Efficient Propagation of Epistemic Uncertainty in the Median Ground‐Motion Model in Probabilistic Hazard Calculations

2019 ◽  
Vol 109 (5) ◽  
pp. 2063-2072 ◽  
Author(s):  
Maxime Lacour ◽  
Norman A. Abrahamson
Keyword(s):  
Ground Motion ◽  
Traditional Approach ◽  
Epistemic Uncertainty ◽  
Hazard Analysis ◽  
Full Range ◽  
Motion Model ◽  
Uncertainty Distribution ◽  
Earthquake Scenarios ◽  
Ground Motion Model ◽  
Pc Method

Abstract A computationally efficient methodology for propagating the epistemic uncertainty in the median ground motion in probabilistic seismic hazard analysis is developed using the polynomial chaos (PC) approach. For this application, the epistemic uncertainty in the median ground motion for a specific scenario is assumed to be lognormally distributed and fully correlated across earthquake scenarios. In the hazard calculation, a single central ground‐motion model (GMM) is used for the median along with the epistemic standard error of the median for each scenario. A set of PC coefficients is computed for each scenario and each test ground‐motion level. The additional computation burden in computing these PC coefficients depends on the order of the approximation but is less than computing the median ground motion from one additional GMM. With the PC method, the mean and fractiles of the hazard due to the epistemic uncertainty distribution of the median ground motion are computed as a postprocess that is very fast computationally. For typical values of the standard deviation of epistemic uncertainty in the median ground motion (<0.2 natural log units), the methodology accurately estimates the epistemic uncertainty distribution of the hazard over the 1%–99% range. This full epistemic range is not well modeled with just a small number of GMM branches uses in the traditional logic‐tree approach. The PC method provides more accuracy, faster computation, and reduced memory requirements than the traditional approach. For large values of the epistemic uncertainty in the median ground motion, a higher order of the PC expansion may be needed to be included to capture the full range of the epistemic uncertainty.

scholarly journals A Non-Ergodic Effective Amplitude Ground-Motion Model for California

2021 ◽  
Author(s):  
Grigorios Lavrentiadis ◽  
Norman A. Abrahamson ◽  
Nicolas M. Kuehn
Keyword(s):  
Standard Deviation ◽  
Ground Motion ◽  
Epistemic Uncertainty ◽  
Amplitude Spectrum ◽  
Time History ◽  
Motion Model ◽  
Small Magnitude ◽  
Varying Coefficients ◽  
Ground Motion Model ◽  
Systematic Effects

Abstract A new non-ergodic ground-motion model (GMM) for effective amplitude spectral (EAS) values for California is presented in this study. EAS, which is defined in Goulet et al. (2018), is a smoothed rotation-independent Fourier amplitude spectrum of the two horizontal components of an acceleration time history. The main motivation for developing a non-ergodic EAS GMM, rather than a spectral acceleration GMM, is that the scaling of EAS does not depend on spectral shape, and therefore, the more frequent small magnitude events can be used in the estimation of the non-ergodic terms. The model is developed using the California subset of the NGAWest2 dataset Ancheta et al. (2013). The Bayless and Abrahamson (2019b) (BA18) ergodic EAS GMM was used as backbone to constrain the average source, path, and site scaling. The non-ergodic GMM is formulated as a Bayesian hierarchical model: the non-ergodic source and site terms are modeled as spatially varying coefficients following the approach of Landwehr et al. (2016), and the non-ergodic path effects are captured by the cell-specific anelastic attenuation attenuation following the approach of Dawood and Rodriguez-Marek (2013). Close to stations and past events, the mean values of the non-ergodic terms deviate from zero to capture the systematic effects and their epistemic uncertainty is small. In areas with sparse data, the epistemic uncertainty of the non-ergodic terms is large, as the systematic effects cannot be determined. The non-ergodic total aleatory standard deviation is approximately 30 to 40% smaller than the total aleatory standard deviation of BA18. This reduction in the aleatory variability has a significant impact on hazard calculations at large return periods. The epistemic uncertainty of the ground motion predictions is small in areas close to stations and past event.

