Geology Reference
In-Depth Information
p(x
a
,t) - p(x
b
, t -W) = f(t - x
a
/c) - f{t + (x
a
- 2x
b
)/c}
(4.3e)
Without loss of generality, we set x
a
= 0 and take x
b
as the positive transducer
separation distance
f(t) - f(t - 2x
b
/c) = p(0,t) - p(x
b
, t - x
b
/c)
(4.3f)
or
f(t) - f(t - 2W) = p(0,t) - p(x
b
, t - W)
(4.3g)
The right side involves subtraction of two measured transducer pressure values,
with one value delayed by the transducer time delay W, while the left side
involves a subtraction of two unknown (to-be-determined upgoing) pressures,
one with twice the time delay or 2W). The deconvolution problem solves for f(t)
given the pressure values on the right and is solved by our 2XDCR*.FOR code.
Method 4-3 is extremely powerful because it eliminates any and all
functions g(t + x/c), that is, all waves traveling in a direction opposite to the
upgoing wave. Thus, g(t + x/c) may apply to mudpump noise, reflections of the
upgoing signal at the mudpump, and reflections of the upgoing signal at a
desurger, regardless of distortion or phase delay, reflections from the rotary hose
connections, and so on. The functional form of the downgoing waves need not
be known and can be arbitrary. This is not to say that all downward moving
noise sources are removed. For example, fluid turbulence noise traveling
downward with the drilling fluid is not acoustic noise will not be removed and
may degrade the performance of Method 4 -3. Additional noise sources and
filters are considered in Chapter 6. The order in which filters are applied will
affect the outcome of any signal processing, and it is this uncertainty that
provides the greatest challenge in signal processor design. The model in
Equation 4.3g is solved exactly, that is, analytically in closed form, and is
implemented in our 2XDCR*FOR software series. In Figure 4.3b, black, red,
green and blue curves appear, respectively, from the bottom to top. The color
coding conventions for our graphical output results are as given as follows.
x Black curve ... upward MWD signal
x Red curve ... XNOISE function
x Green curve ... sum of MWD and XNOISE
x Blue curve ... deconvolved signal
4.3.3
Run 1. Single narrow pulse, S/N = 1, approximately.
Carefully note that the amplitude “A” in the MWD signal function
SIGNAL refers to the difference of two hyperbolic tangent functions, whereas
the amplitude “AMP” in the XNOISE function refers to a sinusoidal function.
They are not the same.
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