Geostatistical interpolation of non-stationary seismic data

The problem of sparsely collected seismic data is one of the main issues in reflection seismology, because most advanced data processing techniques require a dense and regular seismic data grid. We present a geostatistical seismic data interpolation technique based on sequential stochastic simulations with local structural anisotropies. This technique, contrary to conventional existing data-driven seismic interpolation approaches based on sparsity, prediction filters, or rank-reduction, predicts the value of seismic amplitudes at non-sampled locations by exploiting the statistics of the recorded amplitudes, which are used as experimental data for the geostatistical interpolation in the original data domain. Local mean and variance are computed on-the-fly to define intervals of the global conditional distribution function, from where amplitude values are stochastically simulated. The parameters to define subsets of experimental data from which mean and variance are calculated are given by local variogram models, which in turn are obtained from a local dip and azimuth estimation in the t-x-y domain. The geostatistical seismic data interpolation technique is applied to synthetic and real 2D and 3D datasets in both post- and pre-stack domains. Besides being computationally cheaper than other methods, because the interpolation is carried out directly in the original data domain, the proposed technique provides a local quantitative analysis of the reliability of the interpolated seismic samples, which can be exploited in following processing steps.