurasian Plate. The seismogenic fault for the Jiuzhaigou earthquake was associated with a blind fault not shown on the Chinese active fault map (Han et al. 2018). The epicenter was close to the Minjiang, Tazang and Huya faults (Han et al. 2018). Based on the CAP waveform inversion method, Yi et al. (2017) gave the focal mechanism solution to this earthquake. The strikes, dips and rakes of the two nodal planes of the focal mechanism are 156°/79°/− 9° and 248°/81°/− 169°, which are similar to the results from the global centroid moment tensor and USGS solutions. According to the focal mechanism solutions and the spatial distribution of aftershocks, the seismogenic fault for the Jiuzhaigou earthquake was a left-lateral strike-slip fault and is considered to have ruptured a branch of the eastern Kunlun fault system.

The stochastic finite-fault simulation method has been widely recognized as one of the most important tools for generation of synthetic ground-motion records. This method has previously been used to simulate strong motions from several large earthquakes including the 1999 *Mw*7.6 Chi–Chi earthquake (Roumelioti and Beresnev 2003), 2008 *Mw*8.0 Wenchuan earthquake (Ghasemi et al. 2010) and 2011 *Mw*9.0 Tohoku earthquake (Ghofrani et al. 2013). Compared with deterministic and hybrid ground-motion simulation methods, the advantages of the stochastic method are its independence from small earthquake selection and good performance at high frequencies (Motazedian and Atkinson 2005).

In this study, we applied the stochastic finite-fault method proposed by Motazedian and Atkinson (2005) to simulate and analyze accelerograms and response spectra of the Jiuzhaigou earthquake. The region-specific seismic parameters including anelastic attenuation, local site effects and path effects were estimated from previous studies and empirical relationships. Once input parameters were calibrated, ground-motion characteristics such as peak ground acceleration (PGA), Fourier spectra and response spectra were estimated and compared with the observations at all 11 stations. Then, we used the model parameters to simulate the ground scenario in the study area.

## Ground-motion data

The earthquake event was recorded by 66 strong ground-motion stations operated by the China Strong Motion Networks Center (CSMNC). All of the accelerograms were recorded by digital instruments (MR2002/SLJ-100, ETNA/ES-T, and ETNA/SLJ-100). The sample rate was 200 Hz, and the preceding 20 s was prestored as the pre-event part.

_{S30}and epicentral distances. The site class was based on the surface geology reported by the CSMNC and V

_{s30}data derived from the work of Yan et al. (2016). Figure 1 shows the locations of the recording stations, as well as the projection of the fault plane and the epicenter of the earthquake. The maximum amplitudes for this earthquake were recorded at station JZB, where peak ground acceleration (PGA) was 185 cm/s

^{2}for the north–south components.

Information on the strong-motion stations used in this study

Station code | Lat (°N) | Lon (°E) | PGA (cm/s | Vs | Site class | Epicentral distance (km) | |
---|---|---|---|---|---|---|---|

EW | NS | ||||||

JZB | 33.3 | 104.1 | 129.5 | 185.0 | 323 | Soil | 30.6 |

JZY | 33.2 | 104.3 | 45.8 | 66.7 | 312 | Soil | 40.3 |

JZW | 33.0 | 104.2 | 73.8 | 91.7 | 422 | Soil | 41.0 |

SHW | 33.7 | 104.5 | 18.6 | 20.5 | – | Soil | 83.4 |

PWM | 32.6 | 104.5 | 18.6 | 20.9 | 357 | Soil | 91.8 |

DIB | 34.1 | 103.2 | 13.6 | 8.1 | – | Soil | 115.4 |

MXD | 32.0 | 103.7 | 12.2 | 23.3 | 267 | Soil | 129.7 |

MXT | 31.7 | 103.9 | 23.5 | 21.6 | – | Soil | 138.0 |

HSS | 31.9 | 103.4 | 8.6 | 6.4 | – | Soil | 149.8 |

MXN | 31.6 | 103.7 | 6.3 | 6.6 | 391 | Soil | 180.3 |

LXT | 31.6 | 103.5 | 3.4 | 3.4 | 316 | Soil | 185.6 |

## Methodology

*N*subfaults, and each subfault is considered as a point source. Each subfault is simulated using a stochastic point source method. The Fourier acceleration amplitude spectrum is a result of contributions from the earthquake source, path attenuation and site effect, and the radiation from a specific site can be defined by

*C*is the scaling factor,

*M*

_{0}is the moment and

*R*is the shortest distance from the source to the site. The \({\text{Source}}\left( {M_{0} ,f} \right)\) is the displacement source spectrum given by Brune’s omega-squared model and is presented by

*f*

_{c}is the source corner frequency represented by

*β*is the shear-wave velocity in km/s.

