REFRACTION STATICS IN THE WAVE-NUMBER DOMAIN

A new method for refraction statics reduces the computational time without reducing accuracy. The first arrivals, common-offset organized, form the data space. The method involves Fourier transforming any common-offset data vector with respect to the common mid-point. As a result, the data are decomposed in a number of subspaces, associated with the wavenumbers, which can be independently inverted to obtain any wavelength of the near-surface model. The main advantage of the subspace decomposition is a remarkable reduction of the computation time. It also helps us to derive the following conclusion about the ill conditioning of the inverse problem: the uncertainty in estimating refractor velocity is proportional to the wavenumber, whereas estimation of refractor depth is practically unaffected by ill conditioning on the whole spectrum. To reduce the null space of the problem, the solution is further constrained by assuming, for any station, the local symmetry of the weathering within the range of half the critical distance. Final local corrections, applied to the resulting depths and velocities, may improve the accuracy for complex interface geometries. The effects of noisy data, i.e., mispicks and events roughly picked, are also analyzed with respect to the wavelength. This leads to the main conclusion that noise mostly affects the short wavelengths of the velocity. An upgrade of the basic method allows vertical gradients of the velocity to be accounted for. Experimental results validate the theory and prove that good quality and solution robustness can be achieved with this method while computing time is reduced.