ALBERT

Description: Ground‐motion model (GMM) selection and weighting introduce a significant source of uncertainty in U.S. Geological Survey (USGS) seismic hazard models. The increase in moderate moment magnitude induced earthquakes (Mw 4–5.8) in Oklahoma and Kansas since 2009 caused by increased wastewater injection related to oil and gas production (Keranen et al., 2013, 2014; McNamara, Hayes, et al., 2015; Weingarten et al., 2015) provides useful near‐source (≤40  km) instrumental ground‐motion observations for comparisons between central and eastern United States (CEUS) induced (Rennolet et al., 2017) and tectonic (Goulet et al., 2014) earthquakes. In this study, we evaluate more than 50 GMMs using two well‐established probabilistic scoring methods: log likelihood (LLH) (Scherbaum et al., 2004, 2009) and multivariate LLH (MLLH) (Mak et al., 2017). The LLH approach compares the mean and standard deviation (σ) of the observed and modeled ground motions. The MLLH approach advances the LLH method by considering the variability (φ,τ) of multiple correlated variables, namely intra‐ (within) and inter‐ (between) event residuals.For the probabilistic scoring GMM evaluation methods (LLH, MLLH), we compute horizontal‐component peak ground acceleration (PGA) and 1‐s pseudospectral acceleration (PSA1.0) total residuals using GMM software (nshmp‐haz) recently implemented by the USGS National Seismic Hazard Model Project (NSHMP). We observe from LLH and MLLH scores that (1) newer GMMs with lower standard deviations (σ,φ,τ) score better than older GMMs with higher published uncertainty; (2) 2014 CEUS GMMs score better for CEUS tectonic earthquakes than induced earthquakes; (3) Next Generation Attenuation‐West2 Project (NGA‐West2), Grazier (2017, referred as G17), and Atkinson (2015, referred as A15) GMMs score well for CEUS induced earthquake ground motions; and (4) Next Generation Attenuation‐East Project (NGA‐East) GMMs score well for CEUS tectonic earthquake ground motions. We also use the LLH and MLLH scores to evaluate GMM weights applied in past USGS seismic hazard forecasts and to inform weighting of GMMs in future seismic hazard forecasts.

Description: We compare estimates of the empirical transfer function (ETF) to the plane SH-wave theoretical transfer function (TTF) within a laterally constant medium for invasive and noninvasive estimates of the seismic shear-wave slownesses at 13 Kiban-Kyoshin network stations throughout Japan. The difference between the ETF and either of the TTFs is substantially larger than the difference between the two TTFs computed from different estimates of the seismic properties. We show that the plane SH-wave TTF through a laterally homogeneous medium at vertical incidence inadequately models observed amplifications at most sites for both slowness estimates, obtained via downhole measurements and the spectral analysis of surface waves. Strategies to improve the predictions can be separated into two broad categories: improving the measurement of soil properties and improving the theory that maps the 1D soil profile onto spectral amplification. Using an example site where the 1D plane SH-wave formulation poorly predicts the ETF, we find a more satisfactory fit to the ETF by modeling the full wavefield and incorporating spatially correlated variability of the seismic properties. We conclude that our ability to model the observed site response transfer function is limited largely by the assumptions of the theoretical formulation rather than the uncertainty of the soil property estimates.

Description: The scale of previously proposed methods for mapping site-response ranges from global coverage down to individual urban regions. Typically, spatial coverage and accuracy are inversely related. We use the densely spaced strong-motion stations in Parkfield, California, to estimate the accuracy of different site-response mapping methods and demonstrate a method for integrating multiple site-response estimates from the site to the global scale. This method is simply a weighted mean of a suite of different estimates, where the weights are the inverse of the variance of the individual estimates. Thus, the dominant site-response model varies in space as a function of the accuracy of the different models. For mapping applications, site-response models should be judged in terms of both spatial coverage and the degree of correlation with observed amplifications. Performance varies with period, but in general the Parkfield data show that: (1) where a velocity profile is available, the square-root-of-impedance (SRI) method outperforms the measured V (sub S30) (30 m divided by the S-wave travel time to 30 m depth) and (2) where velocity profiles are unavailable, the topographic slope method outperforms surficial geology for short periods, but geology outperforms slope at longer periods. We develop new equations to estimate site response from topographic slope, derived from the Next Generation Attenuation (NGA) database.

Description: Using velocity profiles from sites in Japan, California, Turkey, and Europe, we find that the time-averaged shear-wave velocity to 30 m (V (sub S30) ), used as a proxy for site amplification in recent ground-motion prediction equations (GMPEs) and building codes, is strongly correlated with average velocities to depths less than 30 m (V (sub Sz) , with z being the averaging depth). The correlations for sites in Japan (corresponding to the KiK-net network) show that V (sub S30) is systematically larger for a given V (sub Sz) than for profiles from the other regions. The difference largely results from the placement of the KiK-net station locations on rock and rocklike sites, whereas stations in the other regions are generally placed in urban areas underlain by sediments. Using the KiK-net velocity profiles, we provide equations relating V (sub S30) to V (sub Sz) for z ranging from 5 to 29 m in 1-m increments. These equations (and those for California velocity profiles given in Boore, 2004b) can be used to estimate V (sub S30) from V (sub Sz) for sites in which velocity profiles do not extend to 30 m. The scatter of the residuals decreases with depth, but, even for an averaging depth of 5 m, a variation in logV (sub S30) of + or -1 standard deviation maps into less than a 20% uncertainty in ground motions given by recent GMPEs at short periods. The sensitivity of the ground motions to V (sub S30) uncertainty is considerably larger at long periods (but is less than a factor of 1.2 for averaging depths greater than about 20 m). We also find that V (sub S30) is correlated with V (sub Sz) for z as great as 400 m for sites of the KiK-net network, providing some justification for using V (sub S30) as a site-response variable for predicting ground motions at periods for which the wavelengths far exceed 30 m.

