Wave-equation trace interpolation

Spatial aliasing in multichannel seismic data can be overcome by solving an inversion in which the model is the section that would be recorded in a well sampled zero-offset experiment, and the data are seismic data after normal moveout (NMO). The formulation of the (linear) relation between the data and the model is based on the wave equation and on Fourier analysis of aliasing. A processing sequence in which one treats missing data as zero data and performs partial migration before stacking is equivalent to application of the transpose of the operator that actually needs to be inverted. The inverse of that operator cannot be uniquely determined, but it can be estimated using spatial spectral balancing in a conjugate-gradient iterative scheme. The first iteration is conventional processing (including prestack partial migration). As shown in a field data example in which severe spatial aliasing was simulated, a few more iterations are necessary to achieve significantly better results.