Stochastic Finite-fault Model Research Articles

Sensitivity study for stochastic finite-fault model in eastern North America

The reliability of structures depends on the uncertainties of random characteristics of strong ground motions. This study investigates the sensitivity level of the stochastic finite-fault ground-motion simulation model in response to major uncertain input variables, with special focus on eastern North America. The finite-fault model is one of the most useful methods to simulate ground motion for a large earthquake. The variance-based sensitivity analysis using the Monte Carlo-based procedure is considered to compute the set of sensitivity indices of the input variables to estimate the contribution of each uncertain input parameter. The variables that have a dominant influence on the uncertainty of simulated ground motions are identified. The analytical results show that the stress parameter, fault model variables (including faulting geometry, heterogeneous slip distribution and location of hypocentre within fault plane) and site-amplification factor are the main sources of uncertainty, while path variables, such as distance, anelastic attenuation and upper crust attenuation, have relatively little effect.

The ground motion simulation of Kangding Mw6.0,2014 by the stochastic finite-fault model

The November 22, 2014, Kangding strike-slip earthquake (Mw 6.0) occurred on the Southern Section of the Xianshuihe Fault Zone. Its epicenter was at 101.69°E, 30.26°N, source mechanism strikes N33°E, dips 82°, and slipped at an angle of –9°. In this work, we simulated ground motions by the stochastic finite-fault model(SFFM), including peak ground acceleration, peak velocity, and acceleration time-histories caused by this earthquake.

Overview of Ground-Motion Issues for Cascadia Megathrust Events: Simulation of Ground-Motions and Earthquake Site Response

Ground motions for earthquakes of M7.5 to 9.0 on the Cascadia subduction interface are simulated based on a stochastic finite-fault model, and used to estimate average response spectra for reference firm soil conditions. The simulations are first validated by modeling the wealth of ground-motion data from the the 2011 M9.0 Tohoku earthquake of Japan. Adjustments to the calibrated model are then made to consider average source, attenuation and site parameters for the Cascadia region. This includes an evaluation of the likely variability in stress drop for large interface earthquakes, and an assessment of regional attenuation and site effects. We perform best-estimate simulations for a preferred set of input parameters. Typical results suggest mean values of 5%-damped pseudo-acceleration in the range from about 100 to 200 cm/s2, at frequencies from 1 to 4 Hz, for firm-ground conditions in Vancouver. Uncertainty in most-likely value of the parameter representing stress drop causes variability in simulated response spectra of about ±50%. Uncertainties in the attenuation model produce even larger variability in response spectral amplitudes – a factor of about two at a closest distance to the rupture plane (Rcd) of 100 km, becoming even larger at greater distances. It is thus important to establish the regional attenuation model for ground-motion simulations, and to bound the source properties controlling radiation of ground motion. We calculate theoretical 1D spectral amplification estimates for four selected Fraser River Delta sites to show how the presence of softer sediments in the region may alter the predicted ground motions. The amplification functions are largely consistent with observed spectral amplification at Fraser River delta sites, suggesting amplification by factors of 2.5 to 5 at the peak frequency of the site; we note that deep sites in the delta have a low peak frequency, ~0.3 Hz. This work will aid in seismic hazard assessment and mitigation efforts in the active Cascadia region of southwestern B.C. An important consideration is that the uncertainties are large and present a dominant unknown when assessing seismic risk. We find that variability in the expected motions exceeds a factor of two even on rock-like sites, with uncertainty

Hybrid broadband simulation of strong-motion records from the September 16, 1978, Tabas, Iran, earthquake (M w 7.4)

