Historical evolution of the input parameters of ergodic and non-ergodic ground motion models (GMMs): A review

Ground motion models (GMMs) are key empirical components in Performance-Based Earthquake Engineering (PBEE) and the assessment of the seismic hazard as they relate seismic intensity measures (IMs) to earthquake features such as source (), path (), and site () terms. Each term can be divided into sub-terms that are functions of input variables, also known as proxies. Nowadays, GMMs exist to model onshore, offshore and induced earthquakes. The main task for GMM developers has been to refine their predictive power by providing an unbiased, simple parametric model that can potentially be extrapolated, i.e. the model can be used outside the boundaries of the earthquake dataset with some confidence. This required the distinction between epistemic and random residuals and to move from fixed to non-linear grouped mixed-effects models or Gaussian models with a more complex covariance matrix to move from ergodic to partially or fully-path nonergodic formulations. Also, nonlinearities have been introduced, and the number of input variables and coefficients has increased dramatically. Consequently, regression analyses became more complex, susceptible to the trade-off (i.e., correlations), and prone to overfitting. Therefore, the earthquake feature terms, their sub-terms with coefficients and their proxies, and functional forms have strongly impacted the predictive power of both ergodic and nonergodic GMMs. This paper intends to review the historical evolution of GMMs with a specific focus on the general classification of input parameters for subduction and crustal earthquakes. The review of each term, sub-term, and associated proxies will provide a general overview, show alternatives for the case of data-scarce regions, and potentially support the development of future GMMs.