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Restoration of missing offsets and trace interpolation is an interesting and important problem in seismic data processing. Based on the parabolic Radon transform, a method is presented for missing offset restoration, resampling and regularization of prestack individual CMP gathers. The method is also valid for resampling spatially aliased seismic data.The method is based on the parabolic assumption of the seismic events which is generally verified after a partial NMO correction in the CMP organization of the data. The essence of the method consists of a band-limited forward parabolic Radon transform of the data containing zero traces at the missing offset locations. The curvature range is chosen to map properly the coherent energy while the zero traces map beyond that range. After inverse transform the originally zero traces are partly filled with information. Several iterations of forward and inverse transform, every time replacing the zero traces in the original gather with the partially reconstructed ones, almost fully restore the zero traces.Efficient and fast algorithms can be built up to process data having a uniform geometry. Examples on synthetic as well as on field data demonstrate clearly the robustness of the method.

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This paper presents a new feature selection (FS) algorithm based on the wrapper approach using neural networks (NNs). The vital aspect of this algorithm is the automatic determination of NN architectures during the FS process. Our algorithm uses a constructive approach involving correlation information in selecting features and determining NN architectures. We call this algorithm as constructive approach for FS (CAFS). The aim of using correlation information in CAFS is to encourage the search strategy for selecting less correlated (distinct) features if they enhance accuracy of NNs. Such an encouragement will reduce redundancy of information resulting in compact NN architectures. We evaluate the performance of CAFS on eight benchmark classification problems. The experimental results show the essence of CAFS in selecting features with compact NN architectures.

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A method of velocity analysis based on the common focusing point (CFP) method is presented. The two important aspects of the method are the use of the CFP domain and the use of a new parameterization—a vertical velocity gradient to describe the lateral velocity variation within a layer. The layer velocity is defined with only two parameters: an average velocity [Formula: see text]and a vertical velocity gradient (β). Layer velocity parameterization using [Formula: see text] and β assumes that the lithology of the layer is constant and that the overburden and fluid pressure increase linearly with depth. This type of parameterization is suitable for areas with gross changes in lithology (clastic‐carbonate‐salt) and for rock in hydrostatic equilibrium. A layer‐based model is required for these areas. The salt dome data example presented belongs to this type of area, so the layer‐based model with the defined parameterization produced a very good subsurface velocity model. The method is based on the principle of equal traveltime between the focusing operator and the corresponding focus point response. The velocity estimation problem is formulated as a constrained parametric inversion process. The method of perturbation is applied where linear assumptions are made; the velocity inversion, however, is a nonlinear problem, and the model parameter updates are computed iteratively using Newton’s method. The velocity model is built by layers in a top‐down approach, which makes the problem quasi‐linear.

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