Transient Variable Area Downhole Inverse Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 147

upgoing wave from the pulser and the downward wave that reflects at the
drillbit. Again, these waves reverberate within the drill collar because the cross-
sectional area changes abruptly between drill collar and drillpipe. The black
curve uses red data only and represents the recovered 'p(t). In all cases, the
recovery is excellent. Note that, as a programming check, various choices for
DECAY, namely, 1.0, 0.1, 0.5 and 0.75 were run, and as expected, the software
simply rescaled the green curve.
5.1.3 Run 1. Phase-shift-keying, 12 Hz carrier wave.

C CASE 1. High data rate PSK phase shift keying.
IF(NCASE.EQ.1) THEN
C F is frequency in Hz, AMP is delta-p amplitude in lbf/ft^2 (PSF),
C sampling time DT in seconds.
C 2*PI*F cycles in 2*PI secs, or F cycles per sec, F is Hz.
C One cycle requires time PERIOD = 1/F.
IF(T.LE.0.0) DELTAP = 0.
IF(T.GE.0.0) THEN
PI = 3.1415926
AMP = 0.5
F = 12.
PERIOD = 1./F
IF(T.GE.0.0.AND.T.LE.2.*PERIOD) DELTAP =
1 +AMP*SIN(2.*PI*F*T)
IF(T.GE.2.*PERIOD) DELTAP = abs(-AMP*SIN(2.*PI*F*T))
ENDIF
ENDIF

Figure 5.1b . Phase-shift-keying, 12 Hz carrier wave.

5.1.4 Run 2. Phase-shift-keying, 24 Hz carrier wave.
In this higher frequency run, notice that the red curve is very different and
highly distorted from the green curve. The recovered black curve is very good.

C CASE 2. High data rate PSK phase shift keying.
IF(NCASE.EQ.2) THEN
C F is frequency in Hz, AMP is delta-p amplitude in lbf/ft^2 (PSF),
C sampling time DT in seconds.
C 2*PI*F cycles in 2*PI secs, or F cycles per sec, F is Hz.
C One cycle requires time PERIOD = 1/F.
IF(T.LE.0.0) DELTAP = 0.