*G*(

*R*) is the distance-dependent geometrical spreading function, \({\text{An}}\left( {f,R} \right) = \exp \left[ { - \pi fR/Q\left( f \right)\beta } \right]\) is the anelastic whole path attenuation function, where

*Q*(

*f*) is the frequency-dependent quality factor and

*β*is the shear-wave velocity of the crust. The path effects depend on the source location due to different paths between source and site and control the attenuation characteristics of simulated ground motion.

*f*) and the upper crust attenuation factor

*V*(

*f*):

The amplification factor mainly results from the seismic impedance effect through the velocity gradient in the surface layers. There are several methods to estimate the site amplification, such as the standard spectral ratio method and the horizontal-to-vertical ratio method. The upper crust attenuation factor is a high-frequency truncation filter, commonly described as a high-cut filter, which is controlled by the *kappa* parameter. The decay parameter *kappa* represents the effect of intrinsic attenuation upon the wave field as it propagates through below the site.

*nl*and

*nw*are the numbers of subfaults along the strike and dip of the main fault, respectively, and \(\Delta t_{ij}\) is the relative delay time from the

*ij*th subfault to the site.

## Modeling parameters

Input parameters for the stochastic finite-fault model of the Jiuzhaigou earthquake

Parameters | Model | Reference |
---|---|---|

Moment magnitude ( | 6.5 | CENC |

Hypocenter location | 103.82°E, 33.20°N | CENC |

Strike and dip angle | 156°, 79° | Yi et al. (2017) |

fault length and width (km) | Model 1: 32 × 30 (1.52 × 2) Model 2: 23 × 15 (1 × 1) | Zhang et al. (2017) Leonard (2010) |

Slip distribution | Model 1: estimated by Zhang et al. (2017) Model 2: random distribution | Zhang et al. (2017) |

Stress drop (bars) | 38.5 | This study |

Shear-wave velocity (km/s) | 3.6 | Ghasemi et al. (2010) |

Density (g/cm | 2.7 | Ghasemi et al. (2010) |

Rupture velocity | 0.8 × (Shear-wave velocity) | Ghasemi et al. (2010) |

Pulsing area percentage | 50% | Ghasemi et al. (2010) |

Geometric spreading | 1/ | Ghasemi et al. (2010) |

Distance-dependent duration | 0 for | Atkinson and Boore (1995) |

Quality factor | 84.9 | Wang et al. (2017) |

Site amplification | Quarter-wavelength approximation of amplification | Yu and Li (2012) |

Kappa (s) | 0.0206 | This study |

In the present study, we used the source parameters given by CENC where the epicenter of the earthquake obtained was 33.20°N, 103.82°E and the focal depth was 20 km. The stress drop parameter was the most important parameter controlling the high-frequency spectral amplitudes and high-frequency energy content. According to the research of Wang et al. (2017), the stress drop for this earthquake was 38.5 bars. The fault dimension and slip distribution affected the high-frequency seismic radiation (Causse et al. 2010), which controlled the seismic moment of each subfault. In this study, we used two different fault models to investigate the effects of different source models on the variations in the ground-motion levels.

**Slip model 1**

**Slip model 2**

For model 2, we used the random slip model and the central starting point in order to simulate future events for which the corresponding slip distribution will be unknown. The fault plane dimension was estimated by the empirical relationship of Leonard (2010). The fault plane was divided into 23 × 15 subfaults with dimensions of 1 km × 1 km.

Path effects were defined as a combination of geometrical spreading, anelastic attenuation and ground-motion duration effects. For the anelastic attenuation, the frequency-dependent relation quality factor \(Q = 84.9f^{0.71}\) obtained from Wang et al. (2017) for the northwest Sichuan region was used in the present study. To account for the geometrical spreading, we used a bilinear model defined in Ghasemi et al. (2010) to express the geometric spreading function. The bilinear model was simply assumed to be 1/*R* for distances less than 75 km and 1/*R*^{0.5} for distances beyond 75 km. The ground-motion duration at hypocentral distance could be represented by a distance-dependent duration model obtained by Atkinson and Boore (1995).

*κ*values for horizontal and vertical components are closely related to elevation and velocity images at 0–10 km depth. In this study, the spectral decay method proposed by (Anderson and Hough 1984) was applied

*f*

_{e}represents the starting frequency of the linear trend,

*f*

_{max}denotes the ending frequency (Douglas et al. 2010) and

*R*is the epicentral distance. We estimated \(\kappa\) in the Jiuzhaigou region using data from moderate-to-large earthquakes recorded by the CSMNC during the 2008 Wenchuan and 2017 Jiuzhaigou earthquakes. The distribution of the \(\kappa\) values with the epicentral distance of the recording seismic stations is shown in Fig. 3. The best fit line to the \(\kappa\) factor for the average horizontal components versus epicentral distance was obtained as \(0.00005R + 0.0206\).