A horizontal ground-motion model for crustal and subduction earthquakes in Taiwan

2020 ◽  
Vol 36 (2) ◽  
pp. 463-506 ◽  
Author(s):  
Shu-Hsien Chao ◽  
Brian Chiou ◽  
Chiao-Chu Hsu ◽  
Po-Shen Lin
Keyword(s):  
Ground Motion ◽  
Hazard Analysis ◽  
Response Spectrum ◽  
Likelihood Method ◽  
Biased Sampling ◽  
Motion Model ◽  
Subduction Earthquakes ◽  
Ground Motion Model ◽  
Single Station ◽  
Horizontal Ground Motion

In this study, a new horizontal ground-motion model is developed for crustal and subduction earthquakes in Taiwan. A novel two-step maximum-likelihood method is used as a regression tool to develop this model. This method simultaneously considers both the correlation between records and the biased sampling because of random truncation. Moreover, additional ground-motion data can be considered to derive more reliable analysis results. The functional form of the proposed ground-motion model is constructed using the response spectrum of the reference ground-motion scenario and different scalings of the source, path, and site to illustrate the ground-motion characteristics. The variabilities in the ground-motion intensity that result from different events, stations, and records are developed individually to derive a single-station sigma. The proposed ground-motion model may be useful for predicting ground-motion intensity and performing site-specific probabilistic seismic hazard analysis in Taiwan.

Probabilistic Seismic Hazard Analysis Based on Arias Intensity in the North–South Seismic Belt of China

2021 ◽  
Author(s):  
Li Xuejing ◽  
Weijin Xu ◽  
Mengtan Gao
Keyword(s):  
Seismic Hazard ◽  
Ground Motion ◽  
Hazard Analysis ◽  
Seismic Hazard Analysis ◽  
Probabilistic Seismic Hazard ◽  
Motion Model ◽  
Seismic Belt ◽  
Arias Intensity ◽  
The North ◽  
Ground Motion Model

ABSTRACT Arias intensity (IA), as an important seismic parameter, which contains the information of amplitude, frequencies, and duration of ground motion, plays a crucial role in characterizing seismic hazard such as earthquake-induced landslides. In this article, we conducted probabilistic seismic hazard analysis (PSHA) based on IA in China’s north–south seismic belt. We adopted the seismic sources and seismicity parameters used in the fifth generation of the Seismic Ground Motion Parameter Zoning Map of China, and two ground-motion model of IA. The results show that the values of IA are greater than 0.11 m/s in most regions of the north–south seismic belt. The provincial capital cities and most prefecture-level cities in the seismic zone are located in the region with IA-values greater than 0.32 m/s. The values of IA are above 0.54 m/s in the region around the main fault zone. This means that the north–south seismic belt is prone to extremely high-seismic hazard, particularly earthquake-induced landslides. Therefore, it is important to strengthen the evaluation and prevention of earthquake-induced landslides in this area. As we have found significant differences in the values of IA calculated from different ground-motion model, it is necessary to study the ground-motion model of IA for the western geological environment of China. In addition, the PSHA based on IA gives more consideration to the influence of large earthquakes than that based on peak ground acceleration. Therefore, IA plays an important role in seismic design of major engineering projects. The results of this article are of great scientific significance for understanding the seismic hazard of the north–south seismic belt.

Efficient Propagation of Epistemic Uncertainty for Probabilistic Seismic Hazard Analyses (PSHAs) Including Partial Correlation of Magnitude–Distance Scaling

2021 ◽  
Author(s):  
Maxime Lacour ◽  
Norman Abrahamson
Keyword(s):  
Seismic Hazard ◽  
Random Process ◽  
Ground Motion ◽  
Partial Correlation ◽  
Epistemic Uncertainty ◽  
Hazard Analysis ◽  
Correlation Structure ◽  
Probabilistic Seismic Hazard ◽  
Gaussian Random Process ◽  
Earthquake Scenarios

ABSTRACT Probabilistic seismic hazard analysis (PSHA) is moving from ergodic ground-motion models (GMMs) to nonergodic GMMs that account for site-source-specific source, path, and site effects and which require a much larger number of GMM branches on the logic tree to capture the full epistemic uncertainty. An efficient method for computing PSHA with a large number of GMM branches was developed by Lacour and Abrahamson (2019) using polynomial chaos (PC) expansion with the key assumption that the epistemic uncertainty in the median ground motion is fully correlated. In the current study, we remove the assumption of full correlation using a multivariate PC expansion. The correlation structure of the available median GMMs across scenarios is computed empirically. The median ground motion is modeled as a Gaussian random process with the correlation structure of the GMMs across the range of relevant earthquake scenarios. This Gaussian random process is discretized using the Karhunen–Loeve expansion, which leads to multivariate PC expansions of uncertain hazard curves. The hazard fractiles can be reconstructed during an efficient postprocessing phase that includes the effects of partial correlation between the GMMs. Multivariate PC expansions require significantly more terms than for the fully correlated case, which increases the calculation time by about a factor of 5, but it is still much more efficient than direct sampling of the branches of the GMM logic for a large number of branches. An example hazard calculation shows that the effect of using partial correlation in place of full correlation of the GMMs is small for the Next Generation Attenuation-West2 (NGA-West2) set of GMMs, indicating that the fully correlated assumption may be adequate for many applications. The multivariate PC method can be used to evaluate the effects of the partial correlation of the GMMs for sets of GMMs that are different from the NGA-West2 GMMs.

