Asymmetric chirplet transform - Part 2: Phase, frequency, and chirp rate

An asymmetric chirplet transform, also called the asymmetric Gaussian chirplet model (AGCM), was recently introduced for fast and accurate extraction of important information from seismic signals. Unlike Fourier or wavelet transforms with fixed base functions, the AGCM is an adaptive sparse representation based on the physical parameters of the given data. The atoms of AGCM, so-called chirplets, display asymmetric oscillation-attenuation properties. The AGCM decomposes seismic signals into nonstationary compressed plane waves. The waves or atoms consist of two parts with seven physical parameters: the envelope and frequency parts. We have determined how to reconstruct the envelope part (e.g., envelope amplitude and arrival time) of the seismic data. We concentrate on the frequency part that involves three parameters: phase, frequency, and chirp rate. A Newton method with a step-size choice is established to deal with the highly oscillating frequency part of AGCM. The model parameters or coefficients in the transform domain may not only provide explicit physical interpretation (e.g., local phase of signal), but they can also be potentially used for feature extraction and other applications. Numerical results indicate excellent approximation results with good runtime performance. Physically reasonable parameter interpretation is demonstrated.