Enhanced Ultra-Deep Seismic Low-Frequency Components via a Double-Parameter W-Transform

Ultra-deep seismic interpretation requires the full utilization of the low-frequency components of seismic signals. Compared to time-frequency analysis (TFA) methods such as wavelet transform and S-transform (ST), the W-transform (WT) method can improve the time resolution of the low-frequency band of the time-frequency (TF) spectra and highlight the low-frequency components. However, there is a nondifferentiable problem in the standard deviation function of WT, which causes the peak energy of time spectra to split at the dominant frequency. To address this problem, a new double-parameter WT (DWT) method, including time-varying dominant frequency, is proposed to overcome the defects of original WT. The parameter set of the transform is optimized using a TF distribution concentration measurement criterion and Rényi entropy, with the optimal parameter set being selected adaptively. Test results of synthetic data and field data show that the DWT eliminates the problem of spectral energy splitting at the dominant frequency. In addition, the focusing performance of different frequency components in the TF spectra is superior. The low-frequency band of the TF spectra exhibits higher time resolution, providing an effective means to highlight the low-frequency information of ultra-deep seismic signals.