Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 120

Figure 4.3f . MWD pulse in non-periodic noise (desurger distortion field).

4.4 Method 4-4. Directional filtering - differential equation
method requiring two transducers (software reference,
SAS14D*.FOR, Option 3 only) .

4.4.1 Physical problem.
The problem considered here is identical to that of Method 4-3. However,
the signal processing method is based on a differential as opposed to a difference
delay equation. “Differential” refers to “differential equation based” while
“difference” refers to algebraic equations with non-infinitesimal separations.
We emphasize that, in practice, the drillpipe pressure field consists of slowly
varying hydrostatic and rapidly changing wave components. The effects of the
former on Methods 4-3 and 4-4 are small, thus simplifying signal processing.

Schematic

f(t - x/c) g(t + x/c)

x a x b

x

Figure 4.4a. General bi-directional waves.