Stochastic Finite-fault Method Research Articles

Probabilistic seismic demand analysis for bridges based on earthquake scenarios

The current probabilistic seismic demand analysis of structures predominantly considers the correlation between the ground motion intensity measure (IM) and structural seismic demand, but fails to effectively capture regional source characteristics. It is essential to integrate earthquake engineering with seismic response of structures using source parameters to quantify regional ground motion uncertainties and determine appropriate IMs. This study presented a probabilistic seismic demand analysis method for structures based on earthquake scenarios, characterized by 1) utilizing the stochastic finite-fault method to simulate ground motions at a specific site instead of employing multiple seismic waves from different source areas, and 2) incorporating the correlation between IMs and the key indicator of source parameters, stress drop, into the probabilistic seismic demand analysis. Taking a continuous girder bridge as an example, the performance of the stress drop and 14 individual IMs in predicting the longitudinal seismic demand and reflecting source characteristics was evaluated. The results revealed that it was difficult to establish a reliable relationship between the stress drop and structural seismic demand. Owing to the complexities of ground motion and structural parameters, the individual IMs were challenging to effectively capture their characteristics simultaneously. Therefore, composite IMs have been proposed to cover the characteristics of both the source and seismic demand. The optimal solutions were derived using a multi-objective genetic algorithm, which exhibited desirable capabilities in both aspects, providing a comprehensive guide for the seismic performance assessment of regional transportation networks.

Hybrid broadband simulation of long-period ground motion in far-field basins based on group delay model

Shallow seismic events often induce long-period ground motions in distant sedimentary basins, which can cause damage to structures. The current design earthquake input is usually based on amplitude, while the equally essential phase characteristics of far-field basin seismic waves are often ignored. To address this issue, this paper proposes a semi-empirical model based on group delay, which integrates the effects of source, path, local site, and basin on group delay, we characterize randomness of group delay through a parametric Gaussian probability framework, and approximates the frequency non-stationarity of positive and negative dispersion by introducing piecewise spline gradient regression. As an improvement of the stochastic finite fault method, the proposed method solves the problem that the original method cannot sufficiently reflect the phase characteristics and frequency non-stationarity of basin-induced seismic waves. Based on this model, the stochastic finite fault method and the spectral element method are combined to perform the hybrid simulation of basin ground motion, and the earthquake of 2003 Tokachi-Oki verifies the reliability of the proposed method.

Comprehensive seismic loss model of Tehran, Iran in the case of Mosha fault seismic scenario using stochastic finite-fault method

This paper presents the results of a study caried out to assess probable seismic loss, in term of damage to the residential buildings and the number of fatalities, in the case of Mosha Fault seismic scenario in Tehran, Iran. Accordingly, seismic risk components (including seismic hazard, exposure model and fragility curves) are evaluated. The stochastic finite-fault method with dynamic corner frequency is applied for quantifying ground motion values. The results shows that PGA on the soil surface could range between 0.1 g to 0.45 g. Then, a reliable model of building exposure by analyzing census data from Tehran is compiled. This model included 19 different classes of buildings and is used to evaluate the potential damage to buildings from seismic scenario. The results indicate that the median of damage ratio from 100,000 iterations for the whole of the city is about 6% ± 1.54%. The study found that the central and eastern parts of Tehran are the most vulnerable areas, with an estimated 15,952 residents at risk of losing their lives in this scenario. This is equivalent to 0.2 percent of total population of Tehran. The finding from this study can be used by local authorities to provide appropriate emergency-response and preparedness plans in the case of Mosha Fault seismic scenario.

Accessing Near-Field Strong Ground Motions Using a Multi-Scheme Method in the Kalawenguquan Fault, Xinjiang, China

The middle segment of the Kalawenguquan fault has been active since the Holocene, with a maximum credible earthquake magnitude of MS 7.5. We established two source models based on empirical relationships, as well as geological, geomorphological, and seismic characteristics. Taking into account the uncertainties of simulation parameters, we adopted the stochastic finite-fault method to calculate all combinations of a multi-scheme simulation. The effects of different source models, initial rupture points, and site locations on the prediction of ground motion parameters were analyzed. The results indicate that when a site is located on a smaller asperity and is a certain distance from the largest asperity, the simulation results are higher. For different sites, when the initial rupture point is located near the smaller rather than the larger asperity, the acceleration response spectra are higher. Our results show that the relationships between the initial rupture points, asperities, and sites have a significant impact on the simulation results. Therefore, our study highlights the relevance of determining the initial rupture point and source model to obtain a reasonable evaluation for near-field strong ground motion simulations at major infrastructures.

