Scattering and dip angle decomposition in relation with subsurface offset extended wave-equation migration

An angle-dependent reflection coefficient is recovered by seismic migration in the angle-domain. We propose a post-migration technique for computing scattering and dip angle common-image gathers (CIGs) from seismic images, extended by the subsurface offset, in relation with wave-equation migration methods. Our methodology suggests a system of Radon transform operators by introducing local transform relations between the subsurface offset image and the angle-domain components. In addition to the commonly used decomposition of the scattering-angle, the methodology associates the wave-equation migration with dip-domain images as well. The same post-migration subsurface offset image is employed to decompose scattering and dip angle CIGs individually, or to decompose a multi-angle CIG by showing simultaneously both angles on the gather's axis. A unique dip-angle response of seismic reflections is introduced as a spot-like signature, focused at the specular dip of the subsurface reflector. It differs from the well-studied smile-like response usually associated with reflections in the dip-domain. The contradiction is clarified by the nature of the subsurface offset extension, and by emphasizing that the angles are decomposed from the subsurface offset image after the imaging condition, without directly involving the propagating incident and scattered wavefields. Several synthetic and field data examples demonstrate the robustness of our decomposition technique, by handling various subsurface models, including seismic diffractions. It is our belief that dip-angle information, decomposed by wave-equation migration, would have a great impact in making the scattering-angle reflection coefficient more reliable and noise-free, in addition to the acceleration of wave-equation inversion methods.