This paper presents a simulation of three components of near-field ground shaking recorded during the main shock at three stations of the September 16, 1978, Tabas (M w = 7.4), Iran, earthquake, close to the causative fault. A hybrid method composed of a discrete wavenumber method developed by Bouchon (Bouchon in Bull Seismol Soc Am 71:959–971, 1981; Cotton and Coutant in Geophys J Int 128:676–688, 1997) and a stochastic finite-fault modeling based on a dynamic corner frequency proposed by Motazedian and Atkinson (Bull Seismol Soc Am 95:995–1010, 2005), modified by Assatourians and Atkinson (Bull Seismol Soc Am 97:935–1949, 2007), is used for generating the seismograms at low (0.1–1.0 Hz) and high frequencies (1.0–20.0 Hz), respectively. The results are validated by comparing the simulated peak acceleration, peak velocity, peak displacement, Arias intensity, the integral of velocity squared, Fourier spectrum and acceleration response spectrum on a frequency-by-frequency basis, the shape of the normalized integrals of acceleration and velocity squared, and the cross-correlation with the observed time-series data. Each characteristic is compared on a scale from 0 to 10, with 10 being perfect agreement. Also, the results are validated by comparing the simulated ground motions with the modified Mercalli intensity observations reported by reconnaissance teams and showed reasonable agreement. The results of the present study imply that the damage distribution pattern of the 1978 Tabas earthquake can be explained by the source directivity effect.

The Stochastic Finite-Fault Modeling Based on a Dynamic Corner Frequency Simulating of Strong Ground Motion for Earthquake Scenario of North Tabriz Fault

The occurrence of the historical and machine Earthquakes, near to the North Tabriz Fault in NW Iran is an evidence for the seismic activity of this fault, which records a historical earthquake with a magnitude more than 7. Using the existing experimental relations, seismicity, and the fault geometry, a Mw 7.7 earthquake scenario was defined. The stochastic finite-fault modeling based on a dynamic corner frequency shows good agreement with common attenuation patterns. The shake map illustrates that Baghmisheh, Roshtieh, Ellahieh, Valiamr, and Eram region on Tabriz are at high hazard areas, and the maximum acceleration is located at the north direction with the same azimuth similar to fault strike.

Stochastic finite-fault simulation of ground motion from the August 11, 2012, M w 6.4 Ahar earthquake, northwestern Iran

In this study, the 11 August 2012 Mw 6.4 Ahar earthquake is investigated using the ground motion simulation based on the stochastic finite-fault model. The earthquake occurred in northwestern Iran and causing extensive damage in the city of Ahar and surrounding areas. A network consisting of 58 acceleration stations recorded the earthquake within 8–217 km of the epicenter. Strong ground motion records from six significant well-recorded stations close to the epicenter have been simulated. These stations are installed in areas which experienced significant structural damage and humanity loss during the earthquake. The simulation is carried out using the dynamic corner frequency model of rupture propagation by extended fault simulation program (EXSIM). For this purpose, the propagation features of shear-wave including \( {Q}_s \) value, kappa value \( {k}_0 \), and soil amplification coefficients at each site are required. The kappa values are obtained from the slope of smoothed amplitude of Fourier spectra of acceleration at higher frequencies. The determined kappa values for vertical and horizontal components are 0.02 and 0.05 s, respectively. Furthermore, an anelastic attenuation parameter is derived from energy decay of a seismic wave by using continuous wavelet transform (CWT) for each station. The average frequency-dependent relation estimated for the region is \( Q=\left(122\pm 38\right){f}^{\left(1.40\pm 0.16\right)}. \) Moreover, the horizontal to vertical spectral ratio \( H/V \) is applied to estimate the site effects at stations. Spectral analysis of the data indicates that the best match between the observed and simulated spectra occurs for an average stress drop of 70 bars. Finally, the simulated and observed results are compared with pseudo acceleration spectra and peak ground motions. The comparison of time series spectra shows good agreement between the observed and the simulated waveforms at frequencies of engineering interest.

