TY - JOUR

T1 - Reconstruction of seismic signals by the S-transform ridges

AU - Serdyukov, Aleksander S.

AU - Yablokov, Aleksander V.

AU - Azarov, Anton V.

AU - Shilova, Tatiana V.

N1 - Funding Information: The research was supported by Russian Science Foundation (project no. 18-77-00043). Publisher Copyright: © 2019 SEG

PY - 2019/8/10

Y1 - 2019/8/10

N2 - We have addressed the problem of seismic data frequency-time filtration based on the S-transform. The S-transform provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. The S-transform has been widely used in different seismic data-processing applications. The standard S-transform filtration method is based on its invertibility. In a sense of time localization, this method is not optimal, because the calculation of the inverse S-transform includes the time averaging. We propose an alternative filtration method which is based on the reconstruction of a signal by S-transform ridges. We approximate the Fourier phase spectrum of the reconstructed signal by the phase of S-transform ridge. We derive the integral equation which expresses the S-transform ridge amplitudes in terms of Fourier amplitude spectrum of the reconstructed signal. The introduced equation is solved to find the signal amplitude numerically, using truncated singular value decomposition. We get both the phase and amplitude off the signal. Thus, the signal can be extracted from the S-transform spectrum only by the ridges. We believe it is promising in a sense of maximum usage of time-localization properties of the S-transform during frequency-time filtration. The results of synthetic data processing confirm the promising prospects of the proposed method.

AB - We have addressed the problem of seismic data frequency-time filtration based on the S-transform. The S-transform provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. The S-transform has been widely used in different seismic data-processing applications. The standard S-transform filtration method is based on its invertibility. In a sense of time localization, this method is not optimal, because the calculation of the inverse S-transform includes the time averaging. We propose an alternative filtration method which is based on the reconstruction of a signal by S-transform ridges. We approximate the Fourier phase spectrum of the reconstructed signal by the phase of S-transform ridge. We derive the integral equation which expresses the S-transform ridge amplitudes in terms of Fourier amplitude spectrum of the reconstructed signal. The introduced equation is solved to find the signal amplitude numerically, using truncated singular value decomposition. We get both the phase and amplitude off the signal. Thus, the signal can be extracted from the S-transform spectrum only by the ridges. We believe it is promising in a sense of maximum usage of time-localization properties of the S-transform during frequency-time filtration. The results of synthetic data processing confirm the promising prospects of the proposed method.

UR - http://www.scopus.com/inward/record.url?scp=85121878852&partnerID=8YFLogxK

U2 - 10.1190/segam2019-3215756.1

DO - 10.1190/segam2019-3215756.1

M3 - Conference article

AN - SCOPUS:85121878852

SP - 4680

EP - 4684

JO - SEG Technical Program Expanded Abstracts

JF - SEG Technical Program Expanded Abstracts

SN - 1052-3812

T2 - Society of Exploration Geophysicists International Exposition and 89th Annual Meeting, SEG 2019

Y2 - 15 September 2019 through 20 September 2019

ER -