A Cascaded Synchrosqueezing Transform for Precise Analysis of Seismic Signal

Time-frequency (TF) analysis represents a potent tool for processing and interpreting seismic data. Synchrosqueezing transforms (SSTs) remarkably enhance frequency resolution by accumulating coefficients along the frequency axis. However, their TF resolution is related to their mother's TF transforms. The high-order Fourier-based SST (FSST) with a long window exhibits improved frequency resolution, albeit at the cost of mixing detailed frequency variations. Conversely, a high-order FSST with a short window provides enhanced time resolution but suffers from low-frequency resolution and component interference between multiple components of a complex signal. To ameliorate this, our study proposes a cascaded high-order FSST. Our proposed approach commences with a long-window high-order FSST to decompose a complicated signal into multiple components. Subsequently, a short-window high-order FSST is applied to each component. By summing the squeezed TF representations of all components, we generate a TF representation that boasts the improved TF resolution with the cost of involving multiple high-order FSSTs. The visual evaluation and sparsity measure are used to show our method's efficacy and TF resolution over common high-order FSST through a synthetic multicomponent signal (MCS) with two components. The wavelets interference would make the seismic signal's frequency component change. Therefore, further substantiation comes from two wavelet-interference-related examples: the field data example about cycle interbeds and an HST-induced seismic data example, wherein our proposed transform demonstrates its superior ability in precisely tracking subtle frequency variations with time and its advantages over common high-order FSST in extracting cycle thin-interbeds' thickness variation along depth and characterizing the HST speed.