Weighted functional data analysis for the calibration of ground motion models in Italy

31/2022

Weighted functional data analysis for the calibration of ground motion models in Italy

Monday 9th May 2022

Bortolotti, T; Peli, R.; Lanzano, G; Sgobba, S.; Menafoglio, A

Motivated by the crucial implications of Ground Motion Models (GMM) in terms of seismic hazard analysis and civil protection planning, this work extends a scalar ground motion model for Italy to the framework of Functional Data Analysis. The inherent characteristic of seismic data to be incomplete over the observation domain entails embedding the analysis in the context of partially observed functional data. This work proposes a novel methodology that combines pre-existing techniques of data reconstruction with the definition of observation-specific functional weights, which enter the estimation process to reduce the impact that the reconstructed parts of the curves have on the final estimates. The classical methods of smoothing and concurrent functional regression are extended to include weights. The advantages of the proposed methodology are assessed on synthetic data. Eventually, the weighted functional analysis performed on seismological data is shown to provide a natural smoothing and stabilization of the spectral estimates of the GMM.