The optimal fractional S transform of seismic signal based on the normalized second-order central moment

• We propose a new fractional S transform method.
• We introduce the normalized second-order central moment algorithm to get optimal order.
• This proposed method can rapidly obtain better precise seismic spectral decomposition results than S transform.

As the extension of time-bandwidth product (TBP) in the fractional domain, the generalized time-bandwidth product (GTBP) provides a rotation-independent measure of compactness. A new fractional S transform (FrST) is proposed to avoid missing the physical meaning of the fractional time–frequency plane. FrST is based on the GTBP criterion and the time–frequency rotation property of fractional Fourier transform (FrFT). In addition, we introduce the normalized second-order central moment (NSOCM) calculation method to determine the optimal order. The optimal order searching process can be converted into the NSOCM calculation. Compared with TBP search algorithms, the NSOCM approach has higher computational efficiency. The qualitative advantage of the NSOCM approach in the optimal order selection is demonstrated by a series of model tests. The optimal FrST based on NSOCM (OFrST) can produce more compact time–frequency support than the S transform. The real seismic data spectral decomposition results show that the proposed algorithm can obtain single-frequency visualization with better time-frequency concentration, thereby enhancing the precision of reservoir prediction.