A procedure to develop a backbone ground-motion model: A case study for its implementation

2021 ◽  
pp. 875529302110145
Author(s):  
Sinan Akkar ◽  
Özkan Kale ◽  
M Abdullah Sandıkkaya ◽  
Emrah Yenier
Keyword(s):  
Normal Distribution ◽  
Ground Motion ◽  
Epistemic Uncertainty ◽  
Motion Model ◽  
Logic Tree ◽  
Ground Motion Model ◽  
Stable Continental Region ◽  
Trivariate Normal ◽  
Motion Characterization

The backbone modeling in ground-motion characterization (GMC) is a useful methodology to describe the epistemic uncertainty in median ground-motion predictions. The approach uses a backbone ground-motion model (GMM) and populates the GMC logic tree with the scaled and/or adjusted versions of the backbone GMM to capture the epistemic uncertainty in median ground motions. The scaling and/or adjustment should represent the specific features and uncertainties involved in source, path, and site effects at the target site. The identification of the backbone model requires different considerations specific to the nature of the ground-motion hazard problem. In this article, we present a scaled backbone modeling approach that considers the magnitude- and distance-scaling predictors as well as their correlation to address the epistemic uncertainty in median ground-motion predictions. This approach results in a trivariate normal distribution to fully define a range of epistemic uncertainty in a model sample space. The simultaneous consideration of magnitude and distance scaling while defining the epistemic uncertainty and the methodology followed for the simplified representation of trivariate normal distribution in ground-motion logic tree are the two important features in our procedure. We first present the proposed approach that is followed by a case study for Central and Eastern North America (CENA) stable continental region. The case study discusses the underlying assumptions and limitations of the proposed approach.

Non-ergodic FAS Ground-Motion Model for France

2020 ◽  
Author(s):  
Chih Hsuan Sung ◽  
Norman Abrahamson ◽  
Nicolas Kuehn ◽  
Paola Traversa ◽  
Irmela Zentner
Keyword(s):  
Standard Deviation ◽  
Ground Motion ◽  
Epistemic Uncertainty ◽  
Geographical Location ◽  
Gaussian Process Regression ◽  
Motion Model ◽  
Data Set ◽  
Small Magnitude ◽  
Ground Motion Model ◽  
Anelastic Attenuation

&lt;p&gt;In this study, we use an ergodic ground motion model (GMM) of California of Bayless and Abrahamson (2019) as a backbone and incorporate the varying-coefficient model (VCM) to develop a new French non-ergodic GMM based on the French RESIF data set (1996-2016). Most of the magnitudes of this database are small (Mw = 2.0 &amp;#8211; 5.2), so we adopt the Fourier amplitude spectral GMM rather than the spectral acceleration model, which allows the use of small magnitude data to constrain path and site effects without the complication of the scaling being affected by differences in the response spectral shape. For the VCM, the coefficients of GMPE can vary by geographical location and they are estimated using Gaussian process regression. That is, there is a separate set of coefficients for each source and site coordinate, including both the mean coefficients and the epistemic uncertainty in the coefficients. Moreover, the epistemic uncertainty associated with the predicted ground motions also varies spatially: it is small in locations where there are many events or stations and it is large in sparse data regions. Finally, we modify the anelastic attenuation term of a GMM by the cell-specific approach of Kuehn et al. (2019) to allow for azimuth-dependent attenuation for each source which reduces the standard deviation of residuals at long distances. The results show that combining the above two methods (VCM &amp; cell-specific) to lead an aleatory standard deviation of residuals for the GMM that is reduced by ~ 47%, which can have huge implications for seismic-hazard calculations.&lt;/p&gt;

scholarly journals A Non-Ergodic Ground-Motion Model of Fourier Amplitude Spectra for France

2021 ◽  
Author(s):  
Chih-Hsuan Sung ◽  
Norman Abrahamson ◽  
Nicolas M. Kuehn ◽  
Paola Traversa ◽  
Irmela Zentner
Keyword(s):  
Seismic Hazard ◽  
Ground Motion ◽  
Epistemic Uncertainty ◽  
Skewed Distribution ◽  
Motion Model ◽  
Data Set ◽  
Small Magnitude ◽  
Ground Motion Model ◽  
The Mean ◽  
Hazard Level

