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 reflection. We use spectral simulation methods to fit 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 field data verify that the proposed method can recover the amplitude spectrum of the strata reflectivity, 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.
Similar content being viewed by others
References
Bracewell, R. N., 2000, The Fourier integral and Its Applications, 3rd ed., [M]. Boston: McGraw-Hill, U. S. A, 256–260.
Carlos, A. M., and Margrave, G. F., 2005, Phase correction in Gabor deconvolution: 75th Annual International Meeting, SEG, Expanded Abstracts, 2173–2176.
Chen, B. Y., Chen, M. W., and Yi, W. Q., 1997, Time and space and subsection frequency phase correction: Oil Geophysical Prospecting (in Chinese), 32(1), 103–108.
Claerbout, J. F., 1977, Parsimonious deconvolution: Stanford Exploration Project, 13, 1–9.
Cohen, L., 1995, Time-Frequency Analysis: Theory and Applications [M]. N j: Prentice Hall, Inc., U. S. A, 25–27.
Durak, L., and Arikan, O., 2003, Short-time Fourier transform: two fundamental properties and optimal implementation: IEEE Trans. on signal Processing, 51(5), 1231–1242.
Ferber, R., 2005, A filter bank solution to absorption simulation and compensation: 75th Annual International Meeting, SEG, Expanded Abstracts, 2170–2172.
Gabor, D., 1946, Theory of Communication: Journal of IEEE, 93(3), 429–457.
Gao, J. H., Chen, W. C., Li, Y. M., and Tian, F., 2003, Generalized S transform and seismic response analysis of thin interbeds: Chinese Journal of Geophysics (in Chinese), 46(4), 526–532.
Gao, S. W., Zhou, X. Y., and Cai, J. M., 2001, Surfaceconsistent phase correction for reflection wave: Oil Geophysical Prospecting (in Chinese), 36(4), 480–487.
Levy, S., and Oldenburg, D. W., 1982, The deconvolution of phase-shifted wavelets: Geophysics, 47(9), 1285–1294.
Levy, S., and Oldenburg, D. W., 1987, Automatic phase correction of common-midpoint stacked data: Geophysics, 52(1), 51–59.
Li, K. P., Li, Y. D., and Zhang, X. G., 2000, A method to compensation earth filtering based on wavelet packet: Chinese Journal Of Geophysics, 43(4), 542–549.
Li, Q. Z., 1994, The road to Precision Prospecting—High Resolution Seismic Prospecting System Analysis (in Chinese).: Petroleum Industry Press, Beijing, 89–92.
Li, T. C., He, Y. M., Sun, J., Xu, Z. Q., Liu, J. M., Qin, D. M., and Zhu, J. M., 2010, Research and application of frequency amplitude compensation by frequency decomposition based on generalized S transformation: Computing Techniques for Geophysical and Geochemical exploration(in Chinese), 36(6), 583–586.
Liu, X. W., Nian, J. B., and Liu, H., 2006, Generalized S-transform based seismic attenuation analysis: Progress in Exploration Geophysics (in Chinese), 29(1), 14–19.
Ma, J. Q., Li, Q. C., and Wang, M. D., 2010, Stratigraphic absorption-compensation based on the generalized S-transform: Coal Geology and Exploration (in Chinese), 38(4), 65–68.
Mansinha, L., Stockwell, R. G., and Lowe, R. P., 1997, Pattern analysis with two dimensional spectral localization: Application of two dimensional S-transform: Physics Section A, 239(3), 286–295.
Margrave, G. F., 1998, Theory of nonstationary linear filtering in the Fourier domain with application to timevariant filtering: Geophysics, 63, 244–259.
Margrave, G. F., and Lamoureux, M. P., 2001, Gabor deconvolution: CREWES Research Report. 13, 241–276.
McFadden, P. D., Cook, J. G., and Forster, L. M., 1999, Decomposition of gear vibration signals by generalized S-transform: Mechnical Systems and Signal Process, 13(4), 691–707.
Mirko van der Baan and Fomel, S., 2009, Nonstationary phase estimation using regularized local kurtosis maximization: Geophysics, 74(6), A75–A80.
Mirko van der Baan, 2012, Bandwidth enhancement: Inverse Q filtering or time-varying wiener deconvolution: Geophysics, 77(4), V133–V142.
