| Abstract: | The aim of refracted arrivals inversion is the computation of near-surface information, i.e. first-layer thicknesses and refractor velocities, in order to estimate the initial static corrections for the seismic data. The present trend is moving towards totally automatic inversion techniques, which start by picking the first breaks and end by aligning the seismic traces at the datum plane. Accuracy and computational time savings are necessary requirements. These are not straightforward, because accuracy means noise immunity, which implies the processing of large amounts of data to take advantage of redundancy; moreover, owing to the non-linearity of the problem, accuracy also means high-order modelling and, as a consequence, complex algorithms for making the inversion. The available methods are considered here with respect to the expected accuracy, i.e. to the model they assume. It is shown that the inversion of the refracted arrivals with a linear model leads to an ill-conditioned problem with the result that complete separation between the weathering thickness and the refractor velocity is not possible. This ambiguity is carefully analysed both in the spatial domain and in the wavenumber domain. An error analysis is then conducted with respect to the models and to the survey configurations that are used. Tests on synthetic data sets validate the theories and also give an idea of the magnitude of the error. This is largely dependent on the structure; here quantitative analysis is extended up to second derivative effects, whereas up to now seismic literature has only dealt with first derivatives. The topographical conditions which render the traditional techniques incorrect are investigated and predicted by the error equations. Improved solutions, based on more accurate models, are then considered: the advantages of the Generalized Reciprocal Method are demonstrated by applying the results of the error analysis to it, and the accuracy of the non-linear methods is discussed with respect to the interpolation technique which they adopt. Finally, a two-step procedure, consisting of a linear model inversion followed by a local non-linear correction, is suggested as a good compromise between accuracy and computational speed. |
