A method is provided of processing multi-component seismic data acquired by emitting multi-component seismic energy at a source location and acquiring seismic data at a multi-component seismic receiver located at a greater depth than the source location. The seismic data are decomposed into up-going constituents and down-going constituents. A de-signature and de-multiple operator is calculated from the down-going constituents of the seismic data and from properties of the medium surrounding the receiver.