Weighted Functional Data Analysis for the Calibration of a Ground Motion Model in Italy

Abstract

Motivated by the crucial implications of Ground Motion Models 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 of oscillation periods entails embedding the analysis in the context of partially observed functional data and performing data reconstruction. This work proposes a novel methodology that accounts for the fact that parts of the curves are directly observed and other parts are reconstructed, thus, characterized by greater uncertainty. The method defines observation-specific functional weights, which enter the estimation process to reduce the impact that the less reliable portions 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 Ground Motion Model considered. Supplementary materials for this article are available online.