Jack W. Baker

Quantitative Classification of Near-Fault Ground Motions Using Wavelet Analysis

A method is described for quantitatively identifying ground motions containing strong velocity pulses, such as those caused by near-fault directivity. The approach uses wavelet analysis to extract the largest velocity pulse from a given ground motion. The size of the extracted pulse relative to the original ground motion is used to develop a quantitative criterion for classifying a ground motion as “pulselike.” The criterion is calibrated by using a training data set of manually classified ground motions. To identify the subset of these pulselike records of greatest engineering interest, two additional criteria are applied: the pulse arrives early in the ground motion and the absolute amplitude of the velocity pulse is large. The period of the velocity pulse (a quantity of interest to engineers) is easily determined as part of the procedure, using the pseudoperiods of the basis wavelets. This classification approach is useful for a variety of seismology and engineering topics where pulselike ground motions are of interest, such as probabilistic seismic hazard analysis, ground- motion prediction (“attenuation”) models, and nonlinear dynamic analysis of structures. The Next Generation Attenuation (nga) project ground motion library was processed using this approach, and 91 large-velocity pulses were found in the fault- normal components of the approximately 3500 strong ground motion recordings considered. It is believed that many of the identified pulses are caused by near-fault directivity effects. The procedure can be used as a stand-alone classification criterion or as a filter to identify ground motions deserving more careful study.

Conditional Mean Spectrum: Tool for Ground-Motion Selection

A common goal of dynamic structural analysis is to predict the response of a structure subjected to ground motions having a specified spectral acceleration at a given period. This is important, for example, when coupling ground motion hazard curves from probabilistic seismic hazard analysis with results from dynamic structural analysis. The prediction is often obtained by selecting ground motions that match a target response spectrum, and using those ground motions as input to dynamic analysis. The commonly used Uniform Hazard Spectrum (UHS) is shown here to be an unsuitable target for this purpose, as it conservatively implies that large-amplitude spectral values will occur at all periods within a single ground motion. An alternative, termed a Conditional Mean Spectrum (CMS), is presented here. The CMS provides the expected (i.e., mean) response spectrum, conditioned on occurrence of a target spectral acceleration value at the period of interest. It is argued that this is the appropriate target response spectrum for the goal described above, and is thus a useful tool for selecting ground motions as input to dynamic analysis. The Conditional Mean Spectrum is described, its advantages relative to the UHS are explained, and practical guidelines for use in ground motion selection are presented. Recent work illustrating the impact of this change in target spectrum on resulting structural response is briefly summarized.

Correlation of Spectral Acceleration Values from NGA Ground Motion Models

Ground motion models (or “attenuation relationships”) describe the probability distribution of spectral acceleration at an individual period, given a set of predictor variables such as magnitude and distance, but they do not address the correlations between spectral acceleration values at multiple periods or orientations. Those correlations are needed for several calculations related to seismic hazard analysis and ground motion selection. Four NGA models and the NGA ground motion database are used here to measure these correlations, and predictive equations are fit to the results. The equations are valid for periods from 0.01 seconds to 10 seconds, versus similar previous equations that were valid only between 0.05 and 5 seconds and produced unreasonable results if extrapolated. Use of the new NGA ground motion database also facilitates a first study of correlations from intra- and inter-event residuals. Observed correlations are not sensitive to the choice of accompanying ground motion model, and intra-event, inter-event, and total residuals all exhibit similar correlation structure. A single equation is thus applicable for a variety of correlation predictions. A simple example illustrates the use of the proposed equations for one hazard analysis application.

A Computationally Efficient Ground-Motion Selection Algorithm for Matching a Target Response Spectrum Mean and Variance

Dynamic structural analysis often requires the selection of input ground motions with a target mean response spectrum. The variance of the target response spectrum is usually ignored or accounted for in an ad hoc manner, which can bias the structural response estimates. This manuscript proposes a computationally efficient and theoretically consistent algorithm to select ground motions that match the target response spectrum mean and variance. The selection algorithm probabilistically generates multiple response spectra from a target distribution, and then selects recorded ground motions whose response spectra individually match the simulated response spectra. A greedy optimization technique further improves the match between the target and the sample means and variances. The proposed algorithm is used to select ground motions for the analysis of sample structures in order to assess the impact of considering ground-motion variance on the structural response estimates. The implications for code-based design and performance-based earthquake engineering are discussed.

Efficient Analytical Fragility Function Fitting Using Dynamic Structural Analysis

Estimation of fragility functions using dynamic structural analysis is an important step in a number of seismic assessment procedures. This paper discusses the applicability of statistical inference concepts for fragility function estimation, describes appropriate fitting approaches for use with various structural analysis strategies, and studies how to fit fragility functions while minimizing the required number of structural analyses. Illustrative results show that multiple stripe analysis produces more efficient fragility estimates than incremental dynamic analysis for a given number of structural analyses, provided that some knowledge of the buildings capacity is available prior to analysis so that relevant portions of the fragility curve can be approximately identified. This finding has other benefits, given that the multiple stripe analysis approach allows for different ground motions to be used for analyses at varying intensity levels, to represent the differing characteristics of low-intensity and high-intensity shaking. The proposed assessment approach also provides a framework for evaluating alternate analysis procedures that may arise in the future.

