Abstract
The traditional compressed sensing method for improving resolution is realized in the frequency domain. This method is affected by noise, which limits the signal-to-noise ratio and resolution, resulting in poor inversion. To solve this problem, we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics. Moreover, the reconstruction of the sparse reflection coefficient is implemented by the mixed L1_L2 norm algorithm, which converts the L0 norm problem into an L1 norm problem. Additionally, a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error. The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods. It not only has better denoising and smoothing effects but also improves the recognition accuracy of thin interbeds. The actual data application also shows that the new method can effectively expand the seismic frequency band and improve seismic data resolution, so the method is conducive to the identification of thin interbeds for beach-bar sand reservoirs.
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References
Bai, L., Lu, H., and Liu, Y., 2020, High-efficiency observations: compressive sensing and recovery of seismic waveform data: Pure and Applied Geophysics, 177(1), 469–485.
Baraniuk, R. G., 2007, Compressive sensing: IEEE Signal Processing Magazine, 24(4), 118–121.
Beck, A., and Teboulle, M., 2009, A fast iterative shrinkage-thresholding method for linear inverse problem: SIAM Journal Imaging Sciences, 2(1), 183–202.
Candes, E. J., and Romberg, J., 2007, Sparsity and incoherence in compressive sampling: Inverse Problems, 23(3), 969–985.
Cao, J. J., Wang, Y. F., and Yang, C. C., 2012, Seismic data restoration based on compressive sensing using regularization and zero-norm sparse optimization: Chinese Journal of Geophysics (in Chinese), 55(2), 239–251.
Chai, X., Tang, G., Peng, R., et al., 2018, The linearized Bregman method for frugal full-waveform inversion with compressive sensing and sparsity-promoting: Pure and Applied Geophysics, 175(3), 1085–1101.
Chen, S. S., and Saunders, M. A., 2001, Atomic decomposition by basis pursuit: SIAM Review, 43(1), 129–159.
Chopra, S., Castagna, J., and Portniaguine, O., 2006, Thin-bed reflectivity inversion: 76th Annual International Meeting, SEG, Expanded Abstracts, 2057–2061.
Ding, Y., Du, Q., Liu, L., et al., 2019, Low-Frequency Compensation of Seismic Data Based on Compressed Sensing: 81st EAGE Conference and Exhibition, European Association of Geoscientists & Engineers, 1, 1–5.
Donoho, D. L., 2006, Compressed sensing: IEEE Transactions on Information Theory, 52(4), 1289–1306.
Figueiredo, M. A. T., Nowak, R. D., and Wright, S. J., 2007, Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems: IEEE Journal of Selected Topics in Signal Processing, 1(4), 586–597.
Gan, S., Wang, S., Chen, Y., et al., 2016. Compressive sensing for seismic data reconstruction via fast projection onto convex sets based on seislet transform: Journal of Applied Geophysics, 130, 194–208.
Han, L., Zhang, Y., and Han, L., 2012, Compressed sensing and sparse inversion based low-frequency information compensation of seismic data: Journal of Jilin University (Earth Science Edition) (in Chinese), 42(3), 259–264.
Kong, D., and Peng, Z., 2017, Seismic reflectivity inversion using spectral compressed sensing: 2nd IEEE International Conference on Computer & Communications, 1024–1027.
Li, X., Aravkin, A. Y., van Leeuwen, T., et al., 2012, Fast randomized full-waveform inversion with compressive sensing: Geophysics, 77(3), A13–A17.
Mallat, S. G., and Zhang, Z., 1993, Matching pursuits with time-frequency dictionaries: IEEE Transactions on Signal Processing, 41(12), 3397–3415.
Puryear, C. I., and Castagna, J. P., 2006, An algorithm for calculation of bed thickness and reflection coefficients from amplitude spectrum: 76th Annual International Meeting, SEG, Expanded Abstracts, 1767–1770.
Parent, A., Morin, M., and Lavigne, P., 1992, Propagation of super-Gaussian field distributions: Optical and Quantum Electronics, 24(9), S1071–S1079.
Robinson, E. A., 1967, Predictive decomposition of time series with application to seismic exploration: Geophysics, 32(3), 418–484.
Song, H. H., 2015, Study on fast fixed point algorithm and its application based on compressed sensing, MS Thesis, Nanjing University of Posts and Telecommunications, Nanjing.
Song, W. Q., and Wu, C. D., 2017, Seismic data resolution improvement based on compressed sensing: Oil Geophysical Prospecting(in Chinese), 52(2), 214–219+191.
Tropp, J. A., and Gilbert, A. C., 2007, Signal recovery from random measurements via orthogonal matching pursuit: IEEE Transactions on Information Theory, 53(12), 4655–4666.
Tsaig, Y., and Donoho, D. L., 2006, Extensions of compressed sensing: Signal Processing, 86(3), 549–571.
Widess, M. B., 1973, How thin is a thin bed?, Geophysics, 38(6), 1176–1180.
Zhang, R., and Castagna, J., 2011, Seismic sparse-layer reflectivity inversion using basis pursuit decomposition: Geophysics, 76(6), R147–158.
Zhang, R., and Zhang, K., 2016, Compressed sensing Inversion for thin-bed resolution in depth domain: SPG/SEG 2016 International Geophysical Conference, 516–518.
Zhou, W., 2013, L1-norm minimization algorithms and applications: MS Thesis, South China University of Technology, Guangzhou.
Zibulevsky, M., and Elad M., 2010, L1–L2 optimization in signal and image processing: IEEE Signal Processing Magazine, 27(3), 76–88.
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This work was supported by the National Science and Technology Major Project (No. 2016ZX05006-002 and 2017ZX05072-001).
Liu Yang received his BS (2016) in Geophysics from China University of Petroleum (East China), he is currently studying for a master’s degree in the Department of Geophysics at China University of Petroleum (East China). His interest is high-resolution seismic data processing. Email: 522927317@qq.com
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Liu, Y., Zhang, JH., Wang, YG. et al. An improved Gaussian frequency domain sparse inversion method based on compressed sensing. Appl. Geophys. 17, 443–452 (2020). https://doi.org/10.1007/s11770-020-0813-y
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DOI: https://doi.org/10.1007/s11770-020-0813-y