Minimizing Ellipsoidal Norm Seismic Data Interpolation with Radon Spectrum Constraints

A data adaptive interpolation is designed under the Radon spectrum constraints for spatially aliased seismic data. The inverse process is formed through constructing an ellipsoidal norm, which can make full use of the information about the Fourier spectrum of the data. The ellipsoidal norm can enhance the relative distribution of the Fourier spectrum and is computed with the help of Radon spectrum. Radon spectrum can helpfully concentrate the energy distribution of the Fourier spectrum. Correspondingly, the aliasing components in the Fourier spectrum can be relatively attenuated. The solution of the interpolation inverse problem is sparser and the inverse process becomes more stable. The numerical examples show the effectiveness of the method. The method is applicable to 2D and 3D seismic survey data recorded sparsely in a horizontal plane. The most common pre-stack applications of the algorithm are common-mid-point and half-offset domain interpolation.