Velocity-independent Marchenko focusing in time- and depth-imaging domains for media with mild lateral heterogeneity

The Marchenko method retrieves Green's functions between the acquisition surface and any arbitrary point in the medium. The process generally involves solving an inversion starting with an initial focusing function, e.g., a direct-wave Green's function from the desired subsurface position, typically obtained using an approximate velocity model. We have formulated the Marchenko method in the time-imaging domain. In that domain, we recognize that the traveltime of the direct-wave Green's function is related to the Cheop's traveltime pyramid commonly used in time-domain processing, which in turn can be readily obtained from the local slopes of the common-midpoint gathers. This observation allows us to substitute the velocity-model-based initial focusing operator with that from a data-driven slope estimation process. Moreover, we found that working in the time-imaging domain allows for the specification of the desired subsurface position in terms of vertical time, which is connected to the Cartesian depth position via the time-to-depth conversion. Our results suggest that the prior velocity model is only required when specifying the position in depth, but this requirement can be circumvented by making use of the time-imaging domain within its usual assumptions (e.g., mild lateral heterogeneity). Provided that those assumptions are satisfied, the estimated Green's functions from the proposed method have comparable quality to those obtained with the knowledge of a prior velocity model.