TY - JOUR

T1 - Research Note: Reconstruction of seismic signals using S-transform ridges

AU - Serdyukov, Aleksander S.

AU - Azarov, Anton V.

AU - Yablokov, Aleksander V.

AU - Shilova, Tatiana V.

AU - Baranov, Valery D.

N1 - Funding Information: We are grateful for the comments by anonymous reviewer and associated editor that improved the manuscript. Aleksander S. Serdyukov, Anton V. Azarov and Aleksander V. Yablokov were supported by the Russian Science Foundation Grant #20‐77‐10023. Publisher Copyright: © 2021 European Association of Geoscientists & Engineers Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/5

Y1 - 2021/5

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 and 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 time averaging. We propose an alternative filtration method based on the reconstruction of a signal by S-transform ridges. We approximate the phase of the Fourier spectrum of the reconstructed signal using the phase of the S-transform ridge. We derive the integral equation, which expresses the S-transform ridge amplitudes in terms of the amplitudes of the Fourier spectrum of the reconstructed signal. The introduced equation is numerically solved to find the signal amplitude using the truncated singular value decomposition. From the results, we obtain both the phase and amplitude of the signal. Thus, the signal can be extracted from the S-transform spectrum only by the ridges. This finding is promising in terms of maximum usage of the time-localization properties of the S-transform during frequency–time filtration. The presented results of ground-roll attenuation from reflection seismic data demonstrate that the proposed S-transform ridge filtration method can be effective in practice.

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 and 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 time averaging. We propose an alternative filtration method based on the reconstruction of a signal by S-transform ridges. We approximate the phase of the Fourier spectrum of the reconstructed signal using the phase of the S-transform ridge. We derive the integral equation, which expresses the S-transform ridge amplitudes in terms of the amplitudes of the Fourier spectrum of the reconstructed signal. The introduced equation is numerically solved to find the signal amplitude using the truncated singular value decomposition. From the results, we obtain both the phase and amplitude of the signal. Thus, the signal can be extracted from the S-transform spectrum only by the ridges. This finding is promising in terms of maximum usage of the time-localization properties of the S-transform during frequency–time filtration. The presented results of ground-roll attenuation from reflection seismic data demonstrate that the proposed S-transform ridge filtration method can be effective in practice.

KW - Data processing

KW - Seismics

KW - Signal processing

UR - http://www.scopus.com/inward/record.url?scp=85099917202&partnerID=8YFLogxK

U2 - 10.1111/1365-2478.13069

DO - 10.1111/1365-2478.13069

M3 - Article

AN - SCOPUS:85099917202

VL - 69

SP - 891

EP - 900

JO - Geophysical Prospecting

JF - Geophysical Prospecting

SN - 0016-8025

IS - 4

ER -