Extended generalized non-hyperbolic moveout approximation

An accurate traveltime approximation has a key role in the success of many seismic data processing, modelling and inversion algorithms. In this paper, we introduce a new explicit six-parameter traveltime approximation as an extension to the known generalized moveout approximation. The parameters of the proposed approximation are estimated at two offsets. Zero-offset two-way time, normal moveout velocity and effective anellipticity are defined at zero offset; the remaining three parameters are defined from traveltime, ray parameter and curvature at a reference offset. Each of these parameters has been previously employed in former traveltime approximations. The proposed method can be used to approximate full offset ray-traced traveltimes by two rays. Potential applications include approximation of migration Green's function and common midpoint forward modelling. It also gives insight for traveltime behaviour in anisotropic media. We provide numerical tests by different sources of non-hyperbolic moveout to show that the proposed method is a general improvement over the original generalized moveout approximation. It improves the accuracy and makes the parameter selection more symmetrical, while adding a minimum computational burden.