Velocity-independent Marchenko method in time- and depth-imaging domains

Abstract

The Marchenko method represents a constructive technique to obtain Green’s functions between the acquisition surface and any arbitrary point in the medium. The process generally involves solving an inversion starting with a direct-wave Green’s function from the desired subsurface position, which is typically obtained using an approximate velocity model. In this study, we first propose to formulate the Marchenko method in the time-imaging 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 and can be readily obtained from the local slopes of the common-midpoint (CMP) gathers. This observation allows us to substitute the need for a prior velocity model with the data-driven slope estimation process. Moreover, we show 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 timeto-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 and its usual assumptions. 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.