Multidimensional interpolation using a model-constrained minimum weighted norm interpolation

Abstract

Fourier-based minimum weighted norm interpolation (MWNI) has been widely used to regularize land seismic data. However, it has difficulty interpolating regular missing data that are spatially aliased. Minimizing the aliasing artifacts is still a technical challenge in MWNI. I have developed a novel method to address the aliasing problem in MWNI using a prior model as constraints. The prior model was constructed by a linear interpolation along dominant dips to produce a fully regular initial model. The spectral weights derived from this initial model are typically not aliased and can be used to constrain the least-squares inversion in MWNI, frequency by frequency, to overcome the aliasing artifacts. This new interpolation scheme expands the capability of conventional MWNI to handle spatially aliased data that are often associated with steeply dipping structures, and it reconstructs more reliable interpolation results. Decimation tests of a simple 2D synthetic data set and a complex 3D synthetic salt model revealed that model-constrained MWNI outperforms the conventional MWNI method in handling spatially aliased data. I applied this method to a land field data set and carried out a comprehensive evaluation of interpolated data through the processes of prestack analyses, prestack time migration, and prestack depth migration. The 5D interpolation successfully filled in missing data, increased spatial sampling of prestack gathers, and considerably improved migrated stacked images from the prestacked time and depth imaging.