Improved W-Transform Incorporating Fast Matching Pursuit Decomposition

Abstract

Time-frequency analysis method is an effective tool to describe the relationship between the time and frequency of seismic signal. Accurate time-frequency results help to better delineate subsurface geological structures. S-transform (ST), due to its high resolution, is known as a kind of pragmatic time-frequency analysis tool in seismic signal processing. However, the center of the energy group estimated by the ST is shifted to the higher frequency. A recently proposed W-transform (WT), which brings in the dominant frequency, solves this problem to some extent. However, the dominant frequency calculated by the temporal average of the instantaneous frequency is unstable, which shows negative value sometimes. Therefore, an improved WT incorporating fast matching pursuit (WT-FMP) decomposition method is proposed to estimate the well-concentrated time-frequency distribution. It decomposes the seismic signal into a series of matched wavelets selected from an over-complete dictionary initially. Furthermore, the whole time-frequency distribution of the signal is generated by superposition of each wavelet’s WT coefficients. The proposed method helps to avoid the dependence on the instantaneous frequency and it owns higher resolution because the time-frequency map for signal is well localized using fast matching pursuit (FMP). Synthetic and field examples are utilized to validate the effectiveness of the proposed WT-FMP method. The results demonstrate its priority in providing more concentrated spectrum and revealing abundant stratigraphic and geological information.