This paper provides an overview and introduction to the development of non-ergodic ground-motion models, GMMs. It is intended for a reader who is familiar with the standard approach for developing ergodic GMMs. It starts with a brief summary of the development of ergodic GMMs and then describes different methods that are used in the development of non-ergodic GMMs with an emphasis on Gaussian process (GP) regression, as that is currently the method preferred by most researchers contributing to this special issue. Non-ergodic modeling requires the definition of locations for the source and site characterizing the systematic source and site effects; the non-ergodic domain is divided into cells for describing the systematic path effects. Modeling the cell-specific anelastic attenuation as a GP, and considerations on constraints for extrapolation of the non-ergodic GMMs are also discussed. An updated unifying notation for non-ergodic GMMs is also presented, which has been adopted by the authors of this issue.

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 $≤180km$) 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 shear‐wave 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.

Conditional ground‐motion models (CGMMs) for estimating Arias intensity (⁠$IA$⁠) for earthquakes in subduction zones are developed. The estimate of $IA$ is conditioned in these models on the estimated peak ground acceleration (PGA), the spectral acceleration at $T=1s$ (SA1), time‐averaged shear‐wave velocity in the top 30 m (⁠$VS30$⁠), and magnitude (⁠$Mw$⁠). Random‐effects regressions are used to develop CGMMs for Japan, Taiwan, South America, and New Zealand. By combining the conditional models of $IA$ with the ground‐motion models (GMMs) for PGA and SA1, the conditional models are converted to scenario‐based GMMs that can be used to estimate the median $IA$ and its standard deviation directly for a given earthquake scenario and site conditions. The conditional scaling approach ensures the estimated $IA$ values are consistent with a design spectrum that may correspond to above‐average spectral values for the controlling scenario. In addition, this approach captures the complex ground‐motion scaling effects found in GMMs for spectral acceleration, such as sediment‐depth effects, soil nonlinearity effects, and regionalization effects, in the developed scenario‐based models for $IA$⁠. Estimates from the new scenario‐based $IA$ models are compared to those from traditional GMMs for $IA$ in subduction zones.

Site response in ground‐motion prediction equations (GMPEs) is primarily characterized as a function of the time‐averaged shear‐wave velocity over the top 30 m of the site profile (⁠ $VS30$⁠). Although the use of $VS30$ as a main site‐response predictor parameter is practical, GMPE site adjustments to different target regions or target site conditions require characterization of the GMPE’s rock‐site response in terms of host $VS$ profile and host kappa. Regional $VS$ profiles and kappa values have been traditionally used to characterize GMPEs host site conditions. These regional site properties may not reflect the average site response in GMPEs. We present a methodology, based on the quarter‐wavelength principles, that allows the derivation of GMPE‐compatible host 1D $VS$ profiles and kappa values. This methodology is applied to the Next Generation Attenuation‐West2 (NGA‐West2) GMPEs to derive GMPE‐specific host $VS$ profiles and kappa for western United States (WUS) site conditions with $VS30$ of 360, 490, 620, 760, and 1100 m/s. This application uses, for input, the GMPEs’ site response in Fourier amplitude spectra domain relative to a reference $VS30$ of 1000 m/s and requires an assigned $VS$ profile for the reference site condition. The impact of the choice of reference $VS$ profile on the results is not large. Comparisons of the derived GMPE‐specific $VS$ profiles for $VS30$ of 760 m/s show differences in the host $VS$ profiles among the NGA‐West2 GMPEs for the same site condition in WUS. Differences are also observed when comparing the derived GMPE‐compatible $VS$ profiles with the commonly used profiles for WUS for $VS30$ of 760 m/s. These differences highlight the importance of using GMPE‐compatible $VS$ profiles and kappa in GMPE adjustments and in site‐response analyses. Limitations of this approach for soft site conditions are discussed.