The shifted hyperbola was first introduced almost 40 years ago as an alternative to the conventional NMO hyperbola. In previous works it has been shown that the shifted hyperbola has unique properties, which make it a feasible alternative to conventional NMO stacking. In addition to the appealing fact, that, due to the independence of the zero-offset reference traveltime, the shifted hyperbola generally leads to stretch-free NMO correction, it was also demonstrated that, for the same reason, its moveout correction can be implemented in a highly parallel fashion. For multi-layered inhomogeneous media, previous authors have found that the shifted hyperbola provides high accuracy, which in certain situations can surpass the conventional NMO approach. Despite all its successes, to our knowledge, the shifted hyperbola has never been convinvincingly extended to 3D acquisitions. In this work, we introduce a formulation of the shifted hyperbola that is valid in three dimensions. The new approximation allows an efficient implementation and does not cause the undesired effect of wavelet stretch. A numerical 3D example indicates that the new 3D shifted hyperbola, is more accurate than the conventional 3D NMO, and hence, bears the potential of an improved stacked volume and more reliable stacking parameters.


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