Amplitude spectrum compensation and phase spectrum correction of seismic data based on the generalized S transform

Abstract

We propose a method for the compensation and phase correction of the amplitude spectrum based on the generalized S transform. The compensation of the amplitude spectrum within a reliable frequency range of the seismic record is performed in the S domain to restore the amplitude spectrum of refl ection. We use spectral simulation methods to fi t the time-dependent amplitude spectrum and compensate for the amplitude attenuation owing to absorption. We use phase scanning to select the time-, space-, and frequencydependent phases correction based on the parsimony criterion and eliminate the residual phase effect of the wavelet in the S domain. The method does not directly calculate the Q value; thus, it can be applied to the case of variable Q. The comparison of the theory model and fi eld data verify that the proposed method can recover the amplitude spectrum of the strata refl ectivity, while eliminating the effect of the residual phase of the wavelet. Thus, the wavelet approaches the zero-phase wavelet and, the seismic resolution is improved.

A time-varying wavelet phase extraction method using the wavelet amplitude spectra

“…First, time-varying wavelet amplitude spectra are estimated by using the time-frequency spectral modelling method, the theory of which was described in the literatures of Zhou et al (2014) and Dai, Wang, Li, Zhang, and Tan (2016), and that is to say A(t + t, ω) and A(t, ω) in equation 11have been extracted.…”

Stockwell-like frames for Sobolev spaces

“…The time frequency method which is behind the construction of Stockwell frames is the S-transform. The S-transform has been studied in several papers both from an applied point of view (see [8,26]) and a theoretical one (see [15,20]); it can be seen as an hybrid between the Continuous Wavelet Transform and the Short Time wavelet transform, see [13,24]. This hybrid behavior can be described also in terms of representation theory, indeed, the Continuous Wavelet Transform hides a representation of the affine group and the Short Time Fourier Transform is related to the Heisemberg group, while the S-transform is essentially represented by the affine Weyl Heisemberg group, see [19,20] and also [6,16] for other applications of the affine Weyl Heisember group.…”