Compressive Seismic Recon - Is it Interpolation?
Most in the seismic industry are familiar with 5D interpolation. What makes CS-Recon different from interpolation? It's all about the math.
Interpolation
Interpolation assumes that the sampled data is smooth and spatially band-limited and that consecutive samples are not significantly different. In the case of 5D interpolation, this assumption is made in each of the five dimensions. For spatially band-limited data, the results are reliable, and the signal can be recovered accurately.
To satisfy the band-limited assumption with seismic data, first bin the data to a regular grid in each interpolation dimension (typically time, inline, crossline, offset, and azimuth) and then approximate every trace to the bin center before interpolation. Because of this bin-centering mechanism, the original traces are not fully preserved after interpolation.
Compressive Seismic Recon
The underlying assumption in Compressive Seismic is that the sampled data is sparse in some transform domain (e.g. Tau-p) and possesses a certain degree of spatial incoherency. This spatial incoherency ensures that aliased energies are widely scattered in the transform domain, enabling a sparsity-promoting filter to remove these energies while preserving the true signal. Once these conditions are met, the sampled data can be decomposed into linear equations solvable by L1 inversion to obtain reliable and accurate results.
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All seismic datasets satisfy the underlying assumptions of Compressive Seismic to some degree, as there is always some level of spatial incoherency due to random positioning errors or deviations. There is no need for seismic data binned or approximated to the bin center before CS Recon. Our CS-Acquisition (CS-A) designs are optimized for a particular reconstruction transform domain with minimal spatial coherency, ensuring ideal reconstruction. An existing or conventional survey will still be reconstructed impressively (shown below), albeit not as well as a survey designed for CS.
Importantly, with our CS-Recon techniques, all original traces are retained as-is, with no modifications due to bin-centering mechanisms. With interpolation, no matter the bin-centering mechanism, what you end up with is not an original trace.
Conclusion
Compressive Seismic Recon (CS-R) mechanics are very different from mathematical interpolation. A significant advantage of CS-R over interpolation for seismic processing is that all original traces are preserved. Additionally, CS-R uses the power of incoherency and sparsity to remove aliased energies from the data, improving the overall reconstruction result.