A modified stochastic finite-fault method for estimating strong ground motion:Validation and application

We developed a modified stochastic finite-fault method for estimating strong ground motions.An adjustment to the dynamic corner frequency was introduced,which accounted for the effect of the location of the subfault relative to the hypocenter and rupture propagation direction,to account for the influence of the rupture propagation direction on the subfault dynamic corner frequency.By comparing the peak ground acceleration(PGA),pseudo-absolute response spectra acceleration(PSA,damping ratio of 5%),and duration,the results of the modified and existing methods were compared,demonstrating that our proposed adjustment to the dynamic corner frequency can accurately reflect the rupture directivity effect.We applied our modified method to simulate near-field strong motions within 150 km of the 2008 MW7.9 Wenchuan earthquake rupture.Our modified method performed well over a broad period range,particularly at 0.04-4 s.The total deviations of the stochastic finite-fault method(EXSIM)and the modified EXSIM were 0.1676 and 0.1494,respectively.The modified method can effectively account for the influence of the rupture propagation direction and provide more realistic ground motion estimations for earthquake disaster mitigation.

Regional Finite-Fault Source Model for Development of Ground Motion Attenuation Relationship in Sichuan, China

The attenuation relationship of ground motion based on seismology has always been a front subject of engineering earthquake.Among them,the regional finite-fault source model is very important.In view of this point,the general characteristics of regional seism-tectonics,including the dip and depth of the fault plane,are emphasized.According to the statistics of regional seism-tectonics and focal mechanisms in Sichuan,China,and the sensitivity of estimated peak ground acceleration(PGA)attenuation is analyzed,and the dip angle is taken as an average of 70°.Based the statistics of the upper crustal structure and the focal depth of regional earthquakes,the bottom boundary of the sedimentary cover can be used as the upper limit for estimating the depth of upper-edge.The analysis shows that this value is sensitive to PGA.Based on the analysis of geometric relations,the corresponding calculation formula is used,and a set of concepts and steps for building the regional finite-fault source model is proposed.The estimation of source parameters takes into account the uncertainty,the geometric relationship among parameters and the total energy conservation.Meanwhile,a set of reasonable models is developed,which lay a foundation for the further study of regional ground motion attenuation based on seismology.

Improvements of corner frequency and scaling factor for stochastic finite-fault modeling

In this paper, three existing source spectral models for stochastic finite-fault modeling of ground motion were reviewed. These three models were used to calculate the far-field received energy at a site from a vertical fault and the mean spectral ratio over 15 stations of the Northridge earthquake, and then compared. From the comparison, a necessary measure was observed to maintain the far-field received energy independent of subfault size and avoid overestimation of the long- period spectra/level. Two improvements were made to one of the three models （i.e., the model based on dynamic comer frequency） as follows： （i） a new method to compute the subfault comer frequency was proposed, where the subfault comer frequency is determined based on a basic value calculated from the total seismic moment of the entire fault and an increment depending on the seismic moment assigned to the subfault; and （ii） the difference of the radiation energy from each suhfault was considered into the scaling factor. The improved model was also compared with the unimproved model through the far-field received energy and the mean spectral ratio. The comparison proves that the improved model allows the received energy to be more independent of subfault size than the unimproved model, and decreases the overestimation degree of the long-period spectral amplitude.

Ground-motion simulation for the MW6.1 Ludian earthquake on 3 August 2014 using the stochastic finite-fault method

The stochastic finite-fault simulation method was applied to synthesize the horizontal ground acceleration seismograms produced by the MW6.1 Ludian earthquake on August 3,2014.For this purpose,we produced first a total of 200 kinematic source models for the Ludian event,which are characterized by the heterogeneous slip on the conjugated ruptured fault and the slip-dependent spreading of the rupture front.The results indicated that the heterogeneous slip and the spatial extent of the ruptured fault play dominant roles in the spatial distribution of ground motions in the near-fault area.The peak ground accelerations(PGAs)and 5%-damped pseudospectral accelerations(PSAs)at periods shorter than 0.5 s estimated on the resulting synthetics generally match well with the observations at stations with Joyner-Boore distances(RJB)greater than 20 km.The synthetic PGVs and PSAs at periods of 0.5 s and 0.75 s are in good agreement with predicted medians by the Yu14 model(Yu et al.,2014).However,the synthetic results are generally much lower than the predicted medians by BSSA14 model(Boore et al.,2014).Moreover,the ground motion variability caused by the randomness in the source rupture process was evaluated by these synthetics.The standard deviations of PSAs on the base-10 logarithmic scale,Sigma[log10(PSA)],are closely dependent on either the spectral period or the RJB.The Sigma[log10(PSA)]remains a constant approximately 0.55 at periods shorter than 0.1 s,and then increase continuously up to^0.13 as the period increases from 0.1 to 2.0 s.The Sigma[log10(PSA)]values at periods of 0.1‒2.0 s show the downward tendency as the RJB values increase.However,the Sigma[log10(PSA)]​values at periods shorter than 0.1 s decrease as the RJB values increase up to^50 km,and then increase with the increasing RJB.Furthermore,we found that the ground-motion variability shows the significant dependence on the azimuth.

