Seismic data analysis using local time-frequency decomposition

Many natural phenomena, including geologic events and geophysical data, are fundamentally nonstationary exhibiting statistical variation that changes in space and time. Time-frequency characterization is useful for analyzing such data, seismic traces in particular. We present a novel time-frequency decomposition, which aims at depicting the nonstationary character of seismic data. The proposed decomposition uses a Fourier basis to match the target signal using regularized least-squares inversion. The decomposition is invertible, which makes it suitable for analyzing nonstationary data. The proposed method can provide more flexible time-frequency representation than the classical S transform. Results of applying the method to both synthetic and field data examples demonstrate that the local time-frequency decomposition can characterize nonstationary variation of seismic data and be used in practical applications, such as seismic ground-roll noise attenuation and multicomponent data registration. INTRODUCTION Geological events and geophysical data often exhibit fundamentally nonstationary variations. Therefore, time-frequency characterization of seismic traces is useful for geophysical data analysis. A widely used method of time-frequency analysis is the short-time Fourier transform (STFT) (Allen, 1977). However, the window function limits the time-frequency resolution of STFT (Cohen, 1995). An alternative is the wavelet transform, which expands the signal in terms of wavelet functions that are localized in both time and frequency (Chakraborty and Okaya, 1995). However, because a wavelet family is built by restricting its frequency parameter to be inversely proportional to the scale, expansion coefficients in a wavelet frame may not provide precise enough estimates of the frequency content of waveforms, especially at high frequencies (Wang, 2007). Therefore, Sinha et al. (2005, 2009) developed a time-frequency continuous-wavelet transform (TFCWT) to describe time-frequency map more accurately than the conventional continuous-wavelet transform (CWT). The S transform (Stockwell et al., 1996) is another generalization of STFT, which extends CWT and