Geology Reference
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To do this, connect the differential pressure output to a spectrum analyzer.
Is p s a constant? Or does it consist of multiple peaks, as would be expected
of a nonlinear system? What are the 'p's associated with the primary and
higher harmonics? The results can be surprising. Amplitude spectra for the
same siren operating at the same rotation rate Z, for high and low flow
rates, are shown in Figure 9.10a (the vertical and horizontal scales are
different). The left-most peaks represent the primary harmonic associated
with Z, but the shape distributions of the higher harmonics differ owing to
nonlinearity. Optimum shaping would maximize signal strength in the
primary harmonic, and ideally, remove energy from higher ones which
waste energy and increase signal processing complications. If nonlinear
effects are important, it may be necessary to filter out higher harmonics
before ascertaining relationships between 'p, flow rate and frequency.
Figure 9.10a. Signal strength amplitude spectrum measured in wind tunnel.
10. We expand on the results in Figure 9.10a. When these figures represent
'p's, only the “primary harmonic” represents the useful signal, e.g., the 12
Hz component of a siren rotating at 12 Hz. The 'p's associated with 24,
36, 48, 60 Hz and so on, are wasted, in the sense that they are destroyed by
the drillpipe telemetry channel (signals associated with very, very high
frequencies are eliminated by destructive wave interference since the pipe
acts as a low-pass filter, while those for lower high frequencies are simply
removed by thermodynamic attenuation). Intermediate harmonic signals
that arrive at the surface can be problematic since they appear as echoes.
The “true signal” is the one with the lowest frequency. It can be extracted
from the measured transient waveform using standard methods in FFT (Fast
Fourier Transform) analysis. Figure 9.10b provides an illustrative (non-
MWD) calculation. The transient time domain waveform at the left appears
somewhat complicated, but upon Fourier analysis, actually consists of
discrete periodic components as shown at the right. Detailed discussion can
be found in standard signal processing references, e.g., the practical
textbook by Stearns and David (1993) with source code in Fortran and C.
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