Computing device, computer instructions and method for up-down separation of seismic data. The method includes receiving the seismic data, which includes hydrophone data and particle motion data; performing a first up-down separation, which is independent of a ghost model, using as input the hydrophone data and the particle motion data, to obtain first up-down separated data; performing a second up-down separation by using as input a combination of (i) the hydrophone data and/or the particle motion data and (ii) the first up-down separated data, wherein an output of the second up-down separation is second up-down separated data; and generating an image of the subsurface based on the second up-down separated data.