The surface consistent equations are a singular set of linear equations used to process land seismic data. They attempt to project components of a seismic signal to a particular source, or receiver coordinate. Midpoint and offset consistence may also be used.
Long wavelength errors present in a surface consistent statics solution turn up in the stack section as a smeared or even separated wavelet. Errors in surface consistent amplitudes will lead to problems with AVO. Deconvolution operators will also be affected. Conditions that will likely be problematic are areas with a sudden and persistent change in the near surface, such as shooting over lakes, or sand dunes.
In a typical application, the solutions are calculated using a series of Gauss-Seidel iterations, or using conjugate gradients. In this paper, we compare these results with a multigrid method. Our findings show the multigrid method is able to better resolve the long wavelengths with no significant increase in computer time.
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