Subsurface Offset Generalization for Reflection Tomography Inversion

Subsurface offset extended imaging provides a possible link connecting migrated reflections in CIGs with the migration velocity error. However, it describes an artificial scattering geometry that splits the reflection point between incident and scattered waves. The split configuration contradicts basic principles of continuum mechanics, as it represents action-at-a-distance, and has kinematics distinct from those of ordinary physical reflection. The angle-domain image, computed as a Radon transform of the subsurface offset image, implicitly inherits the split configuration and distinguished by its response to erroneous migration velocity. Conventional traveltime inversion techniques, applied for velocity optimization, are incompatible with the split configuration. Hence, they are most likely to fail while inverting traveltimes from the subsurface offset image or its angle-domain transformation. Nevertheless, those images that are being identified with the split geometry still carry valuable information about the migration velocity error. They should be input to traveltime inversion algorithms only after a proper generalization. We present a modified traveltime inversion formulation, appropriate for split reflections in the image space. The net result is a generalized reflection tomography scheme where the traveltime estimation accounts for a possible subsurface offset split.