A fast-convergence POCS seismic denoising and reconstruction method
Ge Zi-Jian1,2, Li Jing-Ye1,2, Pan Shu-Lin3, and Chen Xiao-Hong1,2
1. State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China.
2. CNPC Key Laboratory of Geophysical Prospecting, China University of Petroleum, Beijing 102249, China.
3. School of Geoscience and Technology, Southwest Petroleum University, Chengdu 610500, China.
Abstract：
The efficiency, precision, and denoising capabilities of reconstruction algorithms are critical to seismic data processing. Based on the Fourier-domain projection onto convex sets (POCS) algorithm, we propose an inversely proportional threshold model that defines the optimum threshold, in which the descent rate is larger than in the exponential threshold in the large-coefficient section and slower than in the exponential threshold in the small-coefficient section. Thus, the computation efficiency of the POCS seismic reconstruction greatly improves without affecting the reconstructed precision of weak reflections. To improve the flexibility of the inversely proportional threshold, we obtain the optimal threshold by using an adjustable dependent variable in the denominator of the inversely proportional threshold model. For random noise attenuation by completing the missing traces in seismic data reconstruction, we present a weighted reinsertion strategy based on the data-driven model that can be obtained by using the percentage of the data-driven threshold in each iteration in the threshold section. We apply the proposed POCS reconstruction method to 3D synthetic and field data. The results suggest that the inversely proportional threshold model improves the computational efficiency and precision compared with the traditional threshold models; furthermore, the proposed reinserting weight strategy increases the SNR of the reconstructed data.
Ge Zi-Jian,Li Jing-Ye,Pan Shu-Lin et al. A fast-convergence POCS seismic denoising and reconstruction method[J]. APPLIED GEOPHYSICS, 2015, 12(2): 169-178.
[1]
Abma, R., and Kabir, N., 2006, 3D interpolation of irregular data with a POCS algorithm: Geophysics, 71(6), E91-E97.
[2]
Duijndam, A. W., Schonewille, M. A., and Hindriks, K., 1999, Reconstruction of band-limited signals irregularly sampled along one spatial direction: Geophysics, 64(2), 524-538.
[3]
Galloway, E., and Sacchi, M. D., 2007, POCS method for seismic data reconstruction of irregularly sampled data: CSPG-CSEG-CWLS Joint Convention, 555.
[4]
Gao, J. J., Chen, X. H., Li, J. Y., et al, 2010, Irregular seismic data reconstruction based on exponential threshold model of POCS method: Applied Geophysics, 7(3), 229-238.
[5]
Gao, J. J., Stanton, A., Naghizadeh, M., Sacchi, M. D., et al, 2013, Convergence improvement and noise attenuation consideration for beyond alias projection onto convex sets reconstruction: Geophysical Prospecting, 61(suppl. 1), 138-151.
[6]
Gerchberg, R. W., and Saxton, W. O., 1972, A practical algorithm for the determination of phase from image and diffraction plane pictures: Optik, 35(2), 227-246.
[7]
Hennenfent, G., and Herrmann, F., 2006, Seismic denoising with nonuniformly sampled curvelets: Computing in Science and Engineering, 8(3), 16-25.
[8]
Kabir, M. M. N., and Verschuur, D. J., 1995, Restoration of missing offsets by parabolic Radon transform: Geophysical Prospecting, 43(3), 347-368.
[9]
Kong, L. Y., Yu, S. W., Chen, L., et al., 2012, Application of compressive sensing to seismic data reconstruction: Acta Seismologica Sinica, 34(5), 659-666.
[10]
Kreimer, N., and Sacchi, M. D., 2011, Evaluation of a new 5D seismic volume reconstruction method: Tensor completion versus Fourier reconstruction: Tensor Completion vs. Fourer, Reconstruction: CSPG-CSEG-CWLS Joint Convention, 1-5.
[11]
Li, H. F., and Du, M. H., 2003, Super-resolution Image Restoration Based on Improved POCS Algorithm: Journal of South China University of Technology (in Chinese), 31(10), 24-27.
[12]
Liu, G. C., Chen, X. H., Guo, Z. F., et al., 2011, Missing seismic data rebuilding by interpolation based on curvelet transform: Oil Geophysical Prospecting (in Chinese), 46(2), 237-246.
[13]
Malcolm, A. E., Hoop, M. V. D., and Rousseau, J. H. L., 2005, The applicability of dip moveout/azimuth moveout in the presence of caustics: Geophysics, 70(1), S1-S17.
[14]
Menke, W., 1991, Applications of the POCS inversion method to interpolating topography and other geophysical fields: Geophysical Research Letters, 18(3), 435-438.
[15]
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.
[16]
Naghizadeh, M., and Sacchi, M. D., 2009, f-x adaptive seismic-trace interpolation: Geophysics, 74(1), V 9-V16.
[17]
Oropeza, V., and Sacchi, M., 2011, Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis: Geophysics, 76(3), V25-V32.
[18]
Papoulis, A., 1975, A new algorithm in spectral analysis and band limited extrapolation: IEEE Transactions on Circuits and Systems, CAS-22(9), 735-742.
Spitz, S., 1991, Seismic trace interpolation in the F-X domain: Geophysics, 56(6), 785-794.
[21]
Trad, D. O., 2009, Five-dimensional interpolation: Recovering from acquisition constraints: Geophysics, 74(6), V123-V132.
[22]
Trad, D. O., Ulrych, T. J., and Sacchi, M. D., 2002, Accurate interpolation with high-resolution time-variant Radon transform: Geophysics, 67(2), 644-656.
[23]
Trickett, S., Burroughs, L., Milton, A., et al, 2010, Rank-reduction-based trace interpolation: 80th Ann. Internat. Mtg., Soc. Explor. Geophys., Expanded Abstracts, 1989-1992.
[24]
Wang, S., Gao, X., and Yao, Z., 2010, Accelerating POCS interpolation of 3D irregular seismic data with graphics processing units: Computers and Geosciences, 36(10), 1292-1300.
[25]
Wang, S. Q., and Zhang, J. H., 2014, Fast imaging in painting using exponential-threshold POCS plus conjugate gradient: The Imaging Science Journal, 62(3), 161-170.
[26]
Zhang, H., and Chen, X. H., 2013, seismic data reconstruction based on jittered sampling and curvelet transform. Chinese Journal of Geophysics (in Chinese), 56(6), 1637-1649.
2015, Vol. 12 
