A Link between Machine Learning and Optimization in Ground-Motion Model Development: Weighted Mixed-Effects Regression with Data-Driven Probabilistic Earthquake Classification

Abstract

ABSTRACTThe steady increase of ground-motion data not only allows new possibilities but also comes with new challenges in the development of ground-motion models (GMMs). Data classification techniques (e.g., cluster analysis) do not only produce deterministic classifications but also probabilistic classifications (e.g., probabilities for each datum to belong to a given class or cluster). One challenge is the integration of such continuous classification in regressions for GMM development such as the widely used mixed-effects model. We address this issue by introducing an extension of the mixed-effects model to incorporate data weighting. The parameter estimation of the mixed-effects model, that is, fixed-effects coefficients of the GMMs and the random-effects variances, are based on the weighted likelihood function, which also provides analytic uncertainty estimates. The data weighting permits for earthquake classification beyond the classical, expert-driven, binary classification based, for example, on event depth, distance to trench, style of faulting, and fault dip angle. We apply Angular Classification with Expectation–maximization, an algorithm to identify clusters of nodal planes from focal mechanisms to differentiate between, for example, interface- and intraslab-type events. Classification is continuous, that is, no event belongs completely to one class, which is taken into account in the ground-motion modeling. The theoretical framework described in this article allows for a fully automatic calibration of ground-motion models using large databases with automated classification and processing of earthquake and ground-motion data. As an example, we developed a GMM on the basis of the GMM by Montalva et al. (2017) with data from the strong-motion flat file of Bastías and Montalva (2016) with ∼2400 records from 319 events in the Chilean subduction zone. Our GMM with the data-driven classification is comparable to the expert-classification-based model. Furthermore, the model shows temporal variations of the between-event residuals before and after large earthquakes in the region.