Up/down separation of seismic depth images

Reverse time migration (RTM) is normally based on wavefield modeling that allows wave propagation in all spatial directions. While this is one of the strengths of RTM, it can also lead to undesired effects, including partial image amplitude cancellation for reflectors that are illuminated and imaged from two sides, as well as the appearance of ghost-reflection artifacts if the modeled source- and receiver-side wavefields are both scattered back from a hard model contrast. Both issues can be addressed by separating the seismic depth image into components imaged from above and components imaged from below. I derive and compare two methods that directly achieve such an image up/down separation, without relying on an up/down separation of the individual simulated wavefields used for imaging. The first method is based on the formation of time-shift gathers during imaging and filtering out events with either positive or negative slopes in these gathers, corresponding to imaging from below or above, respectively. The second method is a new image up/down separation approach inspired by previously published wavefield up/down separation approaches. It involves combining a migrated image with an additional version of the image, obtained by applying a temporal Hilbert transform to the input data and a subsequent Hilbert transform in depth on the migrated image. Compared with approaches based on up/down separation of the individual wavefields, the presented direct image up/down separation methods have distinctive advantages. While the approach based on filtering of time-shift gathers is efficient and offers considerable flexibility, the approach based on Hilbert transforms is attractive because of its simplicity since no changes to the migration algorithm itself are required. I demonstrate both image up/down separation methods on synthetic and real data and show that both methods lead to very similar results.