The other source parameters, namely material density, shear-wave velocity and pulsing percentage, were assigned with commonly used values according to a previous study on Wenchuan earthquake simulation (Ghasemi et al. 2010).

## Results and discussion

### Comparison of the different models

Using the model parameters listed in Table 2, we simulated the ground-motion record and compared it with the observed acceleration time series and Fourier amplitude spectra (FAS) as well as the 5%-damped pseudo-acceleration response spectra (PSA) in the EW and NS directions for all selected stations. For the FAS and 5%-damped PSA, we used the horizontal-component geometric mean of the observed ground motion to compare with the simulated record. For simulated acceleration time series, we selected the one with peak value closest to the average of ten trials.

### Spatial distribution of ground-motion intensity

From the PGA distributions of the two models, we find that the main influence area of PGA obtained from model 1 is obviously greater than that from model 2. This result is matched to the area of the fault distribution. The distribution ranges of PGA values are approximately matched with the field observations, which are extended along the northwest direction with the highest amplitudes localized around the epicentral region. The simulation results from model 1 indicate ground motions reaching acceleration levels of 387.41 cm/s^{2} in the epicentral region, and the peak value from model 2 is 368.60 cm/s^{2} in the epicentral region. The simulated maximum intensity in the epicentral area was level IX on the Chinese seismic intensity scale (GB/T 17742 2008), which was similar to the observed maximum intensity.

## Conclusions

In the current study, we simulated strong ground motions recorded for the *Ms*7.0 Jiuzhaigou earthquake based on the stochastic finite-fault method at 11 stations. We used some previous studies and empirical relationships to estimate the specific regional parameters. Based on Fourier amplitude spectra at higher frequencies, \(\kappa_{0}\) for horizontal components was calculated as 0.0206 s. Based on the slip distribution and fault dimension using the research of Zhang et al. (2017), the stochastic simulated result had no significant bias at most of the stations. Using a model with a random slip distribution, the simulated response spectra were also matched to the observed values. These results indicate that the stochastic finite-fault method is not very sensitive to the input slip distributions and fault dimensions. We used two models to simulate the ground scenario at 1116 sites. The simulated maximum intensity at the epicentral area was level IX, which was similar to the observed maximum intensity and indicates that the simulated result could be used to predict an imminent earthquake disaster.

The slip distribution plays an important role in affecting the high-frequency seismic radiation (Causse et al. 2010), and the near-field ground motion is greatly affected by the complexity of the slip distribution and rupture propagation. Perhaps the random slip distributions cause more uncertainties in the near-field ground-motion simulation. According to Beresnev et al. (1998), using the random slip models does not lead to any appreciable decrease in the accuracy of predicting the mean, nor does it increase the standard deviation compared to the actual slip distribution. Ghasemi et al. (2010) simulated the 2008 Wenchuan earthquake using two different slip models and pointed out that the quality of the simulated results decreases at longer periods without information about the slip distribution.

In the regions where real recordings are insufficient, using the stochastic finite-fault method for simulating strong ground motions is useful to understand ground-motion characteristics and distributions particularly. If we obtain enough accurate region-specific input parameters, we can reproduce realistic earthquake ground motions within the period range of engineering interest. In the field of seismic engineering, we mainly focus on the high-frequency band, especially for moderate earthquakes. For future earthquake prediction, even though we did not obtain enough information about the fault plane and slip distribution, we could still estimate the intensity of ground motion if we knew the region-specific input parameters, which could be useful in studies of GMPE and ground-motion characteristics for highly seismic areas of China and in the preparation of hazard maps for these regions.

## Notes

### Authors’ contributions

JZS analyzed the data, interpreted the results and drafted the manuscript. YXY guided the study and gave useful advice about the results. YQL took part in the design of the study. All authors read and approved the final manuscript.

### Acknowledgements

This work was supported by the National Key Research and Development Program of China (2017YFC0404901), the Special Scientific Fund Item for Non-Profit Public Industry of the Ministry of Water Resources (201501034) and the National Natural Science Foundation of China (41574051). The authors also acknowledge valuable comments and suggestions provided by anonymous reviewers.

### Competing interests

The authors declare that they have no competing interests.

### Availability of data and materials

The ground-motion data for this study are provided by the China Strong Motion Network Center at the Institute of Engineering Mechanics, China Earthquake Administration. Ground-motion data are available through the China Earthquake Data Center (http://data.earthquake.cn/index.html).

### Funding

This work is funded as Grant-in-Aid for Scientific Research by the National Key Research and Development Program of China (2017YFC0404901). This work is also supported by the Special Scientific Fund Item for Non-Profit Public Industry of the Ministry of Water Resources (201501034) and the National Natural Science Foundation of China (41574051).

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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