Diffractions always need more advertising. It is true that conventional seismic processing and migration are usually successful in using specular reflections to estimate subsurface velocities and reconstruct the geometry and strength of continuous and pronounced reflectors. However, correct identification of geological discontinuities, such as faults, pinch‐outs, and small‐size scattering objects, is one of the main objectives of seismic interpretation. The seismic response from these structural elements is encoded in diffractions, and diffractions are essentially lost during the conventional processing/migration sequence. Hence, we advocate a diffraction‐based, data‐oriented approach to enhance image resolution—as opposed to the traditional image‐oriented techniques, which operate on the image after processing and migration. Even more: it can be shown that, at least in principle, processing of diffractions can lead to superresolution and the recovery of details smaller than the seismic wavelength. The so‐called reflection stack is capable of effectively separating diffracted and reflected energy on a prestack shot gather by focusing the reflection to a point while the diffraction remains unfocused over a large area. Muting the reflection focus and defocusing the residual wavefield result in a shot gather that contains mostly diffractions. Diffraction imaging applies the classical (isotropic) diffraction stack to these diffraction shot gathers. This focusing‐muting‐defocusing approach can successfully image faults, small‐size scattering objects, and diffracting edges. It can be implemented both in model‐independent and model‐dependent contexts. The resulting diffraction images can greatly assist the interpreter when used as a standard supplement to full‐wave images.

One of the most widespread problems in seismology is the necessity to adjust some a priori given medium structure. As a rule, such a priori information is vertically inhomogeneous component of wave propagation velocity. Such theoretical aspects of the problem as its uniqueness estimates of conditional stability are studied rather well. There axe also a variety of algorithms for its numerical solution. Therefore, in this paper the main attention is paid to numerical analysis of resolving ability and information contents of linearized inversion of multi-offset data.*Domaine de Voluceau, The work was supported by RFBR grants No. 96-01-01515 and 97-05-65280; and by the France-Russian Center of Appl. Math, and Inf. grant "Reliable numerical methods of solutions of nonlinear continually correct problems in application to inverse problems of wave propagation theory". Brought to you by | University of Arizona Authenticated Download Date | 5/31/15 6:15 AM * As we shall see from the presentation below, the case of half-space z > 0 does not have serious changes except the calculations which are more tedious. Brought to you by | University of Arizona Authenticated Download Date | 5/31/15 6:15 AM

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