Statistical Synchrosqueezing Transform and Its Application to Seismic Thin Interbed Analysis

Synchrosqueezing transform (SST) benefits from an instantaneous frequency (IF) estimator in the time-frequency (TF) domain, providing an energy-concentrated TF representation to describe the time-varying frequency of seismic signals. To enhance the concentration performance of SST, this article theoretically proposes a statistical SST (SSST) by constructing a spectrum-weighted IF estimator (SWIFE) in the short-time Fourier transform (STFT) domain. In this SSST, a linear chirp signal is introduced to better capture its chirp rate, and then the quadratic STFT spectra are weighted by a window-related weighting function. On this basis, two equations related to the IF and chirp rate are constructed to derive the SWIFE. Finally, the STFT coefficients are squeezed to the estimated IF trajectories by a frequency fixed-point iterative algorithm, thereby providing a more concentrated TF representation for multicomponent signals than existing advanced methods, while enabling the retrieval of each component. Two synthetic examples and one field seismic data on thin interbeds are utilized to demonstrate the effectiveness of the proposed SSST and show its ability to highlight the time-varying frequency features of seismic signals, which is a promising seismic data analysis tool, such as characterizing thin interbed thickness variations.