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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;
Fund:

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.
 
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