Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 112

Figure 4.2c . 24 Hz carrier, phase shift with large pump noise.
4.3 Method 4-3. Directional filtering - difference equation
method requiring two transducers (software reference,
2XDCR*.FOR) .
4.3.1 Physical problem.
We next consider two-transducer surface signal processing in Methods 4-3
and 4-4. In this section, we have an upgoing pressure signal containing encoded
downhole MWD mud pulse information (plus downhole “ghost reflections”
produced at the pulser) which travels through the standpipe. The signal
continues to the mudpump, where it will reflect at a solid reflector at the pistons
for a positive displacement pump, and at an acoustic free-end for a centrifugal
pump. All types of pumps are permissible for Methods 4-3 and 4-4. Waves can
also reflect at the desurger where, depending on the amplitude and frequency
and the mass-spring-damper properties of the desurger, reflected waves can
distort in both amplitude and shape . In other words, we consider the very
general and difficult problem in which no information about the mudpump and
the desurger will be required - a very powerful signal processing method.
The two-transducer algorithms of Method 4-3 and 4-4, unlike some
schemes, do not require any knowledge of the nature of the mudpump noise
signature or the properties of the desurger distortion and are powerful in these
regards. Surface sound speed is required, which can be determined by simple
timing tests near the rig. Unlike published two-transducer methods, they need
not assume periodic waves and apply generally to transient motions, e.g., there
are no limiting restrictions related to the usual quarter-wavelength properties.
Note that Method 4-3 is based on a difference equation, while Method 4-4 is
based on a differential equation. In the difference equation model, there are no
restrictions on transducer separation, although practical “not too close” and “not
too far away” considerations apply. In the differential equation model, the usual
notions on derivatives hold, which in the acoustic context, of course, suggest
that transducer separations should be a small fraction of the wavelength.