Measuring Loop Quality
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Another problem with loops is that it is difficult to determine which loops are good and which loops are bad. There are several different ways of analyzing loop errors. The three most common methods are "Absolute Error Size", "Percent Error" and "Standard Deviation."
Absolute Error Size. With Absolute Error Size you simply look at the closure error of each loop. Large errors are bad and small errors are good. Unfortunately, no matter how well surveyed a loop is, the accumulated error gets larger as the loops get longer. As a result, long loops will automatically look worse than small loops.
Percent Error. Percent Error is designed to compensate for the fact that long loops have more error. With Percent Error, the quality of a loop is measured by dividing the error by the loop length. This gives a more accurate measure of loop quality. Unfortunately, percent error is not a completely accurate way of measuring loop quality. There are several problems with the way Percent Error works:
1. The Number of Shots. Although Percent Error takes into account the length of a loop, it does not take into account the number of shots in a loop. For example, you could have two loops, each one a 100 feet long. The first loop could have 10 shots in it, the second loop could have three. Although you might think that having more shots would cause more errors; the opposite is true. The errors in one shot have a tendency to cancel out part of the error in other shots. (This is a normal property of random errors.) Thus, if you have more shots covering the same distance, you can expect the errors to be smaller.
2. Instruments. Another problem with Percent Error is that it ignores the way cave survey instruments work. The compass, inclinometer and tape have different error properties and different effects on the kind of errors you would expect from them. For example, if you have a narrow cave where most of the passages run north and south, compass errors are going to be expressed in the east-west direction. Likewise, compass errors do not effect the vertical position of a station, but tape and inclination errors can. This complex interaction between the different instruments and the configuration of the cave can give different errors in different situations. Thus, what would be considered a high quality survey for one cave might be considered very bad for another. Since the Percent Error does not take into account these complex interactions, it does not give an accurate idea of the loop’s quality.
Standard Deviation. The final method of measuring loop quality is Standard Deviation. This technique takes into account the number of shots, the length of each shot, the quality of the instruments and the configuration of each individual shot. It also takes into account the fact that errors tend to add up statistically rather than arithmetically. In other words, because the errors are random, they tend to cancel each other out. This is easy to see. If the errors are random, sometimes you will read the compass slightly to the left of target, sometimes slightly to the right.
Standard Deviation is a measure of the spread of the data. In the case of cave surveys, we want to know what spread of errors we can expect on a good survey that only has random errors in it. Survey errors obeys statistical laws. If a survey loop is good, it will only have random errors in it. Random errors have certain properties that make them predictable. By comparing the prediction with actual errors, you can determine the quality of a loop.
The process starts by using estimates for the level of error for each instrument. The program then walks around the loop, applying the instrument error values to each shot. By summing statistically all the errors around the loop, the program makes an estimate of the size of the errors in the loop. This estimate is the standard deviation. The predicted standard deviation is then compared with the actual errors in the loop. If the errors exceed the prediction, then the loop is probably bad.
The Meaning of STDs. Generally speaking, loops that are more than three times the prediction (or three standard deviations) probably have a blunder in them. Loops with two standard deviations are suspect. However, it is important to understand that standard deviation does not give an absolute good or bad reading. For example, statistics tell us that 99.74% of all good loops will fall within three standard deviations. As a result, we can be pretty sure that any loop beyond three deviations will be blundered. However, even here, there are still 2 chances out of a 1000 that the loop is okay. Sometime the accidental and random errors of the compass, inclinometer and tape combine in just the right way to make an unexpectedly large error.
Caveats. You have to be careful when you make assumptions about loop quality. Even standard deviation can be deceptive. For example, in Groaning cave there is a loop that is 1873 feet long, which has a 15-foot error. This gives a 0.98% closure error and 1.6 standard deviations. Normally, this would be thought of as a good quality loop. However, in this case, most of the error is vertical. Groaning is a relatively flat cave, with only about 30 feet of vertical relief in this part of the cave. When you compare the 15-foot error against the vertical relief, it is 50% of the height, a huge error.
The deceptive part is that the loop closes well horizontally, and looks good in a plan view. However, if you look at the cave in profile, the error stands out like a sore thumb. The lesson here is that you have to put every error in context.