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APPLIED GEOPHYSICS  2017, Vol. 14 Issue (1): 87-95    DOI: 10.1007/s11770-017-0607-z
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3D simultaneous seismic data reconstruction and noise suppression based on the curvelet transform
Zhang Hua1, Chen Xiao-Hong2, and Zhang Luo-Yi1
1. State Key Laboratory Breeding Base of Nuclear Resources and Environment, East China University of Technology,  Nanchang 330013, China.
2. National Engineering Laboratory for Offshore Oil Exploration, China University of Petroleum (Beijing), Beijing 102249, China.
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Abstract Seismic data contain random noise interference and are affected by irregular subsampling. Presently, most of the data reconstruction methods are carried out separately from noise suppression. Moreover, most data reconstruction methods are not ideal for noisy data. In this paper, we choose the multiscale and multidirectional 2D curvelet transform to perform simultaneous data reconstruction and noise suppression of 3D seismic data. We introduce the POCS algorithm, the exponentially decreasing square root threshold, and soft threshold operator to interpolate the data at each time slice. A weighing strategy was introduced to reduce the reconstructed data noise. A 3D simultaneous data reconstruction and noise suppression method based on the curvelet transform was proposed. When compared with data reconstruction followed by denoizing and the Fourier transform, the proposed method is more robust and effective. The proposed method has important implications for data acquisition in complex areas and reconstructing missing traces.
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Key wordscurvelet transform   data reconstruction   three-dimensional denoizing   projections-onto-convex-set algorithm     
Received: 2016-04-25;
Fund:

This research work was sponsored by the National Natural Science Foundation of China (Nos. 41304097 and 41664006), the Natural Science Foundation of Jiangxi Province (No. 20151BAB203044), the China Scholarship Council (No. 201508360061), and Distinguished Young Talent Foundation of Jiangxi Province (2017).

Cite this article:   
. 3D simultaneous seismic data reconstruction and noise suppression based on the curvelet transform[J]. APPLIED GEOPHYSICS, 2017, 14(1): 87-95.
 
