From Displacement to Velocity

If you wish to see waveforms similar to what a velocity geophone would produce, you can use BSU to differentiate the seismic signals. The program to use would be bdif. For example, one could execute the following:

bdif wavV.seg .1

This would produce the result shown in Figure 62. It is a bit hard to compare the displacement to its derivative at this scale, so we can plot the first (near offset) signal from both data sets (wavV.seg and bdifwavV.seg). We issue the following commands:

Figure 62: Plot of file bdifwavV.seg, differentiated wavV.seg simulates what a velocity geophone might see. Compare to Figure 58.

bplt bdifwavV.seg 1 1 0 1 1 0 .2 1 .4 200 3. 3.
bplt wavV.seg 1 1 0 1 1 0 .2 1 .001 200 3. 3.

Figure 63 shows a comparison between the differentiated and original vertical component near offset signals. The differentiation computed in program bdif permits a stability factor since the program uses a bi-linear transform method that places a pole at the Nyquist frequency. In the Z-transform plane, the pole moves from $Z=-1$ to $Z=-(1+stab)$, where $stab$ is the stability factor. In the example above, we set $stab=0.1$. If the data have been filtered to remove any signal at and near the Nyquist frequency, then the stab factor can be small or zero. However, even the slightest amount of noise at the Nyquist frequency will be magnified without a stab factor. Typically, I choose $0.1<stab<.5$.