Centroid-Oriented Extracting Transform and Its Application in Seismic Spectral Decomposition

Time-frequency (TF) analysis (TFA) is a vital spectral decomposition tool for reservoir characterization due to its superiority in analyzing nonstationary signals. Two newly developed TFA methods, the synchroextracting transform (SET) and transient-extracting transform (TET), provide a concentrated TF representation for seismic signals. However, the SET and TET are, respectively, only valid for harmonic signals with slow-varying instantaneous frequencies and transient signals of which the TF ridge almost parallels the frequency axis. This article proposes a centroid-oriented extracting transform (COET) to analyze mixed signals containing harmonic and transient features. First, we construct an objective function in the short-time Fourier transform (STFT) domain to link the most relevant signal features via the TF centroid. Then, the main direction of energy diffusion is defined by the TF centroid to separate the signal into harmonic and transient modes. Finally, a divide-and-conquer strategy is utilized to locally minimize the objective function in the frequency and time directions, respectively, thereby extracting the STFT coefficients at all optimal TF points while keeping the lossless reconstruction of the original signal. Such a COET provides both high time and frequency concentrations with strong noise immunity, as numerical signals elaborate. The application of field seismic data further indicates that the proposed COET clearly highlights the detailed information of different reservoir distributions, which is a promising tool for seismic spectral decomposition.