[1] Abma, R., and Kabir, N., 2006, 3D interpolation of irregular data with a POCS algorithm: Geophysics, 71(5), E91−E97.
[2] Bregman, L., 1965, The method of successive projection for finding a common point of convex sets: Soviet Math, 6(3), 688−692.
[3] Cao, J. J., and Wang, B. F., 2015, An improved projection onto convex sets method for simultaneous interpolation and denoising: Chinese J. Geophys (in Chinese), 58(8), 2935−2947.
[4] Candès, E., and Donoho, D., 1999, Curvelets: a surprisingly effective nonadaptive representation for objects with edges. In Cohen, A., Rabut, C., and Schumaker, L. Eds., Curve and Surface Fitting: Saint-Malo. Vanderbilt Univ. Press.
[5] Candès, E., Demanet, L., Donoho, D., et al., 2006, Fast discrete curvelet transforms: SIAM Multiscale Modeling and Simulation, 5(1), 861−899.
[6] Chiu, S., 2014, Multidimensional interpolation using a model-constrained minimum weighted norm interpolation: Geophysics, 79(5), V191-V199.
[7] Daubechies, I., Defrise, M., and Mol, C. D., 2004, An iterative thresholding algorithm for linear inverse problems with a sparsity constrains: Communications on Pure and Applied Mathematics, 57(11), 1413−1457.
[8] Ely, G., Aeron S, Hao, N., et a1., 2015, 5D seismic data completion and denoising using a novel class of tensor decompositions: Geophysics, 80(4), V83-V95.
[9] Feng, F., Wang, D. L., Zhu, H., et a1., 2013, Estimating primaries by sparse inversion of the 3D curvelet transform and the L1-norm constraint, Applied geophysics, 10(2), 201−209.
[10] Fomel, S., and Liu, Y., 2010, Seislet transform and seislet frame: Geophysics, 75(3), V25-V38.
[11] Gao, J. J., Chen, X. H., Li, J. Y., et a1., 2010, Irregular seismic data reconstruction based on exponential threshold model of POCS method: Applied Geophysics, 7(3), 229−238.
[12] Gao, J. J., Stanton, A., Naghizadeh, M., et al., 2013, Convergence improvement and noise attenuation considerations for beyond alias projection onto convex sets reconstruction: Geophysical prospecting, 61, 138−144.
[13] Gao, J. J., Stanton, A., and Sacchi, M. D., 2015, Parallel matrix factorization algorithm and its application to 5D seismic reconstruction and denoising: Geophysics, 80(6), V173-V187.
[14] Gou, F. Y., Liu, C., Liu, Y., et al., 2014, Complex seismic wavefield interpolation based on the Bregman iteration method in the sparse transform domain: Applied Geophysics, 11(3), 277−288.
[15] Herrmann, F. J., 2010, Randomized sampling and sparsity: Getting more information from fewer samples: Geophysics, 75(6), WB173-WB187.
[16] Jin, S., 2010, 5D seismic data regularization by a damped least-norm Fourier inversion: Geophysics, 75(6), 103-111.
[17] Kreimer, N., and Sacchi, M. D., 2012, A tensor higher-order singular value decomposition for prestack seismic data noise reduction and interpolation: Geophysics, 77(3), V113-V122.
[18] Kreimer, N., Stanton, A., and Sacchi, M. D., 2013, Tensor completion based on nuclear norm minimization for 5D seismic data reconstruction: Geophysics, 78(6), V273-V284.
[19] Liu, G. C., Chen, X. H., Guo, Z. F., et a1., 2011, Missing seismic data rebuilding by interpolation based on curvelet transform: Oil Geophysical Prospecting, 46(2), 237−245.
[20] Liu, Y., Liu, N., and Liu, C., 2015, Adaptive prediction filtering in t-x-y domain for random noise attenuation using regularized nonstationary autoregression: Geophysics, 80(1), V13-V21.
[21] Ma, J., and Plonka, G., 2010, The curvelet transform: IEEE Signal Processing Magazine, 27(2), 118-133.
[22] Ma, J., 2013, Three-dimensional irregular seismic data reconstruction via low-rank matrix completion: Geophysics, 78(5), V181-V192.
[23] Naghizadeh. M., and Sacchi, M. D., 2010, Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data: Geophysics, 75(6), WB189-WB202.
[24] Naghizadeh, M., and Sacchi, M. D., 2007, Multistep autoregressive reconstruction of seismic records: Geophysics, 72(6), V111-V118.
[25] Oropeza, V., and Sacchi, M. D., 2011, Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis: Geophysics, 76(3), V25-V32.
[26] Ozkan, M., Tekalp, M., and Sezan, M., 1994, POCS based restoration of space-varying blurred images: IEEE Transactions on Image Processing, 3(4), 450−454.
[27] Spitz, S., 1991, Seismic trace interpolation in the f-x domain: Geophysics, 56(6), 785-794.
[28] Tang, G., MA, J. W., and Yang, H. Z., 2012, Seismic data denoising based on learning-type overcomplete dictionaries: Applied Geophysics, 9(1), 27−32.
[29] Trad, D., 2009, Five-dimensional interpolation: Recovering from acquisition constraints: Geophysics, 74(6), V123-V132.
[30] Vassallo, M., Ozbek, A., Ozdemir, K., et al., 2010, Crossline wavefield reconstruction from multicomponent streamer data: Part 1 -Multichannel interpolation by matching pursuit (MIMAP) using pressure and its crossline gradient: Geophysics, 75(6), 53-67.
[31] Xue, Y.,Ma, J., and Chen, X., 2013, High-order sparse Radon transform for AVO-preserving data reconstruction, Geophysics 79(2), V13−V22.
[32] Xu, S., Zhang, Y., and Lambare, G., 2010, Antileakage Fourier transform for seismic data regularization in higher dimensions: Geophysics, 75(6), WB113-WB120.
[33] Yang, P. L., Guo, J. H., and Chen, W. C., 2012, Curvelet-based POCS interpolation of nonuniformly sampled seismic records: Journal of Applied Geophysics, 79(2), 90−93.
[34] Yu, S. W., Ma, J. W., Zhang, X. Q., et a1., 2015, Interpolation and denoising of high-dimensional seismic data by learning a tight frame: Geophysics, 80(5), V119-V132.
[35] Yu, S. W., Ma, J. W., and Osher, S., 2016, Monte Carlo data-driven tight frame for seismic data recovery:Geophysics, 81(4), V327-V340.
[36] Zhang, H., and Chen, X. H., 2013, Seismic data reconstruction based on jittered sampling and curvelet transform: Chinese J. Geophys (in Chinese), 56(5), 1637−1649.
[37] Zhang, H., Chen, X. H., and Li, H. X., 2015, 3D seismic data reconstruction based on complex-valued curvelet transform in frequency domain: Journal of Applied Geophysics 113(1), 64−73.
[38] Zhang, H., Chen, X. H., and Wu, X. M., 2013, Seismic data reconstruction based on CS and Fourier theory: Applied Geophysics, 10(2), 170−180.
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