Application of Spatially Correlated and Coherent Records of Scenario Event to Estimate Seismic Loss of a Portfolio of Buildings

This study extends the stochastic finite-fault model (SFFM) to simulate spatially correlated and coherent records for a scenario seismic event and estimates the seismic loss of spatially distributed buildings using the simulated records. The extension incorporates the spatial coherency and the spatially correlated disturbance. The simulated records are used to evaluate nonlinear inelastic responses of buildings modeled as nonlinear single-degree-of-freedom systems and to estimate their aggregate seismic loss. Use of the simulated records in such a manner is advantageous since it is applicable to buildings modeled as single- or multi-degree-of-freedom systems with different hysteretic behaviors. The procedure is used to investigate the sensitivity of the seismic loss of a portfolio of hypothetical buildings in downtown Vancouver subjected to a scenario event. The results show that the probability distribution and the quantile of the seismic loss are influenced significantly by the degree of spatial correlation and by nonlinear inelastic behavior.

Seismic Hazard Assessment of Hengshui Area by the Modified Stochastic Finite Fault Modeling

In recent years, numerical simulation of strong ground motion has been well developed with the progress of earthquake science, and it has become an important approach to estimate strong ground motion. In this research, we improve the original program of EXSIM and the modified program named MEXSIM to calculate the Peak Ground Acceleration (PGA) and Peak Ground Velocity (PGV) which is essential for seismic hazard assessment of Hengshui area. Considering the impact of V30(the average shear-velocity down to 30 m) we calculate the impact of two scenario earthquakes from the rupture processes of Hengshui fault and Qianmotou fault. Comparing to Qianmotou scenario earthquake, if the instability fault is Hengshui fault, the PGA and PGV could be 200-360gal and 20-35cm/s respectively in Hengshui city.

Stochastic finite-fault modeling of M w 5.4 earthquake along Uttarakhand–Nepal border

In this work, an attempt has been made to simulate strong ground motion of M w 5.4 earthquake in Kumaun region of Uttarakhand. The simulation is based on modified stochastic finite modeling technique with dynamic corner frequency (Motazedian and Atkinson in Bull Seismol Soc Am 95:995–1010, 2005). Ground motion is simulated for 24 sites, where a magnitude 5.4 earthquake was recorded. Synthesized ground motion is found in close agreement with recorded ones, when compared in terms of main characteristics such as peak ground acceleration (PGA), Fourier spectra, response spectra and duration. Decay of PGA values with distance is almost same as that of observed ones. Successful modeling of present earthquake gives the confidence to understand and quantify seismic hazard of different parts of Uttarakhand from earthquakes of different magnitudes.

Synthetic seismic intensity for historic earthquakes in the North China Plain: implications for the regional seismic hazard

Multiple approaches are used to study the potential seismic hazard in the North China Craton (NCC, or North China Plain), where approximately 15 % of the Chinese population resides and under which active faults are located. In this study, we develop a new modified Mercalli intensity (MMI) attenuation relationship for the NCC using intensity data from 10 instrumentally recorded events. We then utilize this relationship to infer the magnitude and epicentral location of historic events based on the method proposed by Bakun and Wentworth (Bull Seismol Soc Am 87(6):1502–1521, 1997). In addition, a modified stochastic finite fault model is employed to simulate the strong ground motions caused by these historic events. The simulated peak ground accelerations and velocities are then converted into regional MMI distributions through empirical relationships, and these synthetic MMI maps are compared to field observations. The resultant MMI attenuation versus distance models of the 1976 Mw 7.6 Tangshan event and the 1679 M 8.0 Sanhe-Pinggu event are consistent with the empirical attenuation relationships, and the location and size of the meizoseismal area (>VIII) are consistent with observations. The successful modeling of these historic events indicates that a stochastic finite fault model constrained by the regional MMI attenuation relationship can be used to evaluate a wide range of scenarios based on modern computational simulations. These findings may also provide useful information for the estimation and mitigation of potential seismic hazards in this region.

