Hybrid Spatial Functional Regression for Seismic Wave Analysis

We propose a hybrid Geographically Weighted Functional Regression (hGWFR) framework to model the spatiotemporal evolution of cumulative seismic energy. Unlike standard global models, hGWFR captures local heterogeneity in ground motion attenuation by treating waveforms as continuous functional objects. The model integrates the log-transformed Peak Ground Velocity envelope as a functional predic- tor and hypocentral distance as a scalar covariate. A key methodologi- cal contribution is the enforcement of a physical causality constraint— ensuring energy at time t depends only on past ground motion—via a Constrained Weighted Least Squares (CWLS) procedure. Applied to the I talian INSTANCE dataset, hGWFR reveals significant spatial non- stationarity in energy release. Furthermore, we integrate spatially local- ized conformal prediction to provide distribution-free uncertainty quan- tification. Results demonstrate that hGWFR outperforms global func- tional regression in predictive accuracy and interval reliability, providing a robust tool for seismic hazard assessment.