Several migration methods fail to work when applied to complex geological structures with strong lateral heterogeneity. The generalized migration in the frequency-wavenumber (f-k) domain based on a convolution with a slowness- (inverse of velocity) dependent operator is capable of downward continuation of wavefield in media with strong vertical and lateral variations of velocity. Unfortunately, this method, as presented in the literature, is potentially unstable. We propose a new, stable extrapolator based on the solution of the integral Fredholm equation, which describes a one-way wave equation in the form of a Neumann series. The resulting algorithm of depth migration is implemented in both the frequency-wavenumber (f-k) and frequency-space (f-x) domains and takes into account arbitrary lateral gradients of velocity, using a low-frequency filter (in x-f domain) that is the sum of the power series. The computation time of depth migration by a Neumann series is slightly longer than for split-step Fourier migration. The examples presented suggest that the depth migration by Neumann's series method can be used to map complex structures with strong lateral gradients of velocity.

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