Abstract
Diffractions carry meaningful information on subsurface discontinuities and are regarded as effective tools for high-resolution seismic exploration. However, diffractions often behave as weak events and, therefore, are masked by strong specular reflections. In this study, the diffraction and reflection behaviors in common image gathers have been elucidated. Fortunately, diffractions are observed to be kinematically different from reflections in dip-angle gathers. Under a suitable velocity, diffractions appear as flat events, whereas reflections appear as curves with stationary phase apexes. Therefore, the diffraction energy has a wide and nearly uniform distribution along the flat events, while the reflection energy is concentrated in the Fresnel zone with the stationary phase point. Consequently, a single-order weight function was proposed and tested by measuring the difference between an individual sample and the mean of the entire data set to eliminate the reflection energy. It is observed that the weight function often leads to a reflection residual, if it is based only on the zero-order amplitude information. Therefore, first-order derivative information is used to build the weight function which is also called the double-order weight function, to further suppress reflections and highlight weak diffractions. Synthetic and field data applications demonstrate the feasibility and effectiveness of the proposed weight function in imaging subsurface discontinuities.
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References
Bakhtiari, R., Schwarz, B., Gajewski, D., & Vanelle, C. (2018). Common-reflection-surface-based pre-stack diffraction separation and imaging. Geophysics, 83(1), S47–S55.
Berkovitch, A., Belfer, L., Hassin, Y., & Landa, E. (2009). Diffraction imaging by multi-focusing. Geophysics, 74(6), WCA75–WCA81.
Berryhill, J. R. (1977). Diffraction response for nonzero separation of source and receiver. Geophysics, 42(6), 1158–1176.
Dell, S., & Gajewski, D. (2011). Common-reflection-surface-based workflow for diffraction imaging. Geophysics, 76(5), S187–S195.
Fomel, S. (2002). Applications of plane-wave destruction filters. Geophysics, 67(6), 1946–1960.
Fomel, S., Landa, E., & Taner, M. T. (2007). Poststack velocity analysis by separation and imaging of seismic diffractions. Geophysics, 72(6), U89–U94.
Forel, D., Benz, T., & Pennington, W. D. (2005). Seismic data processing with seismic unix: A 2D seismic data processing primer. SEG.
Gong, X. B., Yu, C. X., & Wang, Z. H. (2016). Separation of pre-stack seismic diffractions using an improved sparse apex-shifted hyperbolic Radon transform. Exploration Geophysics, 48, 476–484.
Hubral, P., Schleicher, J., & Tygel, M. (1996). A unified approach to 3-D seismic reflection imaging, part I: Basic concepts. Geophysics, 61, 742–758.
Karimpouli, S., Malehmir, A., Hassani, H., Khoshdel, H., & Nabi-Bidhendi, M. (2015). Automated diffraction delineation using an apex-shifted Radon transform. Journal of Geophysics and Engineering, 12, 199–209.
Keller, J. B. (1962). Geometrical theory of diffraction. Journal of the Optical Society of America, 52, 116–130.
Khaidukov, V., Landa, E., & Moser, T. J. (2004). Diffraction imaging by focusing-defocusing: An outlook on seismic superresolution. Geophysics, 69(6), 1478–1490.
Klokov, A., & Fomel, S. (2012). Separation and imaging of seismic diffractions using migrated dip-angle gathers. Geophysics, 77(6), S131–S143.
Kozlov, E., Barasky, N., & Korolev, E. (2004). Imaging scattering objects masked by specular reflections. In 74th Annual International Meeting, SEG, Expanded Abstracts, pp. 1131–1134.
Krey, T. (1952). The significance of diffraction in the investigation of faults. Geophysics, 17, 843–858.
Laubach, S., Marrett, R., & Olson, J. (2000). New directions in fracture characterization. The Leading Edge, 19, 704–711.
Li, C. J., Zhao, J. T., Peng, S. P., Cui, X. Q., & Lin, P. (2020). Separating and imaging diffractions of seismic waves in the full-azimuth dip-angle domain. Journal of Geophysics and Engineering, 17, 339–356.
Li, C. J., Zhao, J. T., Peng, S. P., & Cui, X. Q. (2021). Prestack diffraction separation in the common virtual source gather. Geophysics, 86(2), 1MA-W19.
Li, C. J., Zhao, J. T., Peng, S. P., & Zhou, Y. X. (2021). Diffraction imaging using a mathematical morphological filter with a time-varying structuring element. Geophysics, 86(3), A27-WB57.
Liu, L., Vincent, E., Ji, X., Qin, F., & Luo, Y. (2016). Imaging diffractors using wave-equation migration. Geophysics, 81(6), S459–S468.
Lin, P., Peng, S. P., Zhao, J. T., & Cui, X. Q. (2020). Diffraction separation and imaging using multichannel singular-spectrum analysis. Geophysics, 85(1), V11–V24.
Lin, P., Peng, S. P., Zhao, J. T., Cui, X. Q., & Wang, H. H. (2018). L1-norm regularization and wavelet transform: An improved plane-wave destruction method. Journal of Applied Geophysics, 148, 16–22.
Moser, T. J., & Howard, C. B. (2008). Diffraction imaging in depth. Geophysical Prospecting, 56, 627–641.
Paffenholz, J., McLain, B., Zaske, J., Keliher, P. J. (2002). Subsalt multiple attenuation and imaging. In Observations from the Sigsbee2B synthetic dataset: SEG Technical Program Expanded Abstracts, pp. 2122–2125.
Peng, S. P., & Zhang, J. P. (2007). Engineering geology for underground rocks. Springer.
Schwarz, B. (2019). Coherent wavefield subtraction for diffraction separation. Geophysics, 84(3), V157–V168.
Yu, C., Zhao, J., Wang, Y., Wang, C., & Geng, W. (2017). Separation and imaging diffractions by a sparsity-promoting model and subspace trust-region algorithm. Geophysical Journal International, 208, 1756–1763.
Zhao, J. T., Peng, S. P., Du, W. F., & Li, X. T. (2016). Diffraction imaging method by Mahalnobis-based amplitude damping. Geophysics, 81(6), S399–S408.
Zhao, J. T., Sun, X. L., Peng, S. P., Wei, W., & Liu, T. (2019). Separating pre-stack diffractions with SVMF in the flattened shot domain. Journal of Geophysics and Engineering, 16, 389–398.
Zhao, J. T., Yu, C. X., Peng, S. P., & Li, C. J. (2020). 3D diffraction imaging method using low-rank matrix decomposition. Geophysics, 85(1), S1–S10.
Zhu, X., & Wu, R. S. (2010). Imaging diffraction points using the local image matrices generated in pre-stack migration. Geophysics, 75(1), S1–S9.
Acknowledgements
This research is supported by the National Natural Science Foundation of China (Grant nos. 42022031, 41874157), National Key Research and Development Program of China (Grant no. 2020YFE0201300), Fundamental Research Funds for the Central Universities (Grant no. 2020YQMT01, 2021YQDC10), 111 Project (No. B18052), China Postdoctoral Science Foundation (Grant no. 2021M693426). We thank Peng Research Group in CUMTB for support of this work. We express great appreciation to the anonymous reviewers and editors for promotion of this paper.
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Li, C., Peng, S., Lin, P. et al. Imaging Diffractions Using a Double-Order Weight Function. Pure Appl. Geophys. 179, 1053–1067 (2022). https://doi.org/10.1007/s00024-022-02967-4
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DOI: https://doi.org/10.1007/s00024-022-02967-4