Two-dimensional synchrosqueezing transform and its application to tight channel sandstone reservoir characterization

Spectral analyses can effectively highlight the morphological characteristics of tight-channel sandstone reservoirs, which are crucial development targets in the field of unconventional oil and gas. A majority of these methods focus on trace-by-trace analyses of seismic data without lateral constraints. However, they do not depict the morphological characteristics of the channels in detail. Therefore, this study proposes a novel time-frequency (TF) analysis (TFA) method: two-dimensional synchrosqueezing transform (TDSST). The TDSST introduces a space-time window to capture the lateral variation of seismic signals. Then, from a two-dimensional (2D) purely harmonic signal, the instantaneous frequency (IF) and instantaneous wavenumber (IK) estimation formulas were strictly derived in the two-dimensional short-time Fourier transform domain. Furthermore, we define a new twodimensional synchrosqueezing operator (TDSTO) that can squeeze the TF coefficients into the estimated IF and IK trajectories. Finally, the TDSST can effectively reflect the vertical and horizontal changes, and according to the relationship between the wave number and frequency, the wave number parameter can be determined by maximizing the energy of the TDSST. TDSST can provide a highly energy-concentrated TF representation (TFR) while allowing the reconstruction of signals. Compared to other TFA methods, TDSST can provide a more laterally continuous spectral decomposition that clearly describes tight-channel sandstone reservoirs, even in a strongly noisy environment. The reliability of TDSST is validated through the utilization of both synthetic model and seismic field data.