The WIM method for refraction statics

We know that first breaks may be efficiently inverted in the wavenumber-offset domain to determine a robust estimate of the near-surface model. This domain is indicated particularly for regularly covered surveys so that data can be Fourier transformed without interpolation problems. However, it usually happens that data are collected with irregular spacing of the source points. In this case the initial interpolation may bias the solution. An efficient method to prevent bias consists of an iterative model-driven interpolation. The database is decomposed and recomposed iteratively according to a linear approach to fill in the data space with model consistent first arrivals. The method is proved to converge to the unbiased solution and will be called the wavenumber iterative modeling (WIM) method. Experiments, both on synthetic and real data, show that convergence occurs after few iterations so that the procedure is still quite efficient. Moreover, the WIM method can be extended easily to automatically detect and remove the mispicks and suppress coherent and incoherent noise. Simple linear operators are also available for the conversion of the solution to the generalized reciprocal method (GRM) if the interpreter intends to guide the final optimization of the model.