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Loop Closure

Loops. Many caves have passages that wind around in a circle and connect back to themselves. When a survey connects back to itself, it called a loop. If a loop is surveyed perfectly, the survey should come back to the exact point at which it started. If the loop doesn't come back to the exact starting point it is called a closure error. Closure errors indicate that some or all of the survey measurements within a loop have errors.

Closing Loops. If the closure errors are large enough, the shape of the loop and the shape of the cave will be distorted by the errors. For this reason, cave survey programs must have a way of dealing with the effects of these errors. This process of dealing with loop errors is called "closing" loops. Closing loops is a mathematical process that systematically spreads the errors around the cave to minimize the effect of the error on any one shot. In effect, it gives you lots of little errors instead of one big error at the point where the loops close. In this way, there is only minimal distortion of the passages.

Error Types. The kind of error found in a loop has a big effect on how the loops can be closed. There are three types of error in survey data: random errors, systematic errors and blunders.

  1. Random Errors. Random errors are generally small errors that occur during the process of surveying. They result from the fact that it is impossible to get absolutely perfect measurements each time you read a compass, inclinometer or tape measure. For example, your hand may shake as you read the compass, the air temperature may affect the length of the tape, and you may not aim the inclinometer precisely at the target.
  2. Systematic Errors. Systematic errors occur when something causes a constant and consistent error throughout the survey. Some examples of systematic error are: the tape has stretched and is 2 cm too long, the compass has five degree clockwise bias, or the surveyor read percent grade instead of degrees from the inclinometer. The key to systematic errors is that they are constant and consistent. If you understand what has caused the systematic error, you can remove it from each shot with simple math. For example, if the compass has a five degree clockwise bias, you simply subtract five degrees from each azimuth.
  3. Blunders. Blunders are fundamental errors in surveying process. Blunders are usually caused by human errors. Blunders are mistakes in the processing of taking, reading, transcribing or recording survey data. Some typical blunders are: reading the wrong end of the compass needle, transposing digits written in the survey book, or tying a survey into the wrong station.

Least Squares. Most programs use a process for closing loops called Minimizing Least Squares. Least Squares works by solving a large equation that take into account all the redundant data and minimizes the errors. Least Squares assumes that the errors in the survey are random. If the errors are not random, the data violates the mathematical model of Least Squares and the process will not work properly. As a result, if you are going to use Least Squares, special steps must be taken to detect any blunders and compensate for them. Unfortunately, most cave survey programs that use Least Squares do not take the extra steps necessary to deal with blunders. In fact, at this time (March, 2001) the only program I'm aware of that correctly implements Least Squares, is Survex a British surveying program.

Handling Blunders. If a program uses Least Squares and does not handle blunders, the effect is spread the blunder error throughout the cave. This causes well surveyed loops to be contaminated by the errors in the badly surveyed loops. If blunders weren't very common in cave surveys, this might not be a problem, but blunders are very common. I looked at 16 large and relatively famous caves like, Wind, Lechuguilla, Lillburn and Lechuguilla and, on avergage, 26% of the loop had blunders in them. During a recent resurvey of Cave of the Winds, Paul Burger found, on average, one blunder for every 20 shots surveys. Here are some links to more information on loop closure:

Loop Closure In COMPASS. COMPASS uses a loop closure technique that was used by surveyors and cartographers before modern computer were available. It works by closing the best loops first and locking them down so they cannot change. Thus, the worst loops are closed last and the errors from the worst loops are confined to that part of the cave. This way the errors from worst loops cannot spread to contaminate the good loops. This gives a result that is very similiar to a properly done Least Squares, but it is much faster.

The COMPASS loop closer also writes the closed data to a file that is identical to the raw survey data, except that the shot data has been adjusted to close the loops. This means that you can actually test the data and see that the loop errors have gone to zero. You can also look at which shots the closer adjusted. This is useful for finding blunders.

This screen shows general information about the loop closure process. Here, the display shows that there are two loops where length of the loop is zero. Zero length loops cannot be closed and they may indicate a data entery error. Also, some loops cannot be closed because all the shots in the loop have excluded from closing.

Station Information:
Index       Station Parent    Len    Azm   Dip  Status
100  -         FE19    99   38.7m.  110.3    6.0 UnClosed ($0000)
101  -         FE20   100   38.1m.   95.8   20.0 UnClosed ($0000)
102  -         FE21   101   43.3m.  150.4   -2.0 UnClosed ($0000)
103  -         FE22   102   52.2m.  260.9  -28.0 UnClosed ($0000)
104  -         FE23    84   68.7m.  168.3  -18.6 Closed   ($0001)

The statistics display also shows how each shot was handled and the resulting adjustment. Here the statistics show four unclosed shots and one closed shot. The unclosed shots may not be part of a loop or they may be specifically excluded from closing.

Closure Information:
Index: 50  Station One: 981  Station Two: 907  Common: 907
Loop Length:   402.8m.
Residual Error - North: 0.0000m. East: 0.0000m. Vert.: 0.0000m.
Loop Status: Closed   ($0001)

Closure Is Between: FFP4-FFN29
        Common point: FFN29

Index: 51  Station One: 983  Station Two: 903  Common: 903
Loop Length:   619.7m.
Residual Error - North: 0.0000m. East: 0.0000m. Vert.: 0.0000m.
Loop Status: Closed   ($0001)

Closure Is Between: FFP6-FFN25
        Common point: FFN25

The final statistical display shows how the each loop has been effected by closure process. Here you see two loops whose residual errors are zero. If for some reason, the program wasn't able to close one of the loops, the errors would not be zero.

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