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.

Ground motion simulation for the 21 May 2021 Ms 6.4 Yangbi, China, earthquake using stochastic finite-fault method

On 21 May 2021, a 6.4-magnitude earthquake occurred in Yangbi County, Yunnan Province, China. To reproduce the ground motion characteristics of this earthquake, the stochastic finite-fault method was adopted. The ground motion records were analyzed to determine the source, path, and site parameters. Based on the optimization algorithm, the stress drop was set to 10 bar. The S-wave attenuation relation ( QS = 122.7 f0.44) was calculated by the spectral decay method. For the site effect, the site amplification was corrected using the horizontal-to-vertical spectral ratio method, and the zero-distance kappa filter had a value of 0.0328 s. To verify the reliability of the input parameters, the simulated 5%-damped pseudo-spectral acceleration, time history, and Chinese instrumental intensity were compared with those observed at six stations and finding acceptable consistency. Furthermore, the fitted model was used to simulate the ground motion of 2279 nodal points in the area, and the seismic intensity contours were obtained. Finally, the earthquake damage assessment was performed in the Yangbi County, and the difference between the designed spectral acceleration and that simulated at a specific period was regarded as the degree of earthquake damage. It was found that the reinforced concrete structures near the epicenter have sufficient safety reserves, and the earthquake damage was not serious. In summary, the stochastic finite-fault method with calibrated parameters could effectively synthesize the ground motion of specific sites, thus providing a basis for the earthquake damage assessment of engineering buildings.

Seismic hazard analysis for engineering sites based on the stochastic finite-fault method

Seismic hazard analyses are mainly performed using either deterministic or probabilistic methods. However, there are still some defects in these statistical model-based approaches for regional seismic risk assessment affected by the near-field of large earthquakes. Therefore, we established a deterministic seismic hazard analysis method that can characterize the entire process of ground motion propagation based on stochastic finite-fault simulation, and we chose the site of the Xiluodu dam to demonstrate the method. This method can characterize earthquake source properties more realistically than other methods and consider factors such as the path and site attenuation of seismic waves. It also has high computational efficiency and is convenient for engineering applications. We first analyzed the complexity of seismogenic structures in the Xiluodu dam site area, and then an evaluation system for ground motion parameters that considers various uncertainties is constructed based on a stochastic finite-fault simulation. Finally, we assessed the seismic hazard of the dam site area comprehensively. The proposed method was able to take into account the complexity of the seismogenic structures affecting the dam site and provide multi-level parameter evaluation results corresponding to different risk levels. These results can be used to construct a dam safety assessment system of an earthquake in advance that provides technical support for rapidly and accurately assessing the post-earthquake damage state of a dam, thus determining the influence of an earthquake on dam safety and mitigating the risk of potential secondary disasters.

Ground-motion simulation using stochastic finite-fault method combined with a parameter calibration process based on historical seismic data

Ground-motion simulation using stochastic finite-fault method combined with a parameter calibration process based on historical seismic data

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 [7]. 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 MW5.4 and MW6.2, 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 MW5.4 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 MW6.2 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.

Spectral Analysis of Subduction Zone Earthquakes for Coastal Stations and Applications to Stochastic Finite-Fault Simulation Method

Accelerograms of 58 subduction zone earthquakes recorded by 25 K-NET coastal stations located in Sagami Bay and its adjacent regions were used to analyze the spectral properties of the source, propagation path, and site effects by using the generalized inversion technique. The inverted [Formula: see text] values vary from 1.7[Formula: see text]MPa to 17.4[Formula: see text]MPa, with an average value of 4.89[Formula: see text]MPa and a standard deviation of [Formula: see text]. Although the depths of the selected earthquakes are confined to 30 km, which is similar to those of the crustal earthquakes, this study obtains an average [Formula: see text] which coincides with the plate-boundary earthquakes rather than the crustal earthquakes. It implies that the stress condition of the plate-boundary region varies from the inland crust. The obtained [Formula: see text] is similar to the previous studies. The [Formula: see text] of the selected stations varies from 0.0479[Formula: see text]s to 0.0904[Formula: see text]s, indicating high-frequency attenuation for the coastal area. The inverted site response shows the systematic tendency for different site classes. The amplification levels of class A sites fluctuate around one between 1[Formula: see text]Hz and 10[Formula: see text]Hz. Class B sites indicate peak amplification at the resonant frequency distributed between 3[Formula: see text]Hz and 10[Formula: see text]Hz. Most of the Classes D and E sites have peak amplification below about 4[Formula: see text]Hz. Using the inversion results as the input parameters of the stochastic finite-fault method, an [Formula: see text] subduction zone earthquake was simulated. The resulting response spectra corresponded to the observations and confirmed that the inverted parameters are reasonable.

