3D refraction statics in the wavenumber domain

The wavenumber iterative modelling (WIM) method was first introduced to estimate the static corrections for 2D land profiles by performing first-break inversion in the wavenumber domain. The WIM algorithm presents some useful advantages, of robustness, stability and flexibility. Robustness is obtained by intensive exploitation of all the available data and by application of an automatic function for mispick removal. Stability is the result of an iterative procedure that ensures convergence towards a stable and plausible solution even at the end of the profile where the problem is normally ill-posed. Finally, flexibility is due to the possibility of solving for multilayered structures and of estimating vertical gradients of the velocity.This work extends the WIM method to three dimensions. The extension is feasible because the three-dimensional (3D) problem can be decomposed into a number of small independent problems, one for any pair of wavenumbers k _x ,  k _y . The extension preserves the above-mentioned advantages. The parameters of the estimated model are affected differently by noise: the analysis of the input/output noise transfer function demonstrates that the high spatial frequencies of the velocity distributions are the components that are most affected by noise; thus, the algorithm includes a gradual damping of the higher wavenumbers of the velocity parameter. Although the WIM 3D algorithm requires a larger amount of RAM compared with other standard approaches, considerable reduction in CPU run time can be achieved as every wavenumber pair can be treated as an independent linear problem.