Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 116

a small bump at the left, with the single signal buried in the longer trace. The
blue curve shows how the black single pulse is successfully recovered from the
green data using Equation 4.3g. The silence obtained everywhere else also
demonstrates the success of our filtering. Note the signal and noise have
roughly the same amplitude, so that S/N = 1, approximately.
4.3.4 Run 2. Very noisy environment.
In this run, we increase the pump noise significantly, so that the MWD
signal is not visible to the naked eye in the green signal. The time delay
between transducers is 0.01 sec or 10 ms, as before. Here, the signal to noise
ratio is about 1:4 and the same recovery success is achieved.
FUNCTION SIGNAL(T)
C MWD upward wave signal function
C Train of pulses, 0.5 sec width, 0.5 sec separation
C CASE 2. NARROW PULSE WIDTH (Considered in single xducer
method)
C Clearly see interference between upgoing and reflected pulses
A = 10.0
R = 100.0
SIGNAL = A*(TANH(R*(T-0.100))-TANH(R*(T-0.101)))/2.
RETURN
END
C
FUNCTION XNOISE(T)
C Mud pump noise function may also include reflected MWD
C signal, but it is not necessary to add the wave reflection to
C the total noise to demonstrate directional filtering.
C FRQPMP = Hertz freq of pump noise, propagates downward
PI = 3.14159
FRQPMP = 15.
C AMP = 0.25
AMP = 1.
XNOISE = AMP*SIN(2.*PI*FRQPMP*T) + 0.0*SIGNAL(T)
RETURN
END
Figure 4.3c . Very noise environment, S/N about 0.25.