Stochastic Finite-fault Method Research Articles

Path Durations for Use in the Stochastic-Method Simulation of Ground Motions

The stochastic method of ground-motion simulation assumes that the en- ergy in a target spectrum is spread over a duration DT. DT is generally decomposed into the duration due to source effects (DS) and to path effects (DP). For the most commonly used source, seismological theory directly relates DS to the source corner frequency, accounting for the magnitude scaling of DT. In contrast, DP is related to propagation effects that are more difficult to represent by analytic equations based on the physics of the process. We are primarily motivated to revisit DT because the func- tion currently employed by many implementations of the stochastic method for active tectonic regions underpredicts observed durations, leading to an overprediction of ground motions for a given target spectrum. Further, there is some inconsistency in the literature regarding which empirical duration corresponds to DT. Thus, we begin by clarifying the relationship between empirical durations and DT as used in the first author's implementation of the stochastic method, and then we develop a new DP relationship. The new DP function gives significantly longer durations than in the previous DP function, but the relative contribution of DP to DT still diminishes with increasing magnitude. Thus, this correction is more important for small events or subfaults of larger events modeled with the stochastic finite-fault method.

Strong ground motion simulation for the 2013 Lushan MW6.6 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 corner wave number obtained from Wang’s model is adopted to constrain the generation 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 corner 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 Mercalli 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 by stochastic 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.

Stochastic strong ground motion simulations in sparsely-monitored regions: A validation and sensitivity study on the 13 March 1992 Erzincan (Turkey) earthquake

Stochastic simulations have recently become quite popular for estimating synthetic ground motion time histories. For seismically active regions that are not well-monitored or studied extensively, input parameters of the simulations should be carefully selected as the reliability of the simulation results directly depends on the accuracy of the input parameters. In the first part of this study, 13 March 1992 Erzincan (eastern Turkey) earthquake (Mw=6.6), which is recorded at only three strong ground motion stations, is simulated using the stochastic finite-fault method. The source and regional path parameters for this event are adopted from previously validated studies whereas the local site parameters are derived herein. In the second part of the paper, sensitivity of the simulation results with respect to small changes in selected input seismic parameters is investigated. The parameters for which sensitivities are computed include stress drop, crustal shear-wave quality factor and kappa operator. A change of 20% in stress drop value results in 14% change in PGA, whereas a 20% difference in the Q0 value causes 17% change in PGA, and a 20% variation in kappa leads to 15% difference in PGA. Numerical experiments presented in this study prove that the ground motion simulations are prone to trade-off between the source, path and site filters. Hence, input models must be implemented carefully for reliable synthetic ground motions.

An Improved Source Model for Simulation Near-Field Strong Ground Motion Acceleration Time History

The key to near-field strong ground motion simulation based on stochastic finite fault method is to determine the spectrum of ground motion. We present an improved source spectrum model for simulation near-field strong ground motion acceleration time history. We combine Masudas source spectrum model with scaling factor Hij to keep radiation energy conservation and reflect the energy decrease with frequency at low to mid frequencies. We calculate the Fourier amplitude spectrum Fa, accelerate response spectrum Sa, velocity response spectrum Sv and displacement response spectrum Sd of simulation time histories. By comparative analysis of the laws of spectrum values (Fa, Sa, Sv, Sd) with the variation of frequency or period, we discusses the effects of sub-fault dividing scheme, the method of determining scale factor and source spectrum model on spectrum values (Fa, Sa, Sv, Sd). The results show that sub-fault dividing scheme has slightly effect on the model presented in this paper, and the model enable to reflect the sink laws of source spectrum value in mid-to-low frequencies well. We demonstrate that the improved model is superior to other commonly used models.

Ground motion simulations for the 23 October 2011 Van, Eastern Turkey earthquake using stochastic finite fault approach

The 23 October 2011 Van (Mw 7.1) earthquake that occurred in Eastern Turkey resulted in heavy damage particularly in the city of Van and town of Ercis. This paper presents ground motion simulations of Van earthquake by using stochastic finite fault method (EXSIM, Motazedian and Atkinson in Bull Seismol Soc Am 95:995–1010, 2005; Boore in Bull Seismol Soc Am 99:3202–3216, 2009) that provides a simple and effective tool to generate high frequency strong motion. The input parameters related to source, path, and site effects are calibrated on the basis of minimizing the error functions between simulations and observations both in time and frequency domain. Validated model parameters are used to produce synthetics in regional extent with the aim of understanding the level and distribution of the ground shaking particularly in the near fault region where no recordings are available within the 40 km of the epicenter. This paper evaluates the effect of two different slip models on ground motion intensity measures over the area of interest and addresses the variability in the near fault region associated with the source effect. The synthetics are compared with the corresponding estimations of ground motion prediction equations by Boore and Atkinson (Earthq Spectra 24:99–138, 2008), Akkar and Bommer (Seismol Res Lett 81:195–206, 2010) and Akkar and Cagnan (Bull Seismol Soc Am 100:2978–2995, 2010). Our results indicate that despite the limitation of the method for incorporating the directivity effect and inadequate representation of the soil conditions at the individual stations, a satisfactory match between synthetics and observations are obtained both in time and frequency domain. Spatial distributions of the synthetics in regional level also show reasonable correlation with ground motion prediction equations and damage observations.

