The phase-screen and the split-step Fourier methods, which allow modeling and migration in laterally heterogeneous media, are generalized here so as to increase their accuracies for media with large and rapid lateral variations. The medium is defined in terms of a background medium and a perturbation. Such a contrast formulation induces a series expansion of the vertical slowness in which we recognize the first term as the split-step Fourier approximation and the addition of higher-order terms of the expansion increases the accuracy. Employing this expansion in the one-way scalar propagator yields the scalar one-way generalized-screen propagator. We also introduce a generalized-screen representation of the reflection operator. The interaction between the upgoing and downgoing fields is taken into account by a Bremmer series. These results are then cast into numerical algorithms. We analyze the accuracy of the generalized-screen method in complex structures using synthetic models that exhibit significant multipathing: the IFP 2-D Marmousi model and the SEG-EAGE 3-D salt model. As compared with the split-step Fourier method, in the presence of lateral medium variations, the generalized-screen methods exhibit an increased accuracy at wider angles of propagation and scattering. As a result, in the process of migration, we can choose a member of the family of our generalized- screen algorithms in accordance with the complexity of the medium (velocity model).

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