[This article is in progress, but is now complete enough to be usefull, feedback is welcome. ]
This article is a more basic article than my Internal Angles article, and probably should be read before that one..
For any real surveyors that wander by here, the background is hand held compasses surveying lava tubes. Angle readings are typically to the nearest half degree, and the magnetic anomalies in lava tubes are often 10 or 20 degrees and sometimes more.
This article was prompted by my reading once again that "Fore- and back-sights cannot correct for erroneous readings caused by distortion of the earth's magnetic field" this time in "The Effects of Lava on Compass Readings: Part 1" - Dale Green [Compass and Tape, Vol. 16, Number 4, Issue 56 (December 2004)