Norman A. Abrahamson

Summary of the Abrahamson & Silva NGA Ground-Motion Relations

Empirical ground-motion models for the rotation-independent average horizontal component from shallow crustal earthquakes are derived using the PEER NGA database. The model is applicable to magnitudes 5–8.5, distances 0–200 km, and spectral periods of 0–10 sec. In place of generic site categories (soil and rock), the site is parameterized by average shear-wave velocity in the top 30 m (VS30) and the depth to engineering rock (depth to VS =1000 m/s). In addition to magnitude and style-of-faulting, the source term is also dependent on the depth to top-of-rupture: for the same magnitude and rupture distance, buried ruptures lead to larger short-period ground motions than surface ruptures. The hanging-wall effect is included with an improved model that varies smoothly as a function of the source properties (M, dip, depth), and the site location. The standard deviation is magnitude dependent with smaller magnitudes leading to larger standard deviations. The short-period standard deviation model for soil sites is also distant-dependent due to nonlinear site response, with smaller standard deviations at short distances.

AN IMPROVED METHOD OF MATCHING RESPONSE SPECTRA OF RECORDED EARTHQUAKE GROUND MOTION USING WAVELETS

Dynamic nonlinear analysis of structures requires the seismic input to be defined in the form of acceleration time-series, and these will generally be required to be compatible with the elastic response spectra representing the design seismic actions at the site. The advantages of using real accelerograms matched to the target response spectrum using wavelets for this purpose are discussed. The program RspMatch, which performs spectral matching using wavelets, is modified using new wavelets that obviate the need to subsequently apply a baseline correction. The new version of the program, RspMatch2005, enables the accelerograms to be matched to the pseudo-acceleration or displacement spectral ordinates as well as the spectrum of absolute acceleration, and additionally allows the matching to be performed simultaneously to a given spectrum at several damping ratios.

An Overview of the NGA Project

The “Next Generation of Ground-Motion Attenuation Models” (NGA) project is a multidisciplinary research program coordinated by the Lifelines Program of the Pacific Earthquake Engineering Research Center (PEER), in partnership with the U.S. Geological Survey and the Southern California Earthquake Center. The objective of the project is to develop new ground-motion prediction relations through a comprehensive and highly interactive research program. Five sets of ground-motion models were developed by teams working independently but interacting with one another throughout the development process. The development of ground-motion models was supported by other project components, which included (1) developing an updated and expanded PEER database of recorded ground motions, including supporting information on the strong-motion record processing, earthquake sources, travel path, and recording station site conditions; (2) conducting supporting research projects to provide guidance on the selected functional forms of the ground-motion models; and (3) conducting a program of interactions throughout the development process to provide input and reviews from both the scientific research and engineering user communities. An overview of the NGA project components, process, and products is presented in this paper.

Why Do Modern Probabilistic Seismic-Hazard Analyses Often Lead to Increased Hazard Estimates?

The basic elements of probabilistic seismic-hazard analysis (psha) were established almost four decades ago and psha has now become the most widely used approach for estimating seismic-design loads. Although the use of psha is widespread, considerable confusion remains regarding the details of how the calculations should be performed. This situation is largely a result of the way the discipline of psha evolved through a series of articles, reports, and software packages. This article demonstrates that the feature of psha about which there is perhaps the greatest degree of misunderstanding is the treatment of the aleatory variability in ground- motion prediction equations, which exerts a very pronounced influence on the calculated hazard. Probabilistic hazard studies performed in recent years have frequently resulted in appreciably higher design ground motions than had been obtained in previous assessments carried out in the 1970s and 1980s, often sparking controversial debate. Although several factors may contribute to the higher estimates of seismic hazard in modern studies, the main reason for these increases is that in the earlier studies the ground-motion variability was either completely neglected or treated in a way that artificially reduced its influence on the hazard estimates.

On the Use of Logic Trees for Ground-Motion Prediction Equations in Seismic-Hazard Analysis

Logic trees are widely used in probabilistic seismic hazard analysis as a tool to capture the epistemic uncertainty associated with the seismogenic sources and the ground-motion prediction models used in estimating the hazard. Combining two or more ground-motion relations within a logic tree will generally require several conversions to be made, because there are several definitions available for both the predicted ground-motion parameters and the explanatory parameters within the predictive ground-motion relations. Procedures for making conversions for each of these factors are presented, using a suite of predictive equations in current use for illustration. The sensitivity of the resulting ground-motion models to these conversions is shown to be pronounced for some of the parameters, especially the measure of source-to-site distance, highlighting the need to take into account any incompatibilities among the selected equations. Procedures are also presented for assigning weights to the branches in the ground-motion section of the logic tree in a transparent fashion, considering both intrinsic merits of the individual equations and their degree of applicability to the particular application.

