The VSP, shown on the right ( bottom), is composed of 64 traces. Each trace is associated with a position in depth of the borehole geophone. The vertical axis represents the different depths of the geophone . The horizontal axis represents the listening time, here between 0.2 and 1.2 seconds. Here, the depth of the geophone is represented by the record number ( number ranging between 16 to 79). The frequency ( F) - wave number ( K) diagram of the VSP is shown on the left ( top). The waves which propagate downward, called down-going waves, have the strongest energy and are associated with positive wave-numbers on the F-K diagram. The waves which propagate upward, called up-going waves, have the weakest energy and are associated with negative wave-numbers on the F-K diagram.

We concentrate our observations on the down-going wave. In a constant velocity layer, the arrival time shows a constant delay between two consecutive traces; which translates itself to a line segment in the t-x plane. The down-going wave is made up of various line segments. This translates itself as a centered cloud about a line which corresponds to the mean velocity.

The down-going and up-going waves are shown in the t-x and f-k domains. For a given layer, they have, in absolute value, the same apparent velocity if the dip of the layer is zero. In these conditions, the up-going waves in f-k are symmetries of the down-going waves with relation to the axis k=0. However, the presence of many layers means that each wave type is represented by a cloud of points in the f-k plane. The k axis is shown in reduced wave-number between -0.5 and +0.5. The frequencies are in Hz.

A brief filtering can be accomplished by keeping only positive values of k (the cursor allows k to vary from 0 to 32). The graduations are in sample number for k. The down-going waves are thus selected and by subtraction we can obtain the up-going waves.

Figure on the left shows VSP section after wave-number filter application ( VSP-k). Figure on the right shows either the initial VSP section ( VSP) or the residual section, difference between VSP and VSP-k.
By keeping only positive values of k, the filtered VSP section shows the down-going waves and the residual section shows the up-going waves.
By keeping only negative values of k, the filtered VSP section shows the up-going waves and the residual section shows the down-going waves.
At the end of the video, you can see on the right the down-going waves and on the left the up-going waves.