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APPLIED GEOPHYSICS  2018, Vol. 15 Issue (1): 69-77    DOI: 10.1007/s11770-018-0654-0
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Super-resolution least-squares prestack Kirchhoff depth migration using the L0-norm
Wu Shao-Jiang1,2, Wang Yi-Bo1, Ma Yue3, and Chang Xu2
1. Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China.
2. University of the Chinese Academy of Sciences Beijing, 100049, China.
3. Beijing Research Center, Aramco China, Beijing 100102, China.
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Abstract Least-squares migration (LSM) is applied to image subsurface structures and lithology by minimizing the objective function of the observed seismic and reverse-time migration residual data of various underground reflectivity models. LSM reduces the migration artifacts, enhances the spatial resolution of the migrated images, and yields a more accurate subsurface reflectivity distribution than that of standard migration. The introduction of regularization constraints effectively improves the stability of the least-squares offset. The commonly used regularization terms are based on the L2-norm, which smooths the migration results, e.g., by smearing the reflectivities, while providing stability. However, in exploration geophysics, reflection structures based on velocity and density are generally observed to be discontinuous in depth, illustrating sparse reflectance. To obtain a sparse migration profile, we propose the super-resolution least-squares Kirchhoff prestack depth migration by solving the L0-norm-constrained optimization problem. Additionally, we introduce a two-stage iterative soft and hard thresholding algorithm to retrieve the super-resolution reflectivity distribution. Further, the proposed algorithm is applied to complex synthetic data. Furthermore, the sensitivity of the proposed algorithm to noise and the dominant frequency of the source wavelet was evaluated. Finally, we conclude that the proposed method improves the spatial resolution and achieves impulse-like reflectivity distribution and can be applied to structural interpretations and complex subsurface imaging.
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Key wordssuper-resolution   least-squares   Kirchhoff depth migration   L0-norm   regularization     
Received: 2017-07-09;

This research is supported by the National Natural Science Foundation of China (No. 41422403).

Cite this article:   
. Super-resolution least-squares prestack Kirchhoff depth migration using the L0-norm[J]. APPLIED GEOPHYSICS, 2018, 15(1): 69-77.
[1] Aldawood, A., Hoteit, I., and Alkhalifah, T., 2014, The possibilities of compressed-sensing-based Kirchhoff prestack migration: Geophysics, 79(3), 113−120.
[2] Anagaw, A.Y., and Sacchi, M. D., 2012, Edge-preserving seismic imaging using the total variation method: Journal of Geophysics and Engineering, 9, 138−146.
[3] Aoki, N., and Schuster, G. T., 2009, Fast least-squares migration with a deblurring filter: Geophysics, 74(6), 83−93.
[4] Blumensath, T., and Davies, M. E., 2008, Iterative Thresholding for Sparse Approximations: Journal of Fourier Analysis and Applications, 14(5), 629−654.
[5] Claerbout, J. F., 1992, Earth soundings analysis: processing versus inversion: Blackwell Scientific Publications, Cambridge.
[6] Chen, G. X., Chen, S. C., et al., 2013, Geophysical data sparse reconstruction via L0-norm minimization: Applied geophysics, 2013, 10(2), 181−190.
[7] Dai,W., Wang, X., Schuster, G. T., et al., 2011, Least-squares migration of multisource data with a deblurring filter: Geophysics, 76(5), 135−146.
[8] Dai, W., Fowler, P. J., Schuster, G. T., et al., 2012, Multisource least squares reverse time migration: Geophysical Prospecting, 60(4), 681−695.
[9] Daubechies, I., Defrise, M., and De Mol, C., 2003, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint: Communications on Pure & Applied Mathematics, 57(11), 1413−1457.
[10] Fan, J. W., Li, Z. C., Zhang, K., et al., 2016, Multisource least-squares reverse-time migration with structure oriented filtering: Applied Geophysics, 13(3), 491−499.
[11] Kuehl, H., and Sacchi, M. D., 2003, Least-squares wave-equation migration for Avp/Ava inversion: Geophysics, 68(1), 262−273.
[12] Li, C., Huang, J. P., Li, Z. C., et al., 2017, Preconditioned prestack plane-wave least squares reverse time migration with singular spectrum constraint: Applied Geophysics, 14(1), 73−86.
[13] Liu, G. C., Chen, X. H., Song, J. Y., and Rui, Z. H., 2012, A stabilized least-squares imaging condition with a structure constraint: Applied Geophysics, 9(4), 459−467.
[14] Liu, Y., Teng, J., Xu, T., et al., 2016, An efficient step-length formula for correlative least-squares reverse time migration: Geophysics , 81(4), 221−238.
[15] Liu, Y., Teng, J., Xu, T., et al., 2017, Effects of conjugate gradient methods and step-length formulas on the multiscale full waveform inversion in time domain: Numerical experiments: Pure and Applied Geophysics, 174(5), 1983−2006.
[16] Ma, Y., Luo, Y., and Kelamis, P. G., 2013, Turning noise into signal - use of internal multiples for reflectivity reconstruction: 75th EAGE Conference & Exhibition Incorporating SPE, EUROPEC.
[17] Ma, Y., Zhu, W, Luo, Y., et al., 2015, Super-resolution stacking based on compressive sensing: 85th Annual International Meeting, SEG, Expanded Abstracts, 3502−3506.
[18] Nemeth, T., Wu, C., and Schuster, G. T., 1999, Least-squares migration of incomplete reflection data: Geophysics, 64(1), 208−221.
[19] Nocedal, J., and Wright, S. J., 2006, Numerical optimization: Springer, New York.
[20] Perez, D. O., Velis, D. R., Sacchi, M. D., et al., 2013, High-resolution prestack seismic inversion using a hybrid FISTA least-squares strategy: Geophysics, 78(5), 185−195.
[21] Sacchi, M. D., Constantinescu, C. M., and Feng, J., 2003, Enhancing resolution via nonquadratic regularization—Next generation of imaging algorithms: Annual Convention, Canadian Society of Exploration Geophysicists, Abstracts on CDROM, January.
[22] Schuster, G. T., 1993, Least-squares cross-well migration: 63rd Annual International Meeting, SEG, Expanded Abstracts, 110−113.
[23] Tang, Y., 2009, Target-oriented wave-equation least-squares migration/inversion with phase-encoded Hessian: Geophysics, 74(6), 95−07.
[24] Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49(8), 1259−1266.
[25] Tikhonov, A. N., and Arsenin, V. Y., 1977, Solutions of ill-posed problems: Mathematics of Computation, 32(144), 491−491.
[26] Wang, J., and Sacchi, M., 2007, High-resolution wave-equation amplitude-variation-with-ray-parameter (AVP) imaging with sparseness constraints: Geophysics, 72(1), 11−18.
[27] Wang, Y., Yang, C., and Duan, Q., 2009, On iterative regularization methods for migration deconvolution and inversion in seismic imaging: Chinese Journal of Geophysics, 52(6), 1615−1624.
[28] Wu, S., Wang, Y., Zheng, Y., and Chang, X., 2015, Limited-memory BFGS based least-squares pre-stack Kirchhoff depth migration: Geophysical Journal International, 202(2), 738−747.
[29] Yu, S., 1993, High-resolution seismic survey: Petroleum Industry Press, China.
[30] Zheng, Y., Wang, Y., and Chang, X., 2013, Wave-equation traveltime inversion: Comparison of three numerical optimization methods: Computers & Geosciences, 60(10), 88−97.
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