Peng, C., Zhu, S. J., Sun, J. K., Lin, S. W., Chang, X., and Zhao, J. M., 2007, Dynamic seismic wavelet estimation: Petroleum Geology and Oilfield Development in Daqing (in Chinese), 26(5), 125–128.
Pinnegar, C. R., and Mansinha, L., 2003, The S-transform with windows of arbitrary and varying shape: Geophysics, 68(1), 381–385.
Pinnegar, C. R., and Mansinha, L., 2003, Time local spectral analysis for non-stationary time series: the S-transform for noisy signals: Fluctuation and Noise Letters, 3(3), 357–364.
Ricker, N. H., 1977, Transient waves in visco-elastic media: Elsevier Science Publ Co, 123–136.
Rioul, O., and Vetterli, M., 1991, Wavelets and signal processing: IEEE Signal Processing, 8(4), 14–38.
Rosa, A. L. R., and Ulrych, T. J., 1991, Processing via spectral modeling: Geophysics, 56(8), 1244–1251.
Song, Z. P, Li, J. J., and Zhang, L. P., 2004, Pre-stack constant phase correction: Petroleum Geology and Oilfield Development in Daqing (in Chinese), 23(2), 69–70.
Stockwell, R. G., Mansinha, L., and Lowe, R. P., 1996, Localization of the complex spectrum: the S transform: IEEE Transactions on signal processing, 44(4), 998–1001.
Sun, C. Y., 2000, Spectrum modeling method and its application to seismic resolution improvement: Oil Geophysical Prospecting (in Chinese), 35(12), 27–34.
Wang, Y. H., 2002, A stable and efficient approach of inverse Q filtering: Geophysics, 67(2), 657–663.
Wang, Y. H., 2006, Inverse Q filtering for seismic resolution enhancement: Geophysics, 71(3), 51–61.
Wang, Y. H., 2007, Seismic time-frequency spectral decomposition by matching pursuit: Geophysics, 72, V13–V20, doi:10.1190/1.2387109.
Wang, Y. H., 2010, Multichannel matching pursuit for seismic trace decomposition: Geophysics, 75, V61–V66.
Yu, S. P., 1993, The High Resolution Seismic Processing (in Chinese) [M]. Beijing: Petroleum In dustry Press, China, 162–164.
Yuan, X. G., Song, S. G., Zhang, J. G., Hou, M. Z., and Yang, J. H., 2001, Treatment of stacked seismic data with multiresolution frequency-amplitude compensation: Journal of Central South University of Technology (in Chinese), 32(3), 224–226.
Zhao, B., Yu, S. P., Nie, X. B., and Huang, X. N., 1996, Spectral-modeled deconvolution and its application: Oil Geophysical Prospecting (in Chinese), 31(1), 101–115.
Zhou, X. Y., 1989, Constant phase correction: Oil Geophysical Prospecting (in Chinese), 24(2), 119–129.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research is supported by the National Natural Science Foundation of China (No. 41204091), New Teachers’ Fund for Doctor Stations, the Ministry of Education (No. 20105122120001), and Science and Technology Support Program from Science and Technology Department of Sichuan Province (No. 2011GZ0244).
Zhou Huai-Lai is an associate professor in the College of Geophysics, Chengdu University of Technology. He received his PhD in Earth Exploration and Information Techniques, from Chengdu University of Technology in 2009. He was a postdoctoral research fellow at the Institute of Sedimentary Geology in Chengdu University of Technology from 2010 to 2012. He is presently a postdoctoral research fellow in the University of Oklahoma, USA under the auspices of the China Scholarship Council. His research work is mainly on seismic data processing methods, seismic modeling and imaging, and inversion methods.
Wang Jun is a lecturer at the Institute of Sedimentary Geology, Chengdu University of Technology. His teaching and research interests are in Geology and Sedimentology.
Rights and permissions
About this article
Cite this article
Zhou, HL., Wang, J., Wang, MC. et al. Amplitude spectrum compensation and phase spectrum correction of seismic data based on the generalized S transform. Appl. Geophys. 11, 468–478 (2014). https://doi.org/10.1007/s11770-014-0456-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11770-014-0456-y