Mixed Fourier-Radon reconstruction of irregularly and sparsely sampled seismic data

Seismic data irregularly sampled in two dimensions is transformed to the Fourier/Radon domain using a least squares formulation where the inverse transform, from the Fourier/Radon to the spatial domain is used as a forward model. By a proper choice of the region of support, the total number of parameters is limited (yet such that the actual data is optimally contained), leading to a stable inversion. Subsequently the data can be transformed to any desired grid in the spatial domain. Also, using suitable transforms, signal and noise map to different parts of the transform domain and can be separated. The method is applied to synthetic and marine data. I. Introduction In exploration seismology structural information of the subsurface is obtained by recording the wavefield generated by a source (e.g. dynamite), using many receivers. In 2D seismics, these receivers are positioned along a line at the surface with sampling interval \Deltax r and starting at a certain 'offset' x 0 from the..