Geology Reference
In-Depth Information
Display and source code note: If one examines the black and red curves
above, the green superposition result should be twice the amplitude shown, but it
is not. This is not an error but a difference in plotting conventions. In Methods
4-1 to 4-4, we dealt with pressure levels at the surface. In Methods 4-5 and 4-6,
we instead examine 'p's. In the analytical derivations, and referring to
DELTAP04.FOR and DPOPEN01.FOR, functions UPSIG and DNSIG are used
for the upgoing and downgoing signals, but which are actually 'p functions and
not pressures. The green line is defined as the total (UPSIG+DNSIG)/2 or
(UPSIG-DNSIG)/2. The TOT function is not 'p, but the actual pressure level
that enters the drillpipe. This factor of 2 explains why the black, red and green
all have the same amplitudes. Again, because black and red represent plots of
'p's, while green represents pressure itself. “Equation 21” referred to in both
Fortran source codes is really “left side PRESSURE” = “half the difference of
two DELTA-P functions.” This is the result programmed and plotted.
4.6.5 Run 2. Higher data rate.
Here we consider a higher data rate, and study the dynamics of a pulse with
a width of approximately 0.05 sec, as shown in Figure 4.6c. The time delay
between pulser and drill bit is 0.01 sec. The green signal is the signal that
travels up the drillpipe and does not resemble the intended black signal. The top
blue signal recovers the bottom black signal very well.
C CASE 2
A = 20.0
R = 100.0
SIGNAL=A*(TANH(R*(T-0.100))-TANH(R*(T-0.101)))/2.
Figure 4.6c. Higher data rate, narrower pulse (note distorted green trace).
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