Time-Reassigned Modular High-Resolution Time–Frequency Analysis for Seismic Data and Its Application to Enhanced Denoising Performance

Time–frequency representation (TFR) is essential for analyzing the nonstationary characteristics of seismic signals, providing insights into transient features, such as amplitude modulations and phase shifts. Although time-reassigned methods, like the time-reassigned synchrosqueezing transform (TSST), second-order transient extracting transform (STET), and time-reassigned multisynchrosqueezing transform (TMSST), improve temporal resolution, they struggle to achieve optimal time–frequency localization and energy concentration, limiting their effectiveness in applications such as noise attenuation and subsurface characterization. To address these limitations, we propose the time-reassigned modular high-resolution TFR (TMHTFR), which enhances the reassignment process by accurately mapping time–frequency coefficients to the precise group delay (GD). Unlike previous methods that reassign coefficients to the vicinity of the GD, TMHTFR directly maps them to the precise GD, achieving sharper and more accurate TFRs. In addition, the proposed method is highly flexible and can be easily integrated with alternative GD estimation techniques. A key advantage of TMHTFR is its ability to enhance TF concentration while effectively reducing computational costs. Moreover, TMHTFR inherently produces a TFR with a lower rank structure, which improves its capability for noise separation and sparsity enforcement. To quantitatively assess TF concentration and energy compaction, we utilize Rényi entropy and the concentration measure (CM), confirming that TMHTFR generates a more structured and well-localized representation compared to conventional methods. Experimental validation on synthetic and real seismic data confirms that TMHTFR effectively attenuates random noise while preserving essential signal features, underscoring its potential as a powerful tool for seismic data processing.