Prediction of Broadband Ground-Motion Time Histories: The Case of Tehran, Iran

The northern Tehran fault (NTF) is potentially capable of causing large earth-quakes (Mmax~ 7.2) in a very densely populated area of northern Tehran, Iran. Due to the lack of recorded strong motion data for earthquakes on the fault, a hybrid simulation method is used to calculate broadband (0.1–20 Hz) ground-motion time histories at bedrock level for deterministic earthquake scenarios on the NTF. Low-frequency components of motion (0.1–1.0 Hz) are calculated using a deterministic approach and the discrete wave number-finite element method in a regional one-dimensional (1-D) velocity model. High frequencies (1.0–20.0 Hz) are calculated by the stochastic finite fault method based on dynamic corner frequency. The results were validated by comparing the simulated peak values and response spectra with the empirical ground motion models available for the area and the Modified Mercalli intensity (MMI) observations from historical earthquakes of the region.

Intraevent Spatial Correlation Characteristics of Stochastic Finite-Fault Simulations

Spatially correlated strong ground motions can cause severe seismic da- mage to spatially-distributed buildings and infrastructure. Empirical spatial correlation models for ground-motion measures such as peak ground acceleration and spectral acceleration have been developed using strong ground-motion records from California, Taiwan, and Japan. In this paper, we compare an empirical spatial correla- tion model for the 1999 Chi-Chi, Taiwan, earthquake with that obtained from stochas- tic finite-fault simulations; the stochastic finite-fault method is a widely used technique to generate synthetic ground-motion records for engineering applications and hazard assessment. We show that the stochastic records do not reproduce the ob- served intraevent spatial correlation characteristics and comment on what would be required to make them do so.

Ground-Motion Simulation for the 2008 Wenchuan, China, Earthquake Using the Stochastic Finite-Fault Method

Abstract Strong ground motions recorded during the 2008 Wenchuan, China, earthquake ( M w 7.9) have been simulated using the stochastic finite-fault method proposed by Beresnev and Atkinson (1997, 1998b). The simulations were made for two source models. Both models are based on the fault geometry that was proposed by Koketsu et al. (2008) through inversion of teleseismic body wave data. The slip distribution obtained by this inversion was used for the first source model, while a random slip distribution was used for the second source model. The performance of each source model is quantified by calculating the bias and standard deviation of response spectra predicted by each model. For the first source model, the results show overall agreement between the simulated and observed response spectra in a period range of 0.05–1 s, as well as 4–10 s, but the model overpredicts ground motions in a period range of 1–4 s. For the second source model, the model is biased over a slightly wider period range at longer periods. The performance of the stochastic model to predict observed ground motions is also compared with several empirical ground-motion models by means of statistical tools.

Earthquake time histories compatible with the 2005National building code of Canadauniform hazard spectrum

The seismic design provisions of the 2005 National building code of Canada (NBCC) (NRC 2005) describe earthquake ground motions for which structures are to be designed in terms of a uniform hazard spectrum (UHS) having a 2% chance of being exceeded in 50 years. The “target” UHS depends on location and site condition, where site condition is described by a classification scheme based on the time-averaged shear-wave velocity in the top 30 m of the deposit. For some applications, such as dynamic analysis by time history methods, it is useful to have time histories that represent the types of earthquake motions expected and match the target UHS from the NBCC over some prescribed period range. In this study, the stochastic finite-fault method is used to generate earthquake time histories that may be used to match the 2005 NBCC UHS for a range of Canadian sites. Records are provided for site classes A, C, D, and E. They are freely available at www.seismotoolbox.ca .

Stochastic ground motion simulation of the 12 October 1992 Dahshour earthquake

The stochastic method for finite faults is applied to simulate the ground motion of the 12 October 1992, mb = 5.9, Dahshour earthquake. The method includes discritization of the fault plane into certain number of subfaults, and a ω-squared spectrum is assigned to each of them. Contributions from all subfaults are then empirically attenuated to the observation sites, where they are summed to produce the synthetic acceleration time-history. The method is first tested against its ability of reproducing the recording at Kottamya station. The calibrated model is then applied to calculate the synthetics at a large number of grid points covering the area around the fault plane. Simulated peak values are subsequently used to produce the synthetic peak horizontal acceleration map for the area.

