Earthquake Spectra

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.

A key component of the NGA research project was the development of a strong-motion database with improved quality and content that could be used for ground-motion research as well as for engineering practice. Development of the NGA database was executed through the Lifelines program of the PEER Center with contributions from several research organizations and many individuals in the engineering and seismological communities. Currently, the data set consists of 3551 publicly available multi-component records from 173 shallow crustal earthquakes, ranging in magnitude from 4.2 to 7.9. Each acceleration time series has been corrected and filtered, and pseudo absolute spectral acceleration at multiple damping levels has been computed for each of the 3 components of the acceleration time series. The lowest limit of usable spectral frequency was determined based on the type of filter and the filter corner frequency. For NGA model development, the two horizontal acceleration components were further rotated to form the orientation-independent measure of horizontal ground motion (GMRotI50). In addition to the ground-motion parameters, a large and comprehensive list of metadata characterizing the recording conditions of each record was also developed. NGA data have been systematically checked and reviewed by experts and NGA developers.

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.

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.

This paper contains ground-motion prediction equations (GMPEs) for average horizontal-component ground motions as a function of earthquake magnitude, distance from source to site, local average shear-wave velocity, and fault type. Our equations are for peak ground acceleration (PGA), peak ground velocity (PGV), and 5%-damped pseudo-absolute-acceleration spectra (PSA) at periods between 0.01 s and 10 s. They were derived by empirical regression of an extensive strong-motion database compiled by the “PEER NGA” (Pacific Earthquake Engineering Research Center's Next Generation Attenuation) project. For periods less than 1 s, the analysis used 1,574 records from 58 mainshocks in the distance range from 0 km to 400 km (the number of available data decreased as period increased). The primary predictor variables are moment magnitude (M), closest horizontal distance to the surface projection of the fault plane ( _RJB ), and the time-averaged shear-wave velocity from the surface to 30 m (_VS30). The equations are applicable for M=5–8, _RJB <200 km, and _VS30=180–1300 m/s.

We present a new empirical ground motion model for PGA, PGV, PGD and 5% damped linear elastic response spectra for periods ranging from 0.01–10 s. The model was developed as part of the PEER Next Generation Attenuation (NGA) project. We used a subset of the PEER NGA database for which we excluded recordings and earthquakes that were believed to be inappropriate for estimating free-field ground motions from shallow earthquake mainshocks in active tectonic regimes. We developed relations for both the median and standard deviation of the geometric mean horizontal component of ground motion that we consider to be valid for magnitudes ranging from 4.0 up to 7.5–8.5 (depending on fault mechanism) and distances ranging from 0–200 km. The model explicitly includes the effects of magnitude saturation, magnitude-dependent attenuation, style of faulting, rupture depth, hanging-wall geometry, linear and nonlinear site response, 3-D basin response, and inter-event and intra-event variability. Soil nonlinearity causes the intra-event standard deviation to depend on the amplitude of PGA on reference rock rather than on magnitude, which leads to a decrease in aleatory uncertainty at high levels of ground shaking for sites located on soil.

We present a model for estimating horizontal ground motion amplitudes caused by shallow crustal earthquakes occurring in active tectonic environments. The model provides predictive relationships for the orientation-independent average horizontal component of ground motions. Relationships are provided for peak acceleration, peak velocity, and 5-percent damped pseudo-spectral acceleration for spectral periods of 0.01 to 10 seconds. The model represents an update of the relationships developed by Sadigh et. al. (1997) and incorporates improved magnitude and distance scaling forms as well as hanging-wall effects. Site effects are represented by smooth functions of average shear wave velocity of the upper 30 m (_VS30) and sediment depth. The new model predicts median ground motion that is similar to Sadigh et. al. (1997) at short spectral period, but lower ground motions at longer periods. The new model produces slightly lower ground motions in the distance range of 10 to 50 km and larger ground motions at larger distances. The aleatory variability in ground motion amplitude was found to depend upon earthquake magnitude and on the degree of nonlinear soil response, For large magnitude earthquakes, the aleatory variability is larger than found by Sadigh et. al. (1997).

