Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 124

In Figure 4.4b, black represents the clean upgoing MWD three-pulse
original signal. Red is the recovered pulse - this result is so good that it
partially hides the black signal. The green and blue lines are pressure signals
measured at the two pressure transducers, here separated by thirty feet. From
these green and blue traces, one would not surmise that the red line can be
recovered (only minor “bumps” indicate that the green and blue lines differ).
4.4.4 Run 2. A very, very noisy example.
The results above are very optimistic, but the algorithm is even more
powerful than they suggest. In the run below, a noise amplitude of 200 is
assumed, so that the signal-to-noise ratio ranges from 0.025 to 0.075 depending
on the pulse interval. Simulation inputs are shown below and calculated results
are displayed in Figure 4.4c. The recovery of the three-pulse signal is
remarkable despite the high noise level. In practice, this directional filter will be
used in concert with conventional frequency and random noise filters.
Units: ft, sec, f/s, psi ...
Assume canned MWD signal? Y/N: y
Downward propagating noise (psi) assumed as
N(x,t) = Amplitude * cos {2Ŧ f (t + x/c)} ...
o Enter noise freq "f" (hz): 5
o Type noise amplitude (psi): 200
o Enter sound speed c (ft/s): 5000
o Mean transducer x-val (ft): 1700
o Transducer separation (ft): 30
Figure 4.4c . Recovery of three step pulses from very noisy environment.
The typical frequency spectrum in Figure 6-8b shows mudpump noise in
the 0-25 Hz range, with lower frequencies associated with higher amplitudes.
The results in Figure 4.4b assume large amplitude 15 Hz pump noise, while
Figure 4.4c assumes very large amplitude 5 Hz pump noise. In both cases,
signal recovery is remarkable. We emphasize that time domain integrations, and
not discrete Fourier transforms, are used in both of our approaches.