Stochastic Finite-Fault Modeling Based on a Dynamic Corner Frequency

In finite-fault modeling of earthquake ground motions, a large fault is divided into N subfaults, where each subfault is considered as a small point source. The ground motions contributed by each subfault can be calculated by the stochastic point-source method and then summed at the observation point, with a proper time delay, to obtain the ground motion from the entire fault. A new variation of this approach is introduced based on a corner frequency. In this model, the corner frequency is a function of time, and the rupture history controls the frequency content of the simulated time series of each subfault. The rupture begins with a high corner frequency and progresses to lower corner frequencies as the ruptured area grows. Limiting the number of active subfaults in the calculation of dynamic corner frequency can control the amplitude of lower frequencies. Our dynamic corner frequency approach has several advantages over previous formulations of the stochastic finite-fault method, including conservation of radiated energy at high frequencies regardless of subfault size, application to a broader mag- nitude range, and control of the relative amplitude of higher versus lower frequencies. The model parameters of the new approach are calibrated by finding the best overall fit to a ground-motion database from 27 well-recorded earthquakes in California. The lowest average residuals are obtained for a dynamic corner frequency model with a stress drop of 60 bars and with 25% of the fault actively slipping at any time in the rupture. As an additional tool to allow the stochastic modeling to generate the impulsive long-period velocity pulses that can be caused by forward directivity of the source, the analytical approach proposed by Mavroeidis and Papageorgiou (2003) has been included in our program. This novel mathematical model of near-fault ground mo- tions is based on a few additional input parameters that have an unambiguous physi- cal meaning; the method has been shown by Mavroeidis and Papageorgiou to sim- ulate the entire set of available near-fault displacement and velocity records, as well as the corresponding deformation, velocity, and acceleration response spectra. The inclusion of this analytical model of long-period pulses substantially increases the power of the stochastic finite-fault simulation method to model broadband time his- tories over a wide range of distances, magnitudes, and frequencies.

Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake

The stochastic method for finite faults is applied to simulate strong ground motion from the 7 September 1999, moment magnitude M 5.9 Athens earthquake. The method includes descritization of the fault plane into a certain number of subfaults, each of which is assigned an ω -2 spectrum. A slip-distribution model, derived from previous studies of this earthquake, is used to specifically account for the source effect. Contributions from all subfaults are then empirically attenuated to the observation sites, where they are summed to produce the synthetic acceleration time history. The method is first calibrated against its ability of reproducing the recordings at 19 strong-motion stations, at epicentral distances ranging from 16 to 61 km. The calibrated model is then applied to calculate synthetics at a large number of grid points covering the area around the fault plane. Simulated peak values are subsequently used to produce synthetic peak ground acceleration and spectral acceleration maps at hard rock. Both peak ground acceleration and spectral acceleration maps imply energy directivity toward the east, where most of the damage was concentrated. The directivity effect is most prominent at large periods (>2 sec) and in the period range 0.2 to 0.3 sec. Independent geotechnical studies showed considerable site effect at periods <0.5 sec within the meizoseismal area. This result, coupled with the results of the present study, imply that the damage distribution pattern of the 1999 Athens earthquake can be explained by the destructive combination of two factors: the source directivity and the site effect.

SEISIMPACT-THES: A SCENARIO EARTHQUAKE AFFECTING THE BUILT ENVIRONMENT OF THE PREFECTURE OF THESSALONIKI

In the framework of the "SEISIMPACT-THES" project (Koutoupes et al., 2004; Savvaidis et al., 2004) a GIS database has been designed to include information on a wide range of components related to seismic risk within the broader area of the prefecture of Thessaloniki. One of these components refers to the distribution of strong ground motion produced by large earthquakes and the ability of a potential future user of the database to retrieve information regarding the distribution of strong ground motion from past destructive earthquakes in the area of Thessaloniki, as well as relative information for realistic future scenario earthquakes in the same area. The selection of future scenario earthquakes that may affect this urban region of interest is based on a combined review of historical data, previous probabilistic and deterministic hazard assessments, seismotectonic and microseismicity studies, relocated seismicity in northern Greece and the experience gained from worldwide research. In this study we present the results from hypothetical rupture of one fault that is located at the suburbs of the city, the Asvestochori fault. Empirical relations applicable to Greece (Papazachos &amp; Papazachou 2003), as well as seismicity information are combined to determine the dimensions of the scenario earthquake source. Strong ground motion for the selected scenario is simulated using the stochastic method for finite faults (Beresnev and Atkinson, 1997). Uncertainties due to unknown parameters such as the rupture initiation point and the distribution of slip on the fault plane are taken into account by examining a large number of random scenarios. The average values from these multiple scenarios are then used to compile maps of strong ground motion parameters (e.g. peak ground acceleration and spectral acceleration). Although the examined scenario earthquake is moderate in size (Mw 5.2), the level of the resulting strong ground motion parameters is indicative of the potential destructiveness of the examined source. Due to the simplicity in the underlying assumptions of the stochastic method, the results of this study are a first-order approximation to the problem of defining expected shaking in the wider area of Thessaloniki. Other strong motion simulation methods of more deterministic character will also be applied for the same purpose in the framework of the SEISIMPACT-THES project.