Simultaneous seismic interpolation and statics estimation of land data

Imaging and inversion of land seismic data affected by complex weathering layers near the surface are challenging. When the data are additionally subsampled for economical reasons such as monitoring of sequestrated carbon dioxide and hydrogen, the problem is further exacerbated due to the combined influence of subsampling and weathering layers. First, interpolation performs poorly because the weathering layers reduce the data’s coherency. Second, near-surface corrections require knowledge of the subsurface model, separation between primaries and multiples, as well as subsurface velocity estimation, which are difficult to perform from subsampled data. To overcome these hurdles, we combine seismic interpolation and statics estimation into a joint single rank-reduction-based algorithm. To our knowledge, this is the first time that this has been done. Our method simultaneously accounts for the weathering and subsampling effects, which both contribute to the low-rank (LR) structure destruction typically associated with statics-free densely sampled data, to provide accurate reconstruction. Because an LR approximation is used for statics estimation, we also use it in rank-minimization interpolation as a cost-free initial solution to the optimization problem. As statics estimation and interpolation operate in the midpoint-offset domain, we avoid the cost of transformations back and forth from the source-receiver to the midpoint-offset transform domain. Consequently, our reconstruction, which indicates its potential on synthetic and field data, also is computationally efficient.