The Marchenko method represents a constructive technique toobtain Green�s functions between the acquisition surface andany arbitrary point in the medium. The process generally involvessolving an inversion starting with a direct-wave Green's function from the desired subsurface position, which is typicallyobtained using an approximate velocity model. In thisstudy, we first propose to formulate the Marchenko method inthe time-imaging domain. We recognize that the traveltimeof the direct-wave Green�s function is related to the Cheop�straveltime pyramid commonly used in time-domain processingand can be readily obtained from the local slopes of thecommon-midpoint (CMP) gathers. This observation allowsus to substitute the need for a prior velocity model with thedata-driven slope estimation process. Moreover, we show thatworking in the time-imaging domain allows for the specificationof 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 velocitymodel is only required when specifying the position in depthbut this requirement can be circumvented by making use of thetime-imaging domain and its usual assumptions. Provided thatthose assumptions are satisfied, the estimated Green�s functionsfrom the proposed method have comparable quality tothose obtained with the knowledge of a prior velocity@en