Wavefield extrapolation downward from the surface, as applied in migration and associated inversion methods, is a common procedure to image subsurface reflectors. These methods require adequate (i.e., extensive and unaliased) sampling of the surface wavefield. Seismic tomography on the other hand, relates parameters of the upward propagated wavefield to the diffracting image, and sampling requirements are less severe; it is usually the only option to image deep structures from sparse data. The ordinary form of ray tomography, however, imposes a severe smoothness constraint on the boundary; in particular the 'tops' and 'valleys' of a relatively rough structure are not well-resolved. We have implemented a generalized form of tomography, which uses both the ray term and the diffraction term linearized in the boundary perturbation. We introduce a generalized reflection coefficient that can be linearized in terms of the (unknown) boundary gradient, and we demonstrate the adequacy of this approximation with the help of synthetic seismograms. We compare the performance of the new inversion method with migration and ray tomography in a number of model experiments where a source and receiver array are used to image (1) a rough sea bottom and (2) a rough sedimentary layer boundary. In these experiments the new method is superior, especially in the outer part of the inversion region where migration and seismic tomography suffer seriously because of the lack of adequate surface information. Even for well-controlled surveys there is the potential to successfully image a much larger area of the reflector than is possible with migration. Our experiments involved a single reflector in a known velocity-density structure. The method's applicability or modifications required when relaxing these assumptions, remains to be investigated.

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