Extended common-image-point (CIP) gathers contain all of the necessary information for decomposition of reflectivity as a function of the reflection and azimuth angles at selected locations in the subsurface. This decomposition operates after the imaging condition applied to wavefields reconstructed by any type of wide-azimuth migration method, e.g., using downward continuation or time reversal. The reflection and azimuth angles are derived from the extended images using analytic relations between the space-lag and time-lag extensions. The transformation amounts to a linear Radon transform applied to the CIPs obtained after applying the extended imaging condition. If information about the reflector dip is available at the CIP locations, then only two components of the space-lag vectors are required, thus reducing computational cost and increasing the affordability of the method. Applications of this method include the study of subsurface illumination in areas of complex geology where ray-based methods are not usable and the study of amplitude variation with reflection and azimuth angles if the subsurface illumination is sufficiently dense. Migration velocity analysis could also be implemented in the angle domain, although an equivalent implementation in the extended domain is less costly and more effective.

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