Generation of critical aftershocks using stochastic neural networks and wavelet packet transform

This paper proposes a methodology using wavelet packet transform, principal component analysis, and neural networks in order to generate artificial critical aftershock accelerograms which are compatible with the response spectra. This procedure uses the learning abilities of neural networks, principal component analysis as a dimension reduction technique, and decomposing capabilities of wavelet packet transform on consecutive earthquakes. In fact, the proposed methodology consists of two steps and expands the knowledge of the inverse mapping from mainshock response spectrum to aftershock response spectrum and aftershock response spectrum to wavelet packet transform coefficients of the aftershocks. This procedure results in a stochastic ensemble of response spectra of aftershock (first step) and corresponding wavelet packet transform coefficients (second step) which are then used to generate the aftershocks through applying the inverse wavelet packet transform. Finally, in order to demonstrate the effectiveness of the proposed method, three examples are presented in which recorded critical successive ground motions are used to train and test the neural networks.