Noncausal - - regularized nonstationary prediction filtering for random noise attenuation on 3D seismic data |
Two dimensional - NRNA only considers one space coordinate x. If we use - NRNA on 3D seismic cube, we usually apply - RNA in one space slice. - NRNA reduces the effectiveness because the plane event in 3D cube is predictable along different directions rather than only one direction. Therefore, we should develop 3D - - NRNA to suppress random noise for 3D seismic data.
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Figure 1. The - - prediction filter. The trace is predicted from circumjacent traces (except itself ). |
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Next, we use Fig. 1 to illustrate the idea of - - NRNA. The middle trace is the one we want to predict. Trace can be predicted from circumjacent traces (except itself ). The prediction process includes all different directions. For example, if we use to predict , we can estimate a corresponding coefficient using the described algorithm in the following. - - NRNA uses all around traces to predict the middle trace. Therefore, the prediction uses more information than - NRNA. For all the traces in 3D cube, similar to the trace , we can use circumjacent traces to predict them. Mathematically, we can write the prediction process as
Transform-base methods can also be used for seismic noise attenuation (Ma and Plonka, 2010). Tang and Ma (1991) proposed to total-variation-based curvelet shrinkage for 3D seismic data denoising in order to suppress nonsmooth artifacts caused by the curvelet transform. Because the - - NRNA method uses shaping regularization to solve the ill-posed inverse problem and is complemented in frequency domain, it has higher computation efficiency than curvelet-based methods.
Noncausal - - regularized nonstationary prediction filtering for random noise attenuation on 3D seismic data |