Comparisons of the NGA ground-motion relations

The data sets, model parameterizations, and results from the five NGA models for shallow crustal earthquakes in active tectonic regions are compared. A key difference in the data sets is the inclusion or exclusion of aftershocks. A comparison of the median spectral values for strike-slip earthquakes shows that they are within a factor of 1.5 for magnitudes between 6.0 and 7.0 for distances less than 100 km. The differences increase to a factor of 2 for M5 and M8 earthquakes, for buried ruptures, and for distances greater than 100 km. For soil sites, the differences in the modeling of soil/sediment depth effects increase the range in the median long-period spectral values for M7 strike-slip earthquakes to a factor of 3. The five models have similar standard deviations for M6.5-M7.5 earthquakes for rock sites and for soil sites at distances greater than 50 km. Differences in the standard deviations of up to 0.2 natural log units for moderate magnitudes at all distances and for large magnitudes at short distances result from the treatment of the magnitude dependence and the effects of nonlinear site response on the standard deviation.

Orientation-Independent Measures of Ground Motion

The geometric mean of the response spectra for two orthogonal hori- zontal components of motion, commonly used as the response variable in predictions of strong ground motion, depends on the orientation of the sensors as installed in the field. This means that the measure of ground-motion intensity could differ for the same actual ground motion. This dependence on sensor orientation is most pro- nounced for strongly correlated motion (the extreme example being linearly polarized motion), such as often occurs at periods of 1 sec or longer. We propose two new measures of the geometric mean, GMRotDpp, and GMRotIpp, that are independent of the sensor orientations. Both are based on a set of geometric means computed from the as-recorded orthogonal horizontal motions rotated through all possible non- redundant rotation angles. GMRotDpp is determined as the ppth percentile of the set of geometric means for a given oscillator period. For example, GMRotD00, GMRotD50, and GMRotD100 correspond to the minimum, median, and maximum values, respectively. The rotations that lead to GMRotDpp depend on period, whereas a single-period-independent rotation is used for GMRotIpp, the angle being chosen to minimize the spread of the rotation-dependent geometric mean (normalized by GMRotDpp) over the usable range of oscillator periods. GMRotI50 is the ground- motion intensity measure being used in the development of new ground-motion pre- diction equations by the Pacific Earthquake Engineering Center Next Generation Attenuation project. Comparisons with as-recorded geometric means for a large dataset show that the new measures are systematically larger than the geometric-mean response spectra using the as-recorded values of ground acceleration, but only by a small amount (less than 3%). The theoretical advantage of the new measures is that they remove sensor orientation as a contributor to aleatory uncertainty. Whether the reduction is of prac- tical significance awaits detailed studies of large datasets. A preliminary analysis contained in a companion article by Beyer and Bommer finds that the reduction is small-to-nonexistent for equations based on a wide range of magnitudes and dis- tances. The results of Beyer and Bommer do suggest, however, that there is an increasing reduction as period increases. Whether the reduction increases with other subdivisions of the dataset for which strongly correlated motions might be expected (e.g., pulselike motions close to faults) awaits further analysis.

Summary of the ASK14 Ground Motion Relation for Active Crustal Regions

Empirical ground motion models for the average horizontal component from shallow crustal earthquakes in active tectonic regions are derived using the PEER NGA-West2 database. The model is applicable to magnitudes 3.0–8.5, distances 0–300 km, and spectral periods of 0–10 s. The model input parameters are the same as those used by Abrahamson and Silva (2008), with the following exceptions: the loading level for nonlinear effects is based on the spectral acceleration at the period of interest rather than the PGA; and the distance scaling for hanging wall (HW) effects off the ends of the rupture includes a dependence on the source-to-site azimuth. Regional differences in large-distance attenuation and VS30 scaling between California, Japan, China, and Taiwan are included. The scaling for the HW effect is improved using constraints from numerical simulations. The standard deviation is magnitude-dependent, with smaller magnitudes leading to larger standard deviations at short periods, but smaller standard deviations at long periods. Directivity effects are not included through explicit parameters, but are captured through the variability of the empirical data.

Ground motion evaluation procedures for performance-based design

The objective of performance-based earthquake engineering (PBEE) is the analysis of performance objectives with a specified annual probability of exceedance. Increasingly undesirable performance is caused by increasing levels of strong ground motion having decreasing annual probabilities of exceedance. Accordingly, the evaluation of ground motion intensity measures is a vital component of PBEE. This paper provides a brief synthesis of ground motion analysis procedures within a performance-based design framework, and is a summary of a recent report to which the reader is referred for details. The principal topics addressed are probabilistic characterizations of source, path, and site effects, with the discussion of these effects focusing principally on applications in active regions such as California.

Empirical spatial coherency functions for application to soil-structure interaction analyses

The spatial coherency of strong ground motion from fifteen earthquakes recorded by the Lotung LSST strong motion array is analyzed. The earthquakes range in magnitude from 3.7 to 7.8 and in epicentral distance from 5 to 80 km. In all, a total of 533 station pairs are used with station separations ranging from 6 to 85 meters. Empirical coherency functions for the horizontal component S-waves appropriate for use in engineering analyses are derived from these data. The derived coherency functions are applicable to all frequencies and to separation distances up to 100 m. For these short station separations, the coherency decreases much faster with increasing frequency than with increasing station separation. The computed coherencies indicate that at high frequencies (>10 Hz) over 25 percent of the power of the ground motion is random for station separations greater than 30 m.