Geokon GK-604D, User Manual

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A.3.1 Effect of “Face Error” on reading accuracy
The “face error” or check-sum can only affect the accuracy of the readings if it
affects the calibration of the probe. This is possible because the output of the
probe transducer is proportional to the sine of the inclination from the vertical
and the sine function is non-linear.
Imagine, for a moment, that the electrical axis of the transducer is five degrees
away from being parallel with the axis of the inclinometer. This would give rise
to a “face error” of 01743. (The inclinometer reader displays 20,000 sin
∅
). So,
one set of readings would be all too large by this amount and the other set of
readings from a normal inclinometer survey would be too small by this amount,
but the sum of the two readings would be accurate. The “face errors” having
canceled out. However, if we assume that the hole is almost vertical then the
transducer will be tilted at an angle of 5
°
. The difference in the slope of the
sine function at any point is equal to the cosine of the angle at that point. The
cosine of 0
°
is 1.0000 the cosine of 5
°
is 0.996 so that the effect of this “face
error” on the calibration of the probe is to increase it by a factor of 1/0.996 =
1.004.
The practical implication of this would mean that if the apparent deflection of a
borehole was 100 mm, the true deflection would be 100.4 mm. For practically
all applications, in the real world, the difference is insignificant and is a lot less
than the differences which normally occur from survey to survey i.e. a lot less
than the precision of the inclinometer probe survey. (Lack of precision is caused
by a failure to position the wheels of the probe in exactly the same place from
survey to survey; failure to wait sufficiently long to allow the probe transducer
to come to rest before reading; and random dirt in the inclinometer casing).
Note that the normal system accuracy of an inclinometer probe is ± 7 mm in 30
meters. By comparison it can be seen that the normal system accuracy or
precision is very much larger than the calibration error caused by the “face
error” and that for all practical purposes the “face error” is of no consequence
and can be completely discounted if it is less than 2000 digits.
(As another example, supposing the check-sum was as large as 5000 digits.
This is equivalent to a gross angular error of misalignment of almost 15
degrees. The effect on the calibration would be a little over 3 % so that the
apparent deflection of 100 mm would be out by 3 mm which again is smaller
than the normal data spread due to imprecision).