Generalized Reflection Tomography Formulation Based on Subsurface Offset Extended Imaging

The subsurface offset is a possible link connecting wave-equation migration methods, such as reverse-time migration, with the angle-domain. However, it describes an artificial reflection 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, which distinguishes it from conventional angle-domain decomposition. As a consequence, it shows a dissimilar moveout response to erroneous migration velocity, but still carries valuable information about the migration velocity error. Conventional linearized traveltime inversion techniques, applied for velocity optimization, are most likely to fail while inverting angle-domain images produced from subsurface offset split reflections. These images should be labelled differently to highlight the split mechanism, and input to traveltime inversion algorithms only after a proper generalization. We present a modified linearized traveltime inversion formulation, appropriate for split reflections in the image space. The key ingredient in the algorithm is a subsurface offset depended extension of the traveltime change along migrated split reflection rays. A generalized reflection tomography scheme is proposed accordingly to tie imaging errors, in either the subsurface offset domain or its equivalent angle-domain map, to the migration velocity error.