Appendix A.Checksum Errors
A.1Checksums and "Face Errors" on Inclinometer Probes
Many users have expressed concern about checksums or "face errors" on inclinometer probes. They are concerned with the effect of the "face error" on the accuracy of the readings. The purpose of this section is to show that under normal circumstances the effect of the "face error" or checksum is negligible even with checksums as large as 2000. The only time a problem would arise is if the face error or checksum was to change between the two halves of a survey. Therefore it is extremely important not to bang the probe on the bottom of the borehole between survey halves, and not to handle the probe roughly while out of the hole.
The term "face error" comes from surveying terminology. It is normal for all theodolites to have a "face error" which is caused by imperfections of alignment of the collimation axis and other misalignments. These "face errors" are removed routinely by taking two readings of the theodolite: one angle is measured with the face of the vertical scale on the left of the theodolite and another with the face of the vertical scale on the right of the theodolite. The average of the two readings "face right" and "face left" gives the true angle since the "face error" cancels out.
Similarly, with the inclinometer probe: the "face error" arises from the fact that the axis of the inclinometer probe is not parallel with the electrical axis of the internal, force-balance, servo- accelerometer transducer. Once again, the "face error" is eliminated by taking two surveys of inclinometer readings one with the wheels of the inclinometer probe pointing in one direction and another with the wheels of the probe at 180° to the first direction. If the first set of readings are all too large by the amount of the "face error", then the second set of readings will be too small by the amount of the "face error". Thus, the average (or sum) of the two readings will be a measure of the true inclination, since the effect of the face error will be eliminated.
A.1.1Effect of "Face Error" on Reading Accuracy
The "face error" or checksum 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 nonlinear.
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 ). This would cause 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 that normally occur from survey to survey, i.e., a lot less than the precision of the inclinometer probe survey. (Lack of precision can be 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 ±3 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 checksum 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).
A.1.2Measurement of "Face Error"
The "face error" is the reading shown by the inclinometer probe when it is perfectly vertical. In practice, the easiest way to obtain the "face error" is to run a normal inclinometer survey, with the two sets of readings at 180°, and then to run a profile or deflection report (see Appendix C.2 and Appendix C.3, the column labeled "Diff"). Examination of the data will reveal the average checksum, which is equal to twice the "face error".
A.1.3Setting of the "Face Error" to Zero
There are three ways of setting the "face error" to zero. None of them is necessary from the point of view of improving accuracy. These methods are detailed in the subsections below.
Mechanically
At the time of manufacture, the electrical axis of the transducer is adjusted by means of shims etc., until it points parallel to the axis of the inclinometer probe. This method suffers from the disadvantage that if the "face error" changes due to wear and tear on the probe and rough handling, or shock loading of the transducer then the probe needs to be returned to the factory for dismantling and readjustment.
Electrically
Electronic circuitry can be included in the probe so that the output of the transducer can be adjusted to zero when the probe is vertical. The disadvantage of this method is that it introduces electronic components into the inside of the probe which may alter with time, temperature and humidity and which, if the "face error" changes due to wear and tear or rough handling, will require the probe to be dismantled and the electronic circuitry readjusted. In addition, this form of correction does not really remove the "face error", it only masks it, and if the "face error" is very large, the calibration will be affected.
By Software
The best way for setting the "face error" to zero is by applying an automatic correction to the measured readings using the software capabilities of the inclinometer readout box.
The geokon recommended procedure for setting the "face error" to zero is described in Section 5.2, which covers the subject of "zero shifts", which are the same as "face errors". The advantage of this method lies in its simplicity and the ability to set the "face error" to zero at any time without dismantling the probe.
Another advantage of this method is that it is possible by judicious choice of the "face error" entered into the software program to make one probe give exactly the same digits output as another probe. This is sometimes thought to be desirable where probes are switched, and unbroken continuity of the raw data is desired. It is not necessary for reason of accuracy as has already been explained.
The disadvantage of this method is that, if the probe is changed, the operator must remember to change the zero shift offset in the program to accommodate the "face error" of the new probe.
Checksums of less than 2000 digits are of no consequence and can be completely ignored providing that the inclinometer survey is conducted with two sets of readings at 180° The best method for setting the "face error" to zero is by means of the software capabilities in the inclinometer reader.