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Seismic wavelet phase estimation by l1-norm minimization

GABRIEL R. GELPI1,2 ,  DANIEL O. PÉREZ1,3 ,  DANILO R. VELIS1
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1 Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, and CONICET, La Plata, Argentina.,
2 YPF Tecnología S.A., Av. Del Petróleo s/n, Berisso, Argentina.,
JSE 2019, 28(4), 393–411;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Gelpi, G.R., Pérez, D.O. and Velis, D.R., 2019. Seismic wavelet phase estimation by //- norm minimization. Journal of Seismic Exploration, 28: 393-411. A new method to estimate the phase of the wavelet when only seismic data is available is presented. Starting from the classical convolutional model of the seismic traces, the proposed technique is based in two hypotheses: (1) the wavelet phase can be adequately approximated by a constant; and (2) the series of reflection coefficients is non-Gaussian and/or sparse. Under these hypotheses, the deconvolution is viewed as an inverse problem regularized by the /;-norm. The optimum wavelet phase is then obtained by selecting the constant phase rotation that leads to the deconvolved trace with minimum /;-norm. We test the proposed method on synthetic and field data and we compare the results against those obtained by the classical method based on the Kurtosis maximization of the seismic data. The results show that the proposed technique is more accurate and reliable than the Kurtosis-based approach, especially when the effective data bandwidth is relatively poor and/or the non-Gaussianity hyphotesis is not fully satisfied.

Keywords
/
-norm
sparse-deconvolution
wavelet
phase
Kurtosis
FISTA
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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