A SECOND‐ORDER SYNCHROSQUEEZING S‐TRANSFORM AND ITS APPLICATION IN SEISMIC SPECTRAL DECOMPOSITION

Abstract

AbstractThe Synchrosqueezing S‐transform (SSST) is a novel approach for time‐frequency (T‐F) representation of non‐stationary signals. By “squeezing” T‐F spectrum of the S‐transform (ST) of a signal, the SSST can obtain a high‐resolution T‐F spectrum. However, when the phase of a signal varies non‐linearly with time, the instantaneous frequency (IF) of the signal calculated by the SSST would be inaccurate, causing reduction of the resolution of the T‐F spectrum. In order to improve its performance in imaging such signals, we modify the formula of IF with the help of the second‐order partial derivatives of time and frequency, and propose a second‐order Synchrosqueezing S‐transform (SSST2nd). Synthetic examples show that the SSST2nd not only has obviously higher resolution than commonly used T‐F transforms, but also images the signals of which the IFs vary quadratically or sinusoidally with time better than the SSST. We apply the SSST2nd to perform spectral decomposition of seismic data for natural gas exploration. The results illustrate that the SSST2nd can be used to well detect frequency spectral anomalies correlated with natural gas accumulations. Therefore, it can be concluded that the SSST2nd is a good potential technique for seismic interpretation.