Parameter estimation for predicting near-fault strong ground motion and its application to Lushan earthquake in China

Stochastic finite-fault modelling based on the dynamic corner frequency is a widespread method for synthesizing near-fault ground motions at high frequencies and has been proven to be an effective tool for simulating high-frequency ground motions by researchers globally. Many input parameters, which have more uncertain effects on the synthetic result, are related to sources, sites, and paths in stochastic modelling. Thus, it is difficult to select reasonable parameters. When using the stochastic finite-fault method, the key link to be considered is how to determine the input parameters required for simulations. Based on this fact, this study analyzed and discussed the sensitivity of several important input parameters in the simulation parameters to the simulation results. The results showed that for the Class C site stations, the crustal and local site amplification factors must be considered simultaneously. Overall, the influence of the high-frequency attenuation parameter κ0 calculated using different methods on the simulation results is not evident. For near-fault stations, various upper-edge buried depth synthetic response spectra can be set, and finally, the average value is taken as the final synthetic recorded response spectra. When using the random source model, the rupture starting point must be set on the subfault in the middle along the fault length and width direction. The conclusions provide a basis for a highly reasonable and rapid determination of input parameters when using the stochastic finite-fault simulations for practical engineering applications and can improve the simulation accuracy to apply the finite source modelling to rebuild scenarios and evaluate and alleviate the seismic hazard in the target region.

Comparison of the Dynamic and Static Corner Frequencies in Ground Motion Simulation: Cases Study of Jiuzhaigou Earthquake and Northridge Earthquake

By using the stochastic finite-fault method based on static corner frequency (Model 1) and dynamic corner frequency (Model 2), we calculate the far-field received energy (FRE) and acceleration response spectra (SA) and then compare it with the observed SA. The results show that FRE obtained by the two models depends on the subfault size regardless of high-frequency scaling factor (HSF). Considering the HSF, the results obtained by Model 1 and Model 2 are found to be consistent. Then, similar conclusion was obtained from the Northridge earthquake. Finally, we analyzed the reasons and proposed the areas that need to be improved.

Stochastic Finite-Fault Simulation of the Ms 7.0 Lushan Earthquake Based on Frequency- and Distance-Dependent Radiation Patterns

ABSTRACTThe stochastic finite-fault method (EXSIM) has been extensively used for simulating ground motion at high frequencies. However, its poor performance in low-frequency simulations is a limiting factor that restricts its engineering application. Refining the representation of the radiation pattern in the finite-fault method is an effective strategy to improve low-frequency simulations; to this end, a frequency-dependent radiation pattern has been considered by several researchers. However, this strategy fails to provide an accurate simulation of seismic-wave propagation at distances beyond the near-fault region. Researchers have proposed various approaches for characterizing the radiation pattern variation with distance. This study introduces frequency- and distance-dependent radiation patterns of S waves to the EXSIM. The near-field acceleration records in the east–west and north–south directions of the 2013 Ms 7.0 Lushan earthquake were reconstructed. The proposed method was verified by: (1) comparing broadband simulation results obtained by the improved method with observed results, (2) conducting a misfit analysis to compare the model bias between the improved and original methods, and (3) comparing the observed and simulated peak ground acceleration data with the predicted values of the ground-motion prediction equations (GMPEs) to verify the effectiveness of the GMPEs in describing the regional ground-motion attenuation. The results indicated that the 5%-damped pseudo spectral accelerations at high frequencies (1–20 Hz) and acceleration time history simulated by the improved method were consistent with the observed values. Furthermore, the improved method effectively optimizes the simulation effect at low frequencies (0.05–1 Hz) compared with the original method. Thus, the improvement in the representation of the radiation pattern in EXSIM can better estimate broadband ground motion in the study area.

Probabilistic seismic assessment of reinforced concrete bridges using simulated records

A prominent challenge in performance-based earthquake engineering is to select a suitable set of ground motions records with which to perform probabilistic seismic assessment of structures. The most common approach for engineering purposes is to employ actual recordings of worldwide events, given that large earthquakes do not occur frequently hence regional recordings of such events are usually not widely available. To address this not that uncommon issue, regionally simulated ground motions using a stochastic finite-fault method have been proposed as an alternative to real records. This study aims to explore the use of simulated records through a stochastic finite-fault method in probabilistic seismic assessment frameworks for reinforced concrete bridges, when compared to using real records. Direct seismic losses for a case-study existing bridge and a bridge portfolio are estimated and compared, as the reference risk metric. Finally, the similarities between seismic demands, obtained using both real and simulated record sets, are quantified and discussed via statistical hypothesis testing, resulting fragility curves and expected annual losses. The results show how simulated records can be a promising alternative to real records, becoming particularly useful in the absence of available recorded ground motions with specific seismogenic features.