Low-frequency scaling applied to stochastic finite-fault modeling

Stochastic finite-fault modeling is an important tool for simulating moderate to large earthquakes. It has proven to be useful in applications that require a reliable estimation of ground motions, mostly in the spectral frequency range of 1 to 10 Hz, which is the range of most interest to engineers. However, since there can be little resemblance between the low-frequency spectra of large and small earthquakes, this portion can be difficult to simulate using stochastic finite-fault techniques. This paper introduces two different methods to scale low-frequency spectra for stochastic finite-fault modeling. One method multiplies the subfault source spectrum by an empirical function. This function has three parameters to scale the low-frequency spectra: the level of scaling and the start and end frequencies of the taper. This empirical function adjusts the earthquake spectra only between the desired frequencies, conserving seismic moment in the simulated spectra. The other method is an empirical low-frequency coefficient that is added to the subfault corner frequency. This new parameter changes the ratio between high and low frequencies. For each simulation, the entire earthquake spectra is adjusted, which may result in the seismic moment not being conserved for a simulated earthquake. These low-frequency scaling methods were used to reproduce recorded earthquake spectra from several earthquakes recorded in the Pacific Earthquake Engineering Research Center (PEER) Next Generation Attenuation Models (NGA) database. There were two methods of determining the stochastic parameters of best fit for each earthquake: a general residual analysis and an earthquake-specific residual analysis. Both methods resulted in comparable values for stress drop and the low-frequency scaling parameters; however, the earthquake-specific residual analysis obtained a more accurate distribution of the averaged residuals.

Estimation of Source Parameters of M w 6.9 Sikkim Earthquake and Modeling of Ground Motions to Determine Causative Fault

In this study, source parameters of the September 18, 2011 Mw 6.9, Sikkim earthquake were determined using acceleration records. These parameters were then used to generate strong motion at a number of sites using the stochastic finite fault modeling technique to constrain the causative fault plane for this earthquake. The average values of corner frequency, seismic moment, stress drop and source radius were 0.12 Hz, 3.07 × 1026 dyne-cm, 115 bars and 9.68 km, respectively. The fault plane solution showed strike-slip movement with two nodal planes oriented along two prominent lineaments in the region, the NE-oriented Kanchendzonga and NW-oriented Tista lineaments. The ground motions were estimated considering both the nodal planes as causative faults and the results in terms of the peak ground accelerations (PGA) and Fourier spectra were then compared with the actual recordings. We found that the NW–SE striking nodal plane along the Tista lineament may have been the causative fault for the Sikkim earthquake, as PGA estimates are comparable with the observed recordings. We also observed that the Fourier spectrum is not a good parameter in deciding the causative fault plane.

Effects of Randomness in Fault Rupture and in Soil and Structural Parameters on R. C. Portal Frame Response in Delhi Region

Effects of randomness in fault rupture and in soil parameters (shear wave velocity and thickness of soil layers) and structural parameters of a R. C. portal frame ((shear stiffness and mass density) on the seismic response of the portal frame in the Delhi region has been studied. Bedrock outcrop ground motions have been generated for three earthquakes of magnitudes (MW of 7.5, 8.0 and 8.5) using stochastic finite fault model. One dimensional equivalent linear ground response analyses that takes into account the variations in soil parameters have been carried out at three typical sites. It is seen that randomness in fault rupture contributes predominantly to the variability in the response. It is further seen that the effect of randomness in soil and structural parameters on the seismic response may also be significant.

Stochastic Finite Fault Modeling of Subduction Zone Earthquakes in Northeastern India

In this article, a stochastic finite fault source model is calibrated to estimate ground motion in northeastern India for intermediate depth events originating in the Indo-Burmese tectonic domain. A total of 47 three-component accelerograms from eight events with magnitudes ranging from M w 4.8–6.4 are used to estimate the input source and site parameters of the finite fault source model. Key seismic parameters such as stress drop (Δσ) and site amplification function are determined from the recorded strong motion data. The obtained stress drop of the eight recorded events lies in between 105 and 165 bars.

