An Efficient Amplitude-Preserving Generalized S Transform and Its Application in Seismic Data Attenuation Compensation

The time-frequency analysis tools, which are very useful for anomaly identification, reservoir characterization, seismic data processing, and interpretation, are widely used in discrete signal analysis. Among these methods, the generalized S transform (GST) is more flexible, because its analytical window can be self-adjusted according to the local frequency components of the selected discrete signal, besides there exist another two adjustable parameters to make it superior to the S transform (ST). But the amplitude-preserving ability is a little poor near the boundary because the analytical windows do not satisfy the partition of unity, which is a sufficient condition for amplitude-preserving time-frequency transforms. In order to make the GST with the amplitude-preserving ability, we first design a new analytical window, and then propose an amplitude-preserving GST (APGST), but with a higher computational cost. To accelerate the APGST, we provide two strategies: the 3$\sigma$ criterion in the probability theory is introduced to accelerate the analytical windows summation and a convolution operator is derived to accelerate the time integral or summation, which generates an efficient APGST (EAPGST). Finally, the proposed EAPGST is used for seismic data attenuation compensation to improve the vertical resolution. Detailed numerical examples are used to demonstrate the validity of the proposed EAPGST in amplitude preserving and high efficiency. Field data attenuation compensation result further proves its successful application in improving the vertical resolution. Besides, the proposed EAPGST can be easily extended into other applications in discrete signal analysis, and remote-sensing and seismology fields.