Loop Closing Theory.
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Survey Loops. Many caves have passages that wind around in a circle and connect back to themselves. When this type of passage is surveyed, it is called a loop. If a loop is surveyed perfectly, the survey should come back to the exact point where it started. If the loop doesn't come back to the exact starting point it means that there has been one or more errors in the loop and this is called a closure error. If you process and display a loop without any special processing, all the errors in the loop will be combined on the last shot in the loop and it will be severely distorted. In fact, if the last shot is at a passage junction, the intersection can look totally different from what is in the cave. Even worse, if the closure errors are large enough, the whole shape of the cave can be distorted by the errors. For these reasons, one of the steps in processing of cave data is to close all loops.
Closing Loops. Closing loops is a mathematical process that systematically adjusts each shot in a loop to minimize the effects of errors. This is done by distributing the errors throughout the survey. In effect, it gives you lots of little errors distributed around the loop instead of one big error at the point where the loop closes.
Random Errors and Blunders. A loop closer has to deal with two kinds of errors: Random Errors and Blunders. Random errors are small errors that result from the fact that it is impossible to get absolutely perfect measurements each time you read a compass, inclinometer or tape measure. Random Errors are easy to deal with because they are small and they have mathematically predictable properties. Blunders are more dramatic errors caused by mistakes in the survey process like reading the wrong end of the compass or transposing digits when you write a measurement in the survey book.
Blunders are important in cave surveying, because the environment is difficult and so blunders are much more likely. As a result, blunders are very common in cave surveying. One experiment indicates that one in every twenty shots has a blunder. Also, because the environment is so difficult, it may take many years for a blundered survey to be redone. For this reason, a cave survey loop closer must be able to deal with blunders.
Loop Closing Techniques. Most cave survey programs use a mathematical process called Least Squares to close survey loops. To do Least Squares correctly, the program must analyze the survey data, looking for blunders. If blunders are found, the process must be adjusted to compensate for the blunders and the surveys must be re-closed. If these steps are not taken, the blunders will be propagated throughout the cave, contaminating unblundered surveys and loops and distorting the cave.
Least Squares is an excellent method of closing loops, but most survey programs do it wrong. In the 1970’s there was an article published in the NSS Bulletin describing a simplified Least Squares technique that omitted the important step of dealing with blunders. Unfortunately, most cave survey programs modeled their loop closers after this article and they have severe problems with blunders. In fact, the only program I’m aware of that does Least Square correctly is a British survey program called Survex.
COMPASS’s Loop Closing Technique. COMPASS uses a technique that has been used by surveyors, cartographers and mapmakers up until the 1960’s. It was used to create some of the most accurate surveys in the world. It is particularly well suited to cave surveying because of its speed, simplicities and because it handles blunders well.
The COMPASS loop closer works by examining all the loops in the cave and finding the best and worst errors. It then starts with the best loop and closes it, “locking down” all the stations in the loop so they cannot be adjusted again when any of the later loops are closed. It continues adjusting loops one-by-one until the last and poorest loop is closed. This has the effect of preserving the quality of the good loops while preventing the bad loops from contaminating the rest of the cave. For a complete discussion on various loop-closing techniques, refer to the COMPASS web page at http://fountainware.com/compass
For a detailed explanation of the mechanics of the COMPASS loop closing, click here.