Strong-Ground-Motion Simulation of the 6 April 2009 L'Aquila, Italy, Earthquake

On 6 April 2009, an earthquake of Mw 6:13 (Herrmann et al., 2011) occurred in central Italy, close to the town of L'Aquila. Although the earthquake is considered to be a moderate-size event, it caused extensive damage to the surround- ing area. The earthquake is identified with significant directivity effects: high- amplitude, short-duration motions are observed at the stations that are oriented along the rupture direction, whereas low-amplitude, long-duration motions are observed at the stations oriented in the direction opposite to the rupture. The complex nature of the earthquake combined with its damage potential brings the need for studies that assess the seismological characteristics of the 2009 L'Aquila mainshock. In this study, we present the strong-ground-motion simulation of this particular earthquake using a stochastic finite-fault model with a dynamic corner frequency ap- proach. For modeling the resulting ground motions, we choose two finite-fault source models that take into account the source complexity of the L'Aquila mainshock. In order to test the sensitivity of ground-motion parameters to the seismic wave attenua- tion parameters, we use two different attenuation models obtained in the study region using weak-motion and strong-motion databases. Comparisons are made between the attenuation of synthetics and ground-motion prediction equations (GMPEs). Synthetic ground motions are further compared with the observed ones in terms of Fourier amplitude and response spectra at 21 strong-ground-motion stations that recorded the mainshock within an epicentral distance of 100 km. The spatial distribution of shaking intensity obtained from the Did You Feel It? project and site survey results are compared with the spatial distributions of simulated peak ground-motion intensity parameters. Our results show that despite the limitations of the method in simulating the directivity effects, the stochastic finite-fault model seems an effective and fast tool to simulate the high-frequency portion of ground motions.

Modeling of strong ground motions for 1991 Uttarkashi, 1999 Chamoli earthquakes, and a hypothetical great earthquake in Garhwal–Kumaun Himalaya

In this study, stochastic finite fault modeling is used to simulate Uttarkashi (1991) and Chamoli (1999) earthquakes using all available source, path, and site parameters available for the region. These two moderate earthquakes are recorded at number of stations of a strong motion network. The predicted peak ground accelerations at these stations are compared with the observed data and the ground motion parameters are constrained. The stress drop of Uttarkashi and Chamoli earthquakes is constrained at 77 and 65 bars, respectively, whereas the quality factor Q C is 112 $$ f^{0.97} $$ and 149 $$ f^{0.95} $$ for these two regions. The high-frequency attenuation parameter Kappa is in the range 0.04–0.05. The constrained ground motion parameters are then used to simulate Mw 8.5 earthquake in central seismic gap region of Himalaya. Two scenarios are considered with epicenter of future great earthquake at locations of Uttarkashi and Chamoli earthquakes using above constrained parameters. The most vulnerable towns are the towns of Dehradun and Almora where expected PGA is in excess of 600 cm/s2 at VS30 520 m/s when the epicenter of the great earthquake is at the location of Uttarkashi (1991) earthquake. The towns of Shimla and Chandigarh can expect PGA close to 200 cm/s2. Whereas when the epicenter of the great earthquake is at the location of Chamoli (1999) earthquake, the towns of Dehradun and Almora can expect PGA of around 500 and 400 cm/s2, respectively, at VS30 620 m/s. The National Capital Region, Delhi can expect accelerations of around 80 cm/s2 in both the cases. The PGA contour maps obtained in this study can be used to assess the seismic hazard of the region and identify vulnerable areas in and around central Himalaya from a future great earthquake.

Nonlinear Soil Behavior at the Kashiwazaki-Kariwa Nuclear Power Plant During the Niigata Chuetsu-Oki Earthquake (July, 16, 2007)