Seismic ground motion relationships in southern China based on stochastic finite-fault model

The characteristics of seismic ground motions in southern China are difficult to determine statistically due to a lack of strong ground motion data.In this study,a stochastic finite-fault ground motion model was adopted to simulate the seismic ground motions at bedrock for southern China,based on parameters derived from small and medium earthquakes that have occurred in the region.From these,the response spectra was estimated.A set of ground motion attenuation relationships was then developed based on simulated peak ground motions and response spectral parameters through regression,which would be applicable for use in engineering practice.Through comparisons,it was demonstrated that the proposed ground motion relationships are generally consistent with those obtained from other reported ground motion attenuation models for southern China.

Simulating the strong ground motion of the 2022 MS6.8 Luding,Sichuan,China Earthquake

Stochastic finite-fault simulations are effective for simulating ground motions and are widely used in engineering to determine the impacts of ground motion and develop relevant predictive equations.In this study,the source,path,and site amplification coefficient of western Sichuan Province,China,and stochastic finite-fault simulations were used to simulate the acceleration time series,Fourier amplitude spectra,and 5%damped response spectra of 28 strong-motion stations with rupture distances within 300 km of the 2022 MS6.8 Luding earthquake.The simulation results of 14 stations at rupture distances of 45-185 km match the observation.However,the simulation results of 3 near-and 6 far-field stations at rupture distances of 12-36 km and 222-286 km,respectively,were obviously deviated from the observations.Simulation results of the near-field stations are larger than the observations at high frequencies(>6 Hz).The discrepancy likely comes from the nonlinear site effect of near-field stations,which reduced the site amplification at high frequencies.Simulation result of the far-field stations is smaller than the observation at frequencies above 1 Hz.As these stations are located close to the Longmenshan Fault Zone(LFZ),thus,we obtained a new quality factor(Q)from data of historical events and stations located around LFZ.Using the new Q value,the discrepancies of the high-frequency simulation results of the far-field stations were corrected.This result indicated that the laterally varying Q values can be used to address the impact of strong crustal lateral heterogeneity on simulation.

The 2018 M_S 5.9 Mojiang Earthquake:Source model and intensity based on near-field seismic recordings

On September 8, 2018, an M_S 5.9 earthquake struck Mojiang, a county in Yunnan Province, China. We collect near-field seismic recordings(epicentral distances less than 200 km) to relocate the mainshock and the aftershocks within the first 60 hours to determine the focal mechanism solutions of the mainshock and some of the aftershocks and to invert for the finite-fault model of the mainshock.The focal mechanism solution of the mainshock and the relocation results of the aftershocks constrain the mainshock on a nearly vertical fault plane striking northeast and dipping to the southeast. The inversion of the finite-fault model reveals only a single slip asperity on the fault plane. The major slip is distributed above the initiation point, ～14 km wide along the down-dip direction and ～14 km long along the strike direction, with a maximal slip of ～22 cm at a depth of ～6 km. The focal mechanism solutions of the aftershocks show that most of the aftershocks are of the strike-slip type, a number of them are of the normal-slip type, and only a few of them are of the thrust-slip type.On average, strike-slip is dominant on the fault plane of the mainshock, as the focal mechanism solution of the mainshock suggests, but when examined in detail, slight thrust-slip appears on the southwest of the fault plane while an obvious part of normal-slip appears on the northeast, which is consistent with what the focal mechanism solutions of the aftershocks display. The multiple types of aftershock focal mechanism solutions and the slip details of the mainshock both suggest a complex tectonic setting, stress setting, or both. The intensity contours predicted exhibit a longer axis trending from northeast to southwest and a maximal intensity of Ⅷ around the epicenter and in the northwest.

Dynamic corner frequency in source spectral model for stochastic synthesis of ground motion

The static comer frequency and dynamic comer frequency in stochastic synthesis of ground motion from fi- nite-fault modeling are introduced, and conceptual disadvantages of the two are discussed in this paper. Furthermore, the non-uniform radiation of seismic wave on the fault plane, as well as the trend of the larger rupture area, the lower comer frequency, can be described by the source spectral model developed by the authors. A new dynamic comer frequency can be developed directly from the model. The dependence of ground motion on the size of subfault can be eliminated if this source spectral model is adopted in the synthesis. Finally, the approach presented is validated from the comparison between the synthesized and observed ground motions at six rock stations during the Northridge earthquake in 1994.