Description: The stochastic method of ground-motion simulation assumes that the energy in a target spectrum is spread over a duration D (sub T) . D (sub T) is generally decomposed into the duration due to source effects (D (sub S) ) and to path effects (D (sub P) ). For the most commonly used source, seismological theory directly relates D (sub S) to the source corner frequency, accounting for the magnitude scaling of D (sub T) . In contrast, D (sub P) is related to propagation effects that are more difficult to represent by analytic equations based on the physics of the process. We are primarily motivated to revisit D (sub T) because the function currently employed by many implementations of the stochastic method for active tectonic regions underpredicts observed durations, leading to an overprediction of ground motions for a given target spectrum. Further, there is some inconsistency in the literature regarding which empirical duration corresponds to D (sub T) . Thus, we begin by clarifying the relationship between empirical durations and D (sub T) as used in the first author's implementation of the stochastic method, and then we develop a new D (sub P) relationship. The new D (sub P) function gives significantly longer durations than in the previous D (sub P) function, but the relative contribution of D (sub P) to D (sub T) still diminishes with increasing magnitude. Thus, this correction is more important for small events or subfaults of larger events modeled with the stochastic finite-fault method.

Description: Because of the limited number of strong-motion records that have measured ground response at large strains, any statistical analyses of seismic site-response models subject to strong ground motions are severely limited by a small number of observations. Recent earthquakes in Japan, including the M (sub w) 9.0 Tohoku earthquake of March 2011, have substantially increased the observations of strong-motion records that can be used to compare alternative site-response models at large strains and can subsequently provide insight into the accuracy and precision of site-response models. Using the Kiban-Kyoshin network (KiK-net) downhole array data in Japan, we analyze the accuracy (bias) and variability (precision) resulting from common site-response modeling assumptions, and we identify critical parameters that significantly contribute to the uncertainty in site-response analyses. We perform linear and equivalent-linear site-response analyses at 100 KiK-net sites using 3720 ground motions ranging in amplitude from weak to strong; 204 of these records have peak ground accelerations greater than Formula at the ground surface. We find that the maximum shear strain in the soil profile, the observed peak ground acceleration at the ground surface, and the predominant spectral period of the surface ground motion are the best predictors of where the evaluated models become inaccurate and/or imprecise. The peak shear strains beyond which linear analyses become inaccurate in predicting surface pseudospectral accelerations (PSA; presumably as a result of nonlinear soil behavior) are a function of vibration period and are between 0.01% and 0.1% for periods 〈0.5 s. Equivalent-linear analyses become inaccurate at peak strains of approximately 0.4% over this range of periods. We find that, for the sites and ground motions considered, site-response residuals at spectral periods 〉0.5 s do not display noticeable effects of nonlinear soil behavior. Online Material: Site-specific information and model residuals at 100 KiK-net stations.

Description: For many earthquake engineering applications, site response is estimated through empirical correlations with the time-averaged shear-wave velocity to 30 m depth (V (sub S30) ). These applications therefore depend on the availability of either site-specific V (sub S30) measurements or V (sub S30) maps at local, regional, and global scales. Because V (sub S30) measurements are sparse, a proxy frequently is needed to estimate V (sub S30) at unsampled locations. We present a new V (sub S30) map for California, which accounts for observational constraints from multiple sources and spatial scales, such as geology, topography, and site-specific V (sub S30) measurements. We apply the geostatistical approach of regression kriging (RK) to combine these constraints for predicting V (sub S30) . For the V (sub S30) trend, we start with geology-based V (sub S30) values and identify two distinct trends between topographic gradient and the residuals from the geology V (sub S30) model. One trend applies to deep and fine Quaternary alluvium, whereas the second trend is slightly stronger and applies to Pleistocene sedimentary units. The RK framework ensures that the resulting map of California is locally refined to reflect the rapidly expanding database of V (sub S30) measurements throughout California. We compare the accuracy of the new mapping method to a previously developed map of V (sub S30) for California. We also illustrate the sensitivity of ground motions to the new V (sub S30) map by comparing real and scenario ShakeMaps with V (sub S30) values from our new map to those for existing V (sub S30) maps.

Description: The stochastic method of ground-motion simulation is often used in combination with the random-vibration theory to directly compute ground-motion intensity measures, thereby bypassing the more computationally intensive time-domain simulations. Key to the application of random-vibration theory to simulate response spectra is determining the duration (D (sub rms) ) used in computing the root-mean-square oscillator response. Boore and Joyner (1984) originally proposed an equation for D (sub rms) , which was improved upon by Liu and Pezeshk (1999). Though these equations are both substantial improvements over using the duration of the ground-motion excitation for D (sub rms) , we document systematic differences between the ground-motion intensity measures derived from the random-vibration and time-domain methods for both of these D (sub rms) equations. These differences are generally less than 10% for most magnitudes, distances, and periods of engineering interest. Given the systematic nature of the differences, however, we feel that improved equations are warranted. We empirically derive new equations from time-domain simulations for eastern and western North America seismological models. The new equations improve the random-vibration simulations over a wide range of magnitudes, distances, and oscillator periods. Online Material: SMSIM parameter files, tables of coefficients and model parameters, and shaded contour plots of TD/RV ratios for two WNA models.