Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 110

applies. Again, the measured pressure p measured (t) contains pump noise, the latter
of which is then subtracted from the right side, leaving the noise-free equation
considered in Method 4-1. The interesting question is, “How large can N be
until the signal recovery is bad?” In other words, we want to explore the role of
the “signal to noise” (or, “S/N”) ratio in signal recovery. Usually, “noise” may
be, for instance, white or Gaussian, which generally degrades signal
enhancement procedures; however, as we will show, mudpump noise is not
entirely harmful. Since its direction and acoustic properties can be well
characterized, its effects may be subtracted out as demonstrated below.

4.2.4 Run 1. 12 Hz PSK, plus pump noise with S/N = 0.25.

The source code below generates an MWD signal with an amplitude of
0.25, while the pump noise function possesses an amplitude of 1.0 - thus, the
signal-to-noise ratio is 0.25, which is very small. The pump noise function is
defined in the Fortran block FUNCTION PUMP(T) while the MWD signal
appears in FUNCTION G(T).

FUNCTION G(T)
C
C Test MWD upward waveforms stored here
C CASE 3. PHASE-SHIFTING (F = FREQUENCY IN HERTZ)
PI = 3.14159
A = 0.25
F = 12.
C G = A*SIN(2.*PI*F*T)
C Means 2*PI*F cycles in 2*PI secs, or F cycles per sec, F is
Hz.
C One cycle requires time PERIOD = 1./F
PERIOD = 1./F
IF(T.GE.0.0. AND.T.LE. PERIOD) G = +A*SIN(2.*PI*F*T)
IF(T.GE.PERIOD.AND.T.LE.2.*PERIOD) G = -A*SIN(2.*PI*F*T)
IF(T. GE.2.*PERIOD) G = 0.
RETURN
END

FUNCTION PUMP(T)
PUMP = 1. * SIN(2. * 3.14159 * 15. * T )
RETURN
END
C