Correlation of Response Spectral Values for Multicomponent Ground Motions

Ground-motion prediction (attenuation) models predict the probability distributions of spectral acceleration values for a specified earthquake event. These models provide only marginal distributions, however; they do not specify correlations among spectral accelerations with differing periods or orientations. In this article a large number of strong ground motions are used to empirically estimate these cor- relations, and nonlinear regression is used to develop approximate analytical equa- tions for their evaluation. Because the correlations apply to residuals from a ground- motion prediction, they are in principle dependent on the ground-motion prediction model used. The observed correlations do not vary significantly when the underlying model is changed, however, suggesting that the predictions are applicable regardless of the model chosen by the analyst. The analytical correlation predictions improve upon previous predictions of correlations at differing periods in a randomly oriented horizontal ground-motion component. For correlations within a vertical ground mo- tion or across orthogonal components of a ground motion, these results are believed to be the first of their kind. The resulting correlation coefficient predictions are useful for a range of problems related to seismic hazard and the response of structures. Past uses of previous cor- relation predictions are described, and future applications of the new predictions are proposed. These applications will allow analysts to better understand the properties of single- and multicomponent earthquake ground motions.

NGA-West2 Research Project

The NGA-West2 project is a large multidisciplinary, multi-year research program on the Next Generation Attenuation (NGA) models for shallow crustal earthquakes in active tectonic regions. The research project has been coordinated by the Pacific Earthquake Engineering Research Center (PEER), with extensive technical interactions among many individuals and organizations. NGA-West2 addresses several key issues in ground-motion seismic hazard, including updating the NGA database for a magnitude range of 3.0–7.9; updating NGA ground-motion prediction equations (GMPEs) for the “average” horizontal component; scaling response spectra for damping values other than 5%; quantifying the effects of directivity and directionality for horizontal ground motion; resolving discrepancies between the NGA and the National Earthquake Hazards Reduction Program (NEHRP) site amplification factors; analysis of epistemic uncertainty for NGA GMPEs; and developing GMPEs for vertical ground motion. This paper presents an overview of the NGA-West2 research program and its subprojects.

An Empirically Calibrated Framework for Including the Effects of Near-Fault Directivity in Probabilistic Seismic Hazard Analysis

Forward directivity effects are known to cause pulselike ground motions at near-fault sites. We propose a comprehensive framework to incorporate the effects of near-fault pulselike ground motions in probabilistic seismic hazard analysis (PSHA) computations. Also proposed is a new method to classify ground motions as pulselike or non-pulselike by rotating the ground motion and identifying pulses in all orienta- tions. We have used this method to identify 179 recordings in the Next Generation Attenuation (NGA) database (Chiou et al., 2008), where a pulselike ground motion is observed in at least one orientation. Information from these 179 recordings is used to fit several data-constrained models for predicting the probability of a pulselike ground motion occurring at a site, the orientations in which they are expected relative to the strike of the fault, the period of the pulselike feature, and the response spectrum amplification due to the presence of a pulselike feature in the ground motion. An algorithm describing how to use these new models in a modified PSHA computation is provided. The proposed framework is modular, which will allow for modification of one or more models as more knowledge is obtained in the future without changing other models or the overall framework. Finally, the new framework is compared with existing methods to account for similar effects in PSHA computation. Example applications are included to illustrate the use of the proposed framework, and impli- cations for selection of ground motions for analysis of structures at near-fault sites are discussed.

Statistical Tests of the Joint Distribution of Spectral Acceleration Values

Assessment of seismic hazard using conventional probabilistic seismic hazard analysis (PSHA) typically involves the assumption that the logarithmic spectral acceleration values follow a normal distribution marginally. There are, however, a variety of cases in which a vector of ground-motion intensity measures are considered for seismic hazard analysis. In such cases, assumptions regarding the joint distribution of the ground-motion intensity measures are required for analysis. In this article, statistical tests are used to examine the assumption of univariate normality of logarithmic spectral acceleration values and to verify that vectors of logarithmic spectral acceleration values computed at different sites and/or different periods follow a multivariate normal distribution. Multivariate normality of logarithmic spectral accelerations are verified by testing the multivariate normality of interevent and intraevent residuals obtained from ground-motion models. The univariate normality tests indicate that both interevent and intraevent residuals can be well represented by normal distributions marginally. No evidence is found to support truncation of the normal distribution, as is sometimes done in PSHA. The tests for multivariate normality show that interevent and intraevent residuals at a site, computed at different periods, follow multivariate normal distributions. It is also seen that spatially distributed intraevent residuals can be well represented by the multivariate normal distribution. This study provides a sound statistical basis for assumptions regarding the marginal and joint distribution of ground-motion parameters that must be made for a variety of seismic hazard calculations.

Which Spectral Acceleration Are You Using

Analysis of the seismic risk to a structure requires assessment of both the rate of occurrence of future earthquake ground motions (hazard) and the effect of these ground motions on the structure (response). These two pieces are often linked using an intensity measure such as spectral acceleration. However, earth scientists typically use the geometric mean of the spectral accelerations of the two horizontal components of ground motion as the intensity measure for hazard analysis, while structural engineers often use spectral acceleration of a single horizontal component as the intensity measure for response analysis. This inconsistency in definitions is typically not recognized when the two assessments are combined, resulting in unconservative conclusions about the seismic risk to the structure. The source and impact of the problem is examined in this paper, and several potential resolutions are proposed. This discussion is directly applicable to probabilistic analyses, but also has implications for deterministic seismic evaluations.