TOWARDS A STOCHASTIC GROUND-MOTION MODEL WITH OPTIMIZED GENERALIZATION ERROR DERIVED FROM THE NGA DATASET
KUEHN, N.M., firstname.lastname@example.org; SCHERBAUM, F., email@example.com; RIGGELSEN, C., firstname.lastname@example.org, Institute of Geosciences, University of Potsdam, 14476 Potsdam, Germany.
Empirical ground-motion models used in probabilistic seismic hazard analysis are commonly described by regression models. In selecting the best-fitting model, the issue of overfitting is an ever reoccurring concern. This has long been acknowledged in research fields such as machine learning and artificial intelligence, but is often treated quite informally in engineering seismology. As an additional potential problem, the functional forms used for regression are usually based on Fourier spectral models but applied to response spectral data. Here, these questions are addressed for the NGA dataset, which is the best strong-motion dataset currently at hand. Using a two-step procedure we model this dataset as a stochastic point source model. Initially, a regression model is selected via cross-validation, a well-known methodology counteracting the problem of overfitting. The dependence of the logarithmic response spectrum values on the predictor variables is modeled using polynomials of the magnitude, distance, Vs30, rupture depth and a simple fault-mechanism term as basis functions. The generalization error (GE) of the selected model is considerably lower than for functional forms usually employed in ground motion models. Although not overfit, the resulting model is comparatively complex, comprising 46 parameters, none of which is physically interpretable. Hence, in the second step this polynomial model is approximated by an equivalent stochastic point source model using a genetic algorithm optimization, resulting in a physically interpretable model which is optimized for low GE. Though the response spectra of the polynomial and stochastic model agree fairly well, differences persist indicating effects that cannot be modeled by the stochastic model. Finally, hazard curves for the presented model and the published NGA ground-motion models are compared for simple scenarios.