Modelling and Simulation of Earthquake Ground Motion via Functional Series TARMA Models withWavelet Basis Functions

The present study explores non-stationary Functional Series Time-dependent AutoRegressive Moving Average (FS-TARMA) models with wavelet basis functions for the modelling and simulation of earthquake ground motion. FS-TARMA models constitute conceptual extensions of their conventional (stationary) counterparts, in that their parameters are time-dependent belonging to functional subspaces [

1

]. Wavelets, with their scaling and localization in time, comprise a promising functional basis for “fast” evolutions in the dynamics. The study focuses on the assessment of wavelet based FS-TARMA modelling and simulation for two California earthquake ground motion signals: an El Centro accelerogram recorded during the 1979 Imperial Valley earthquake, and a Pacoima Dam accelerogram recorded during the 1994 Northridge earthquake. A systematic analysis leads to a TARMA(2, 2) model for the El Centro case and a TARMA(3, 2) model for the Pacoima Dam case. Both models are formally validated and their analysis and simulation (synthesis) capabilities are demonstrated via Monte Carlo experiments focusing on important ground motion characteristics.

Figure 1

(a) 2-D plot of the El Centro accelerogram non-parametric STFT-based time-dependent PSD estimate, and (b) 2-D plot of the TARMA (2,2)

[2,2]

-based parametric Melard-Tjøstheim time-dependent PSD estimate.