Abstract We used an ergodic ground-motion model (GMM) of California of Bayless and Abrahamson (Bull Seismol Soc Am 109(5):2088–2105, 2019) as a backbone model and incorporated the varying-coefficient model (VCM), with a modification for anisotropic path effects, to develop a new non-ergodic GMM for France based on the French RESIF data set (1996-2016). Most of the earthquakes in this database have small-to-moderate magnitudes (M2.0 – M5.2). We developed the GMM for the smoothed effective amplitude spectrum (EAS) rather than for elastic spectral acceleration because it allows the use of small magnitude data to constrain linear effects of the path and site without the complication of the scaling being affected by differences in the response spectral shape. For the VCM, the coefficients of GMM can vary by geographical location and they are estimated using Gaussian-process regression. There is a separate set of coefficients for each source and site coordinate, including both the mean coefficients and the epistemic uncertainty in the coefficients. We further modify the anelastic attenuation term of a GMM by the cell-specific approach of Kuehn et al. (Bull Seismol Soc Am 109 (2): 575–585, 2019) to allow for azimuth-dependent attenuation for each source which reduces the standard deviation of the residuals at long distances. As an example, we compute the 5Hz seismic hazard for two sites using the non-ergodic EAS GMM. At the 1 10-4 annual frequency of exceedance hazard level, there can be a large difference between the ergodic hazard and the non-ergodic hazard if the site is close to the available data. The combination of the non-ergodic median ground motion and the reduced aleatory variability can have large implications for seismic-hazard estimation for long return periods. For some sites, the estimated hazard will increase and for other sites the estimated hazard will decrease compared to the traditional ergodic GMM approach. Due to the skewed distribution of the epistemic uncertainty of the hazard, more of the sites will see a decrease in the mean hazard mean hazard at the 1 10-4 hazard level than will see an increase as a result of using the non-ergodic GMM.

scholarly journals A Non-ergodic Spectral Acceleration Ground Motion Model for California Developed with Random Vibration Theory

2021 ◽  
Author(s):  
Grigorios Lavrentiadis ◽  
Norman A. Abrahamson
Keyword(s):  
Standard Deviation ◽  
Ground Motion ◽  
Random Vibration ◽  
Epistemic Uncertainty ◽  
Response Spectrum ◽  
Motion Model ◽  
Small Magnitude ◽  
Vibration Theory ◽  
Ground Motion Model ◽  
Random Vibration Theory

Abstract A new approach for creating a non-ergodic PSA ground-motion model (GMM) is presented which account for the magnitude dependence of the non-ergodic effects. In this approach, the average PSA scaling is controlled by an ergodic PSA GMM, and the non-ergodic effects are captured with non-ergodic PSA factors, which are the adjustment that needs to be applied to an ergodic PSA GMM to incorporate the non-ergodic effects. The non-ergodic PSA factors are based on EAS non-ergodic effects and are converted to PSA through Random Vibration Theory (RVT). The advantage of this approach is that it better captures the non-ergodic source, path, and site effects through the small magnitude earthquakes. Due to the linear properties of Fourier Transform, the EAS non-ergodic effects of the small events can be applied directly to the large magnitude events. This is not the case for PSA, as response spectrum is controlled by a range of frequencies, making PSA non-ergodic effects depended on the spectral shape which is magnitude dependent. Two PSA non-ergodic GMMs are derived using the ASK14 (Abrahamson et al., 2014) and CY14 (Chiou and Youngs, 2014) GMMs as backbone models, respectively. The non-ergodic EAS effects are estimated with the LAK21 (Lavrentiadis et al., In press) GMM. The RVT calculations are performed with the V75 (Vanmarcke, 1975) peak factor model, the Da0.05−0.85 estimate of AS96 (Abrahamson and Silva, 1996) for the ground-motion duration, and BT15 (Boore and Thompson, 2015) oscillator-duration model. The California subset of the NGAWest2 database (Ancheta et al., 2014) is used for both models. The total aleatory standard deviation of the two non-ergodic PSA GMMs is approximately 30 to 35% smaller than the total aleatory standard deviation of the corresponding ergodic PSA GMMs. This reduction has a significant impact on hazard calculations at large return periods. In remote areas, far from stations and past events, the reduction of aleatory variability is accompanied by an increase of epistemic uncertainty.

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