Functional Linear Models for the Analysis of Similarity of Waveforms

Abstract

In seismology methods based on waveform similarity analysis are adopted to identify sequences of events characterized by similar fault mechanism and propagation pattern. Seismic waves can be considered as spatially interdependent, three dimensional curves depending on time and the waveform similarity analysis can be configured as a functional clustering approach, on the basis of which the membership is assessed by the shape of the temporal patterns. For providing qualitative extraction of the most important information from the recorded signals, we propose the use of metadata, related to the waves, as covariates of a functional response regression model. The temporal patterns of this effects, as well as of the residual component, obtained after having taken into account the most relevant predictors, are investigated in order to detect a cluster structure. The implemented clustering techniques are based on functional data depth.