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We present a split-step complex Padé-Fourier migration method based on the one-way wave equation. The downward-continuation operator is split into two downward-continuation operators: one operator is a phase-shift operator and the other operator is a finite-difference operator. A complex treatment of the propagation operator is applied to mitigate inaccuracies and instabilities due to evanescent waves. It produces high-quality images of complex structures with fewer numerical artefacts than those obtained using a real approximation of a square-root operator in the one-way wave equation. Tests on zero-offset data from the SEG/EAGE salt data show that the method improves the image quality at the cost of an additional 10 per cent computational time compared to the conventional Fourier finite-difference method. [ABSTRACT FROM AUTHOR]

A finite-difference method for computing the first-arrival traveltimes by solving the eikonal equation in the celerity domain has been developed. This algorithm incorporates the head and diffraction wave. We also adapt a fast sweeping method, which is extremely simple to implement in any number of dimensions, to obtain accurate first-arrival times in complex velocity models. The method, which is stable and computationally efficient, can handle instabilities due to caustics and provide head wave traveltimes. Numerical examples demonstrate that the celerity domain eikonal solver provides accurate first-arrival traveltimes. This new method is three times accurate more than the second-order fast marching method in a linear velocity model with the same spacing. [ABSTRACT FROM AUTHOR]