Norman Abrahamson

Taxonomy of κ: A Review of Definitions and Estimation Approaches Targeted to Applications

to zero epicentral distance, thus correcting for the regional effect of anelastic Q. In this note,we discuss the use of κ0 in various engineering seismology applications today and why interest in this parameter has been revived. We briefly discuss its possible physical interpretations, and detail the known approaches to estimate κ0 from seismic records. We group these approaches into families according to basic features, such as the range of frequencies over which κ0 is computed and the trade-off with path effects. We then discuss the alternative option for estimating κ0 when site-specific records are not available, based on empirical correlations with V S30. We collect previously published correlations and demonstrate the scatter observed across different studies. Finally, we make suggestions as to how κ0 estimation can be made in a more consistent way with the applications that use it, and how existing correlations can be made more consistent to improve both the inference of κ0 in the absence of site-specific data and the physical understanding of κ0.

A Nonergodic Ground‐Motion Model for California with Spatially Varying Coefficients

Traditional probabilistic seismic‐hazard analysis as well as the estimation of ground‐motion models (GMMs) is based on the ergodic assumption, which means that the distribution of ground motions over time at a given site is the same as their spatial distribution over all sites for the same magnitude, distance, and site condition. With a large increase in the number of recorded ground‐motion data, there are now repeated observations at given sites and from multiple earthquakes in small regions, so that assumption can be relaxed. We use a novel approach to develop a nonergodic GMM, which is cast as a varying‐coefficient model (VCM). In this model, the coefficients are allowed to vary by geographical location, which makes it possible to incorporate effects of spatially varying source, path, and site conditions. Hence, a separate set of coefficients is estimated for each source and site coordinate in the data set. The coefficients are constrained to be similar for spatially nearby locations. This is achieved by placing a Gaussian process prior on the coefficients. The amount of correlation is determined by the data. The spatial correlation structure of the model allows one to extrapolate the varying coefficients to a new location and trace the corresponding uncertainties. The approach is illustrated with the Next Generation Attenuation‐West2 data set, using only Californian records. The VCM outperforms a traditionally estimated GMM in terms of generalization error and leads to a reduction in the aleatory standard deviation by ∼40%, which has important implications for seismic‐hazard calculations. The scaling of the model with respect to its predictor variables such as magnitude and distance is physically plausible. The epistemic uncertainty associated with the predicted ground motions is small in places where events or stations are close and large where data are sparse. Online Material: Maps showing the spatially varying coefficients across California and tables of correlation functions.

Decomposing Leftovers: Event, Path, and Site Residuals for a Small‐Magnitude Anza Region GMPEDecomposing Leftovers: Event, Path, and Site Residuals for a Small‐Magnitude Anza Region GMPE

Ground-motion prediction equations (GMPEs) are critical elements of probabilistic seismic hazard analysis (PSHA), as well as for other applications of ground motions. To isolate the path component for the purpose of building nonergodic GMPEs, we compute a regional GMPE using a large dataset of peak ground accelerations (PGAs) from small-magnitude earthquakes (0:5 ≤ M ≤ 4:5 with >10; 000 events, yielding ∼120; 000 recordings) that occurred in 2013 centered around the ANZA seismic network (hypocentral distances ≤180 km) in southern California. We examine two separate methods of obtaining residuals from the observed and predicted ground motions: a pooled ordinary least-squares model and a mixed-effects maximum-likelihood model. Whereas the former is often used by the broader seismological community, the latter is widely used by the ground-motion and engineering seismology community. We confirm that mixed-effects models are the preferred and most statistically robust method to obtain event, path, and site residuals and discuss the reasoning behind this. Our results show that these methods yield different consequences for the uncertainty of the residuals, particularly for the event residuals. Finally, our results show no correlation (correlation coefficient [CC] <0:03) between site residuals and the classic site-characterization term VS30, the time-averaged shearwave velocity in the top 30 m at a site. We propose that this is due to the relative homogeneity of the site response in the region and perhaps due to shortcomings in the formulation of VS30 and suggest applying the provided PGA site correction terms to future ground-motion studies for increased accuracy. Electronic Supplement: Peak ground acceleration (PGA) dataset.