An Amplitude Preserving S-Transform for Seismic Data Attenuation Compensation

The S-transform (ST), as a time-frequency analysis tool, has been widely used, but the amplitude preserving property is a little poor near the boundary of the selected discrete signal. The reason lies that the summation of the product between the analytical window and the comprehensive window over the sliding step deviates from unity near the boundary in the discrete cases. In order to hold the amplitude preserving property for the discrete signal recovery analysis, an amplitude preserving S-transform (APST) is proposed based on a novel analytical window selection. First, lots of numerical tests are used to analyze the shortcomings of the ST near the boundary for the selected discrete signal and demonstrate the effectiveness and the validity of the proposed APST using the novel analytical window. After that, the proposed APST is used for seismic data attenuation compensation, during which the attenuation function is estimated based on the minimum phase assumption using a statistical variable-step hyperbolic smoothing method. Numerical examples on synthetic and field data demonstrate the validity of the proposed method using the seismogram and time-frequency spectrum comparisons. Besides, the proposed APST can be easily extended into a generalized ST which is more flexible compared with the ST, and it can also be used in seismology, remote sensing, and other related discrete signal analysis fields.