Across-fault ground motions and their effects on some bridges in the 1999 Chi-Chi earthquake

Simply-supported bridges are vulnerable to surface fault rupture as evidenced by several fault-crossing bridges in the 1999 Chi-Chi earthquake. To investigate the seismic collapse mechanism of simply-supported bridges crossing the fault, across-fault ground motions are firstly simulated in the present study. In particular, based on a previously developed fault model of the 1999 Chi-Chi earthquake, broadband across-fault ground motions at six fault-crossing bridges are simulated using the hybrid deterministic-stochastic method, in which the low- and high-frequency components are computed using the deterministic Green’s function method and the stochastic finite-fault modeling method, respectively. The simulation results indicate that the hybrid deterministic-stochastic method can give reasonable predictions to the across-fault ground motions. Furthermore, utilizing the explicit dynamic finite element (FE) code LS-DYNA, behaviors of a three-span simply-supported bridge under a selected pair of across-fault ground motions are numerically simulated. Numerical results indicate that the structural responses and collapse mechanisms are dominated by the low-frequency ground motions. The large differential static offset across the fault is the main reason for the collapse of the simply-supported bridges. This study contributes understandings for the across-fault ground motions and the collapse mechanism of some bridges in the 1999 Chi-Chi earthquake.

Seismic demands of bare and base-isolated steel frames for real against simulated records of a past earthquake

A challenging task in earthquake engineering is investigation of engineering demand parameters under regional records of large earthquakes due to inherently low frequency of these events. Use of simulated records in such cases is a recent alternative. Ground motion simulations were traditionally performed to model physical processes in earthquake occurrences. Nowadays, simulations are also used for engineering purposes. However, detailed assessment of simulated records against real data including their effect on structural response is necessary. The aim herein is to explore how alternative simulation methods differ in terms of engineering demand parameters for multi-degree-of-freedom models and to find out their efficiency in design and assessment of base isolated structures. For this purpose, bare and base-isolated models of a 6-story steel moment-resisting frame are considered. Force-based, displacement-based and energy-based demands are evaluated due to real and simulated records of 2009 L′Aquila (Italy) event (Mw = 6.3). Ground motion simulation approaches include stochastic finite-fault method and hybrid integral-composite techniques. Analyses show that when seismological misfits between the real and simulated records are smaller, closer matches between their engineering demand parameters are observed. Finally, numerical results reveal that simulated motions validated against real data provide alternative sets particularly for regions with sparse observed records.

Simulation of the strong ground motion for the 20 July 2017 (Mw. 6.6) Bodrum–Kos earthquake

A strong earthquake with Mw 6.6 occurred on 20 July, 2017 in Gokova Bay at the southwest part of the Turkey, accompanied by a local tsunami which impacted Bodrum (Turkey) and Kos (Greece). This paper presents simulation of strong ground motions from this earthquake to visualize the extent of spectral acceleration over the region. A stochastic finite fault method based on a dynamic corner frequency is utilized as a simulation tool. For validation of simulation, strong motion recordings from 10 closest stations within 76 km are used. Horizontal to vertical spectral ratio and near surface attenuation parameter (kappa) of shear waves at strong motion recording stations are calculated to account for site effects. The most suitable source parameters; stress drop and pulsing area percentage are found as 2.5 MPa with 30–36% based on the residuals analyses. In general, an acceptable level of consistency is found between observed and simulated ground motions. Simulation is more successful at frequencies of 2 Hz and above. Distribution of spectral accelerations at a larger region is calculated with the best validated model parameters and compared with ground motion prediction equations. In spite of significant scatter of synthetics particularly in the near fault region, at longer epicentral distances the median values of Turkish empirical prediction better approximates the synthetics. The current results and further scenario simulations for the region are believed to complement normal faulting synthetic strong ground motion library of Turkey.

