Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 111

Figure 4.2b . 12 Hz carrier, phase shift in presence of large pump noise.
x Roundtrip delay time = 0.02 sec
x Sampling time = 0.01 sec
For readers of the black and white version of this topic, in Figure 4.2b, curve
colors are black, red, green and blue, respectively, from the bottom to top.
x Black is the combination of the upgoing MWD signal and the downward
pump noise. Because the pump noise amplitude is four times larger, the
black line does not even appear as if it contains an MWD signal.
x Red is the reflection of the upward MWD signal at the surface solid
reflector.
x Green is the sum of the upgoing signal and reflected downward signal, with
the pump noise subtracted out (the pump noise is measured at the pump,
delayed, and then the subtraction is performed).
x Blue is the recovered upgoing signal as assumed (12 Hz with a phase shift),
which appears just as the red signal does (the blue signal is recovered from
green data which is a longer stretched pulse). Note the small signal-to-noise
of 0.25 assumed.
4.2.5 Run 2. 24 Hz PSK, plus pump noise with S/N = 0.25.
We next repeat the calculation of Run 1, but double the carrier frequency
to 24 Hz. The signal and pump noise functions are identical to those of Run 1,
except that for the signal, a value of F = 24 Hz is used instead of F = 12 Hz (we
are therefore running a 24 Hz carrier with a phase shift). Similar comments as
those for Run 1 apply to our very successful recovery, as shown in the blue
signal of Figure 4.2c.
x Roundtrip delay time = 0.02 sec
x Sampling time = 0.01 sec