Records of the Niigata Chuetsu-Oki earthquake (July, 16, 2007, Mw = 6.6, depth ~17 km) and its aftershocks from seismic vertical arrays deployed at the territory of the Kashiwazaki-Kariwa nuclear power plant (~15 km from the fault) are used to study the soil behavior down to ~250 m during strong ground motion. Nonlinear models of soil behavior during the main shock and six aftershocks are constructed, and stresses and strains induced by the strong motion in the soil layers at various depths are estimated. The data are processed using the method developed by Pavlenko and Irikura (Bull Seismol Soc Am 96(6): 2131–2145, 2003) and previously applied for studying the soil behavior in near-fault zones during the 1995 Kobe and 2000 Tottori earthquakes. A rather good agreement between the recorded and simulated acceleration time histories testifies to the validity of the obtained vertical distributions of stresses and strains in soil layers. In the upper, softer layers (~45 m) at the territory of the plant, the shear moduli were reduced by ~30–35% during the main shock and by ~1.5–3% during the aftershocks. The constructed models of soil behavior can be used in scenario earthquake shaking maps of Japan where, based on source modeling parameters, the level of strong motion can be evaluated for the territory of the power plant in future earthquakes with various magnitudes and fault planes. Using methods of stochastic finite-fault modeling of ground motions from the Chuetsu-Oki earthquake, we estimated input motion to the soil layers during the main shock and found that it differs from the imposed motion (recorded by the deepest sensor of the vertical array) by slightly decreased (by a factor of ~1.2) low-frequency (f < 10 Hz) spectral components.

Enhancement of long period components of recorded and synthetic ground motions using InSAR

Tall buildings and flexible structures require a better characterization of long period ground motion spectra than the one provided by current seismic building codes. Motivated by that, a methodology is proposed and tested to improve recorded and synthetic ground motions which are consistent with the observed co-seismic displacement field obtained from interferometric synthetic aperture radar (InSAR) analysis of image data for the Tocopilla 2007 earthquake ( M w =7.7) in Northern Chile. A methodology is proposed to correct the observed motions such that, after double integration, they are coherent with the local value of the residual displacement. Synthetic records are generated by using a stochastic finite-fault model coupled with a long period pulse to capture the long period fling effect. It is observed that the proposed co-seismic correction yields records with more accurate long-period spectral components as compared with regular correction schemes such as acausal filtering. These signals provide an estimate for the velocity and displacement spectra, which are essential for tall-building design. Furthermore, hints are provided as to the shape of long-period spectra for seismic zones prone to large co-seismic displacements such as the Nazca-South American zone.

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 spectral level. Two improvements were made to one of the three models (i.e., the model based on dynamic corner frequency) as follows: (i) a new method to compute the subfault corner frequency was proposed, where the subfault corner 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 subfault 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.

Stochastic Strong Ground Motion Simulation of the 12 November 1999 Duzce (Turkey) Earthquake Using a Dynamic Corner Frequency Approach

On 12 November 1999, only three months after the 17 August 1999 Kocaeli earthquake (Mw 7:4), an earthquake of Mw 7:1 occurred immediately to the east of the Kocaeli rupture in northwestern Turkey resulting in extensive structural damage in the city of Duzce and its surrounding area. It was reported to be a right- lateral strike slip event on the previously unbroken segment of the North Anatolian fault zone with a north-dipping fault plane. This paper presents stochastic finite-fault simulation of near-field ground motions from this earthquake at selected near-fault stations based on a dynamic corner frequency approach using the computer program EXSIM (Motazedian and Atkinson, 2005). The method requires region-specific source, path, and site characterizations as input model parameters. The source mech- anism of the 1999 Duzce event and regional path effects are well constrained from previous studies of the earthquake. The local site effects at the selected stations are studied as a combination of the kappa operator and frequency-dependent soil ampli- fication. The model parameters are validated against recordings and a stress-drop value of 100 bars is estimated for the 1999 Duzce earthquake. The validated model is then used to compute synthetic records around the fault. Distribution of peak ground-motion parameters is observed to be consistent with the building damage dis- tribution in the near-fault region most affected by the seismic shaking. The attenuation of synthetic ground-motion parameters is compared with recent ground-motion pre- diction equations proposed for the region by Gulkan and Kalkan (2002), Ulusay et al. (2004), and Akkar and Bommer (2007), as well as two next generation attenuation models by Boore and Atkinson (2007) and Campbell and Bozorgnia (2007). Despite discrepancies at several stations, stochastic finite-fault modeling based on a dynamic corner frequency approach confirms to be a practical tool to reproduce the ground motions of large earthquakes.