Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 115

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.
AMP = 0.25
XNOISE = AMP*SIN(2.*PI*FRQPMP*T) + 0.0*SIGNAL(T)
RETURN
END
x Time delay between transducers = 0.010 sec = 10 ms
x 30 ft standpipe length/3,000 ft/sec mud sound speed = 0.01 sec, taken as
sampling time in code.
Figure 4.3b . MWD signal with pump noise (S/N = 1, approximately).
Note that the single black upgoing MWD pulse shown in Figure 4.3b is
about 0.05 sec wide, representing a nominal 20 bits/sec, and the red continuous
mud pump signal is roughly the same frequency. This is a difficult test case.
Because both MWD and pump frequencies are about the same, the use of
conventional frequency-based filtering will fail. The green superposition of the
upgoing MWD signal and the pump noise shows a continuous wave signal with