Signal and noise separation in prestack seismic data using velocity-dependent seislet transform |

Under 1D earth assumption, one can consider the classic
hyperbolic model of primary reflection moveouts at near offsets
(Dix, 1955):

This calculation is reverse to the one used in NMO by velocity-independent imaging (Ottolini, 1983b; Fomel, 2007). To calculate local slopes of primaries, we need to know at each time-space location (). This can be accomplished by simultaneously scanning both and according to the hyperbolic NMO equation at each -coordinate position or by

After the VD-slope pattern of primaries is calculated, we can design pattern-based prediction and update operators by using plane-wave construction for the VD-seislet transform to represent only primary reflections. When VD-seislet transform is applied to a CMP gather, random noise spreads over different scales while the predictable reflection information gets compressed to large coefficients at small scales. A simple thresholding operation can easily remove small coefficients. Finally, applying the inverse VD-seislet transform reconstructs the signal while attenuating random noise.

Signal and noise separation in prestack seismic data using velocity-dependent seislet transform |

2015-10-24