Ground motion modelling in northwestern Himalaya using stochastic finite-fault method

This study presents estimates of bedrock level peak ground motion at 2346 sites on a regular grid of 0.2° × 0.2° in northwestern (NW) Himalaya from 543 simulated sources, using the stochastic finite-fault, dynamic corner frequency method, with particular emphasis on Kashmir Himalaya. The earthquake catalogue used for simulating synthetic seismograms is compiled by including both pre-instrumental and instrumental era earthquakes of magnitude Mw ≥ 5, dating back to 260 AD. Acceleration time series thus generated are then integrated to obtain velocity and displacement time series, which are all used to construct a suite of hazard maps of the region. Expected PGA values for the Kashmir Himalaya and Muzaffarabad are found to be ~ 0.3–0.5 g and for the epicentral region of the 1905 Kangra event, to be 0.35 g. These values are consistent with other reported results for these areas e.g., Khattri et al. (Tectonophysics 108:93–134, 1984) and Parvez et al. (J Seismol, 2017. https://doi.org/10.1007/s10950-017-9682-0 ). The PGA values estimated in this study are in general found to be higher than those implied by the official seismic zoning map of India produced by the Bureau of Indian Standards (BIS in Indian Standard criteria for earthquake resistant design of structures part 1 general provisions and buildings (Fifth Revision), vol 1, no 5. Indian Standard, 2002). Even the acceleration-derived intensities for most regions are found to be higher compared with those observed, which apparently is due to the use of a longer duration catalogue (260 AD–2016) for simulation not covered by the observed intensity catalogue and higher magnitude ascribed to historical events. Major events in Kashmir Himalayas, such as those of 1555, 1885 and 2005, are simulated individually to allow comparison with available results. Simulated pseudo-acceleration and velocity response spectra for three sites near the 2005 Kashmir earthquake for which site conditions were available (Okawa in Strong earthquake motion recordings during the Pakistan, 2005/10/8, Earthquake, 2005. https://iisee.kenken.go.jp ) are compared with observed spectra. This study provides a first-order ground motion database for safe design of buildings and other infrastructure in the NW Himalayan region.

Simulation of the Jiuzhaigou, China, earthquake by stochastic finite-fault method based on variable stress drop

An improved stochastic finite-fault method was used to simulate the Mw 6.6 earthquake that occurred on August 8, 2017, in Jiuzhaigou, Sichuan, China. A variation of the stochastic finite-fault method, considering the dynamic corner frequency, was used to overcome the corner frequency. It explains the effect of a given slip distribution on the corner frequency of each subfault. A comparison of the response spectra (damping ratio 5%), spectral ratio (simulated values/observed values), and model deviation demonstrated that the improved corner frequency performs well for the whole periods, especially in short periods from 0.2 to 1 s. Similarly, the revised duration model and the site-amplification factor were applied to simulate the ground motion during the Jiuzhaigou earthquake, and then the response spectra were obtained. The duration of the nine near-field station recordings matched well with the simulated ground motions, and the peak ground acceleration (PGA) of most of the stations matched well with the observed PGA. In the short periods (T < 1 s), a small difference is observed between the simulated response spectra and the observed spectra for most of the stations. However, the response spectra were overestimated within the period range (0.05–10 s). Generally, the simulated ground motions obtained by using the improved model matched well with the observed ground motions, which could be considered the basis for earthquake-resistant design during the postdisaster recovery and the structural dynamic analysis of the Jiuzhaigou region.

Stochastic finite-fault ground motion simulation for the Mw 6.7 earthquake in Lushan, China

The Ya’an, Sichuan Mw 6.7 earthquake occurred on April 20, 2013. In this article, the stochastic finite-fault method (EXSIM) based on dynamic corner frequency, proposed by Motazedian and Atkinson (Bull Seismol Soc Am 95(3):995–1010, 2005), is validated to be an intelligible and productive approach for the generation of high-frequency strong ground motion. The validated model parameters were considered for the simulation at 31 selected stations, which are less than 200 km away from the fault. The input parameters included site condition, source term, and path term. The calibration of the input parameters, such as the stress drop, was achieved by using misfit functions between the observed PSA (pseudo-acceleration response spectra) and simulated PSA in the time domain. Some of the other parameters, such as distance-dependent duration, high-frequency attenuation parameter kappa, and local amplification functions, were calibrated by considering the observed recordings. In this study, we attempted to employ two different slip models for strong ground motion simulation, so that the influence on the simulation results can be revealed. Our results depicted that although the method cannot combine well, the directivity effects and the soil conditions are not adequately represented at individual stations, the synthetics satisfactorily match with the seismic characteristics regarding peak ground acceleration (PGA), response spectra, Fourier spectrum, and time history, for both the time and frequency range considered. The results also demonstrated that there is a slight difference between the simulation results of the two slip models. Finally, we compared the effects of different distance-dependent duration models for the simulated PGA. It illustrates that it is difficult to find a balance between the ground motion duration and PGA at stations with fault distance less than 20 km, which makes the duration and PGA to coincide well with the observed recordings.