Strong ground motion simulation for the 2013 Lushan M_W6.6 earthquake, Sichuan, China, based on the inverted and synthetic slip models

It is well known that quantitative estimation of slip distributions on fault plane is one of the most important issues for earthquake source inversion related to the fault rupture process. The characteristics of slip distribution on the main fault play a fundamental role to control strong ground motion pattern. A large amount of works have also suggested that variable slip models inverted from longer period ground motion recordings are relevant for the prediction of higher frequency ground motions. Zhang et al. （Chin J Geophys 56：1412-1417, 2013） and Wang et al. （Chin J Geophys 56：1408-1411,2013） published their source inversions for the fault rupturing process soon after the April 20, 2013 Lushan earthquake in Sichuan, China. In this study, first, we synthesize two forward source slip models： the value of maximum slip, fault dimension, size, and dimension of major asperities, and comer wave number obtained from Wang＇s model is adopted to constrain the gen- eration of k-2 model and crack model. Next, both inverted and synthetic slip models are employed to simulate the ground motions for the Lushan earthquake based on the stochastic finite-fault method. In addition, for a comparison purpose, a stochastic slip model and another k-2 model （k 2 model II） with 2 times value of comer wave number of the original k-2 model （k 2 model I） are also employed for simulation for Lushan event. The simulated results characterized by Modified Mer- calli Intensity （MMI） show that the source slip models based on the inverted and synthetic slip distributions could capture many basic features associated with the ground motion patterns. Moreover, the simulated MMI distributions reflect the rupture directivity effect and the influence of the shallow velocity structure well. On the other hand, the simulated MMI bystochastic slip model and k 2 model II is apparently higher than observed intensity. By contrast, our simulation results show that the higher frequency ground motion is sensitive to the degree of slip roughness; therefore, we suggest that, for realistic ground- motion simulations due to future earthquake, it is imperative to properly estimate the slip roughness distribution.

Rupture behavior of the 2017 M_(W)6.6 Poso earthquake in Sulawesi,Indonesia

On May 29, 2017, the MW6.6 Poso earthquake occurred in Central Sulawesi, Indonesia, causing moderate damages. The mainshock rupture and primary aftershock cluster occurred in the active Palolo-Sausu tectonic zone, and some aftershocks also took place around the Tokararu fault. However, the rupture mechanism of this earthquake and its relation to regional tectonics are not clear. In this study, the rupture process of the Poso mainshock is estimated by finite-fault waveform inversion, which is constrained by teleseismic bodies and surface waves. The rupture propagates upward unilaterally in a southwest-dipping moderate-angle(~34°) normal fault beneath Tokorondo Mountains, with a notable~15% initial moment release at the first 4 s of the ~12 s rupture duration. The average and peak slip are0.5 m and 1.5 m, respectively. The rupture velocity is relatively slow(less than 2.5 km/s), and the Coulomb stress changes due to the mainshock are obtained using the inverted coseismic slip.

Determination and application of path duration of seismic ground motions based on the K-NET data in Sagami Bay,Japan

Duration models are one of the important parameters in ground-motion simulations.This model varies in different study areas,and plays a critical role in nonlinear structural response analysis.Currently,available empirical models are being globally used in ground-motion simulations,with limited research focusing on path duration in specific regions.In this study,we collected 6,486 sets of three-component strong-motion records from 29 K-NET stations in the Sagami Bay,Japan,and its surrounding areas between January 2000 to October 2018.We extracted the effective duration of 386 pieces of ground-motion records by manually picking up the S-wave arrival time and calculating the significant duration.We then obtained the path duration model of the study area based on the empirical equation of dynamic corner frequency and source duration of Boore(2009).Compared with the results of the available empirical models,the Fourier spectrum of the simulated ground motion from our effective duration model showed higher accuracy in the long-term range,with less fitting residuals.This path duration model was then applied to simulate two earthquakes of M_(W)5.4 and M_(W)6.2,respectively,in the region using the stochastic finite-fault method with a set of reliable source,path,and site parameters determined for the study area.The simulation results of most stations fit well with observation records in the 0-30 Hz frequency band.For the M_(W)5.4 earthquake,the simulated ground motions at KNG005/KNG010/SZO008 stations were relatively weak in the mid to high frequency band(1-30 Hz)because the quality factor and geometric diffusion model used in the simulation were the averages of the entire Sagami Bay region,causing a bias in the results of a few stations owing to local crustal velocity anomalies and topographic effects.For the M_(W)6.2 earthquake,the simulated ground motions were relatively weak at all SZO and TKY stations,mainly because of the close distance from these stations to the epicenter and the complex seismic-wave propagation paths.The analysis suggests that the differences between the simulation results of the two earthquakes were mainly related to complex geological conditions and seismic-wave propagation paths.