An Energy-Concentrated Transform for Improved Time-Frequency Representation of Seismic Signals

Time-frequency (TF) analysis is a useful tool for seismic signal processing, where reliably representing the signal's TF distribution is essential for geological interpretation. However, the traditional short-time Fourier transform (STFT) offers an ambiguous TF representation. While synchroextracting methods improve TF localization, they distort the time-width and bandwidth of seismic signals, which are crucial for applications. To address this issue, we propose a novel TF analysis method, the energy-concentrated transform (ECT), aimed at enhancing TF localization while preserving the essential time-width and bandwidth features of seismic signals. First, we analyze the limitations of the STFT and synchroextracting methods. Next, we introduce an energy suppression operator that concentrates STFT's diffused spectral energy, aligning it with the signal's intrinsic time-width and bandwidth. Additionally, an energy recovery operator is proposed to ensure the consistency of spectral energy with the STFT spectrum. Numerical examples demonstrate the effectiveness of the ECT in enhancing TF localization, improving noise immunity, and preserving critical TF features, making it a promising tool for TF representation in seismic signals.