Reflectivity angle blurring due to illumination variation in images

The seismic imaging method called reverse-time migration (RTM) has extensions, which are used to improve migration velocity models. So-called subsurface ‘Extended Image Gathers’ (EIGs) can be used for this velocity-model inversion, which dominantly exploits their kinematics or phase. In this talk, however, we assume that the velocity model is already correct (optimal) and that the EIGs are as ‘focused’ as they can be. Dynamically, though, an EIG can be related to the ‘reflection function’ for a target interface, which is an intricate multi-dimensional function containing the interface plane-wave reflection coefficients. The relationship of an EIG to such a reflection function will be explained in terms of a high-dimensional blurring function. This theory leads to the conclusion that, in general, there is not just spatial blurring in images, but also blurring over angle of the plane-wave reflection coefficients inside the reflection function. This angle blurring is expected to be most significant where the blurring function varies most rapidly in space. Preliminary salt-model numerical examples indicate how significant the effect may be. It is emphasized that this angle-blurring physics depends on the overburden structure and survey acquisition geometry, and is independent of the deep target scattering physics.