Instantaneous spectral attributes using scales in continuous-wavelet transform

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 [Formula: see text] has better time-frequency resolution than STFT, so the instantaneous spectral attributes from CWT are expected to be better than those from STFT.

Research on the Influence Law and Suppression Methods of Seismic Wavelet Time-varying Nature on Seismic Data Processing

“…Wavelet transform, S transform and generalized S transform are the main methods used for compensation [7,8].…”

Application of the empirical mode decomposition and wavelet transform to seismic reflection frequency attenuation analysis

“…Reine et al (2009) found that variable-window time-frequency transforms such as continuous-wavelet transform (CWT) shows better robustness and accuracy for attenuation measurements than fixed-window transforms. Spectral decomposition from CWT has better time-frequency resolution than short-time Fourier transform (STFT), so the instantaneous spectral attributes from Wavelet transform are expected to be better than those from STFT (Sinha et al, 2009).…”

“…From this wavelet transform the instantaneous frequency of every scale of the real signal is obtained. Wavelet transform provides a natural window for signals that requires high time resolution at high frequencies and high frequency resolution at low frequencies based on the dilation property of a wavelet and does not require preselecting a time window, which is essential in STFT (Sinha et al, 2009). The instantaneous attributes obtained by wavelet analysis have certain effects on the analysis of non-stationary signals such as edge detection (see, for example, Aydin et al, 1996;Schmeelk, 2005) and image compression (see, for example, Lewis and Knowles, 1992;Boix and Cantó, 2010), the time-frequency distribution in time series (see, for example, Farge, 1992), fault diagnosis (see, for example, Jena and Panigrahi, 2012) and lithological characteristics identification (see, for example, Perez-Muñoz et al, 2013) and gas detection(see, for example, Kazemeini et al, 2009).…”

Spectral balancing GPR data using time-variant bandwidth in the t-f domain

“…Bradford and Wu ͑2007͒ apply wavelet decomposition to transform GPR data in the t-f domain. Sinha et al ͑2009͒ present an alternative wavelet transform ͑WT͒, which holds real promise for geophysical data analysis. Here, we use the S-transform, which offers the resolution of WT along with an important advantage of STFT, namely, the accurate estimation of both amplitude and phase ͑Stockwell, 2007͒.…”