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deblending [2017/03/12 01:42]
deblending [2017/03/12 21:21]
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 **Deblending via sparse Stolt Transforms (Amr Ibrahim) ** **Deblending via sparse Stolt Transforms (Amr Ibrahim) **
-Blended ​data is deblended (separatedvia sparse hyperbolic ​apex shited Radon transform ​that is efficiently implemented via Stolt migration/​de-migration operatorsFigure 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 CRGsThe process entails minimizing the cost function ​
-|{{:​asrt_1.jpg?​600|Figure 1. Apex shifted Radon transform}}| 
 +$$ J =  \| {\cal L} m - {d}\|_p^p + \mu \| m \|_q^q$$
 +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.
 +{{ :asrt_1.jpg |}}
 +Figure 1. Four velocity panels of the field data ASHRT model. The inversion used the parameters p = 1 and q = 1.
 +{{ :​research:​figures:​asrt_2jpg.jpg |}}
 +Figure 2. 
 +A Ibrahim, MD Sacchi, 2015, Fast simultaneous seismic source separation using stolt migration and demigration operators, Geophysics [[http://​​doi/​abs/​10.1190/​geo2015-0044.1|External Link]]
deblending.txt ยท Last modified: 2017/03/12 21:21 by msacchi