Instantaneous spectral attributes using scales in continuous-wavelet transform

Abstract

Abstract Instantaneous spectral properties of seismic data — center frequency, root-mean-square frequency, bandwidth — often are extracted from time-frequency spectra to describe frequency-dependent rock properties. These attributes are derived using definitions from probability theory. A time-frequency spectrum can be obtained from approaches such as short-time Fourier transform (STFT) or time-frequency continuous-wavelet transform (TFCWT). TFCWT does not require preselecting a time window, which is essential in STFT. The TFCWT method converts a scalogram (i.e., time-scale map) obtained from the continuous-wavelet transform (CWT) into a time-frequency map. However, our method includes mathematical formulas that compute the instantaneous spectral attributes from the scalogram (similar to those computed from the TFCWT), avoiding conversion into a time-frequency spectrum. Computation does not require a predefined window length because it is based on the CWT. This technique optimally decomposes a multiscale signal. For nonstationary signal analysis, spectral decomposition from CWT/TFCWT has better time-frequency resolution than STFT, so the instantaneous spectral attributes from CWT are expected to be better than those from STFT.