deblending

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deblending [2017/03/12 01:39] msacchi |
deblending [2017/03/12 21:21] msacchi |
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**Deblending via sparse Stolt Transforms (Amr Ibrahim) ** | **Deblending via sparse Stolt Transforms (Amr Ibrahim) ** | ||

- | Blended data is deblended (separated) via sparse hyperbolic apex shited Radon transform that is efficiently implemented via Stolt migration/de-migration operators. Figure 1 | + | Simultaneous source seismic data obtained with random firing times can be separated via the application of robust denoising methods to common receiver gathers (CRG). Source interferences manifest as erratic noise in CRGs and the goal is to develop a robust apex shifted hyperbolic radon transform (ASHRT) tto remove erratic noise in CRGs. The process entails minimizing the cost function |

- | {{ :asrt_1.jpg?600 | Figure 1: Apex shifted Radon transform}} | ||

+ | $$ J = \| {\cal L} m - {d}\|_p^p + \mu \| m \|_q^q$$ | ||

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+ | where $L$ is the Radon operator, $m$ are the coefficients in Radon space that model the data $d$ and $\mu$ is the regularization parameter. Our algorithm adopts $p=1$ (sparse solution) and $q=1$ (robust solution) to denoise CRGs. Figure 1 shows the Radon panel associated to the real data cube in Figure 2. Figure 2 shows the data obtained via a simulated simultaneous source acquisition, the denoised data and the | ||

+ | reconstruction error. | ||

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+ | {{ :asrt_1.jpg |}} | ||

+ | Figure 1. Four velocity panels of the field data ASHRT model. The inversion used the parameters p = 1 and q = 1. | ||

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+ | {{ :research:figures:asrt_2jpg.jpg |}} | ||

+ | Figure 2. | ||

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+ | A Ibrahim, MD Sacchi, 2015, Fast simultaneous seismic source separation using stolt migration and demigration operators, Geophysics [[http://library.seg.org/doi/abs/10.1190/geo2015-0044.1|External Link]] |

deblending.txt ยท Last modified: 2017/03/12 21:21 by msacchi

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