An empirical model for estimating the horizontal pseudo absolute spectral accelerations (PSA) generated by shallow crustal earthquakes is presented in this paper. The model was selected to be simple and the model parameters were estimated using the recordings gathered as part of the New Generation Attenuation (NGA) project. These parameters are presented for sites with an average shear wave velocity in the upper 30 m, _VS30>900 m/s, and for sites with 450 m/s≤_VS30≤900 m/s. Site-specific dynamic response calculations are recommended for estimating spectral ordinates for sites with _VS30≤180 m/s. Parameters for sites with 180 m/s<_VS30<450 m/s are not included in this paper. The median values of peak horizontal ground acceleration (PGA) and PSA for short periods are on the order of 15% to 20% lower for strike slip events and 30% to 40% lower for reverse events than those calculated using pre-NGA relationships. The differences decrease significantly at longer periods. The minimum values of the standard error terms (for moment magnitude, M≥7.5) are about 15% to 30% larger and the maximum values of the standard error terms (for M≤5) are about 2% to 12% larger than the pre-NGA values.

Amplification factors computed from the equivalent-linear method using the program RASCALS are used to develop constraints on the nonlinear soil response for possible use by the NGA ground-motion model developers. The site response computations covered site conditions with average _VS30 values ranging from 160 to 900 m/s, soil depths from 15 to 914 m, and peak accelerations of the input rock motion (_VS30=1100 m/s) between 0.01 g and 1.5 g. Four sets of nonlinear properties of the soils are used: EPRI, Peninsular Range, Imperial Valley, and Bay Mud. The first two soil models are used for _VS30≥270 m/s and the later two are used for _VS30≤190 m/s. Simple parametric models of the nonlinear amplification factors that are functions of the PGA on rock and _VS30 are developed for the EPRI and Peninsula models.

We propose a model for the effect of sedimentary basin depth on long-period response spectra. The model is based on the analysis of 3-D numerical simulations (finite element and finite difference) of long-period (2–10 s) ground motions for a suite of sixty scenario earthquakes (Mw 6.3 to Mw 7.1) within the Los Angeles basin region. We find depth to the 1.5 km/s S-wave velocity isosurface to be a suitable predictor variable, and also present alternative versions of the model based on depths to the 1.0 and 2.5 km/s isosurfaces. The resulting mean basin-depth effect is period dependent, and both smoother (as a function of period and depth) and higher in amplitude than predictions from local 1-D models. The main requirement for the use of the results in construction of attenuation relationships is determining the extent to which the basin effect, as defined and quantified in this study, is already accounted for implicitly in existing attenuation relationships, through (1) departures of the average “rock” site from our idealized reference model, and (2) correlation of basin depth with other predictor variables (such as V_s30).

We present correction factors that may be applied to the ground motion prediction relations of Abrahamson and Silva, Boore and Atkinson, Campbell and Bozorgnia, and Chiou and Youngs (all in this volume) to model the azimuthally varying distribution of the GMRotI50 component of ground motion (commonly called “directivity”) around earthquakes. Our correction factors may be used for planar or nonplanar faults having any dip or slip rake (faulting mechanism). Our correction factors predict directivity-induced variations of spectral acceleration that are roughly half of the strike-slip variations predicted by Somerville et. al. (1997), and use of our factors reduces record-to-record sigma by about 2–20% at 5 sec or greater period.

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.

The Next Generation Attenuation (NGA) relationships for shallow crustal earthquakes in the western United States predict a rotated geometric mean of horizontal spectral demand, termed GMRotI50, and not maximum spectral demand. Differences between strike-normal, strike-parallel, geometric-mean, and maximum spectral demands in the near-fault region are investigated using 147 pairs of records selected from the NGA strong motion database. The selected records are for earthquakes with moment magnitude greater than 6.5 and for closest site-to-fault distance less than 15 km. Ratios of maximum spectral demand to NGA-predicted GMRotI50 for each pair of ground motions are presented. The ratio shows a clear dependence on period and the Somerville directivity parameters. Maximum demands can substantially exceed NGA-predicted GMRotI50 demands in the near-fault region, which has significant implications for seismic design, seismic performance assessment, and the next-generation seismic design maps. Strike-normal spectral demands are a significantly unconservative surrogate for maximum spectral demands for closest distance greater than 3 to 5 km. Scale factors that transform NGA-predicted GMRotI50 to a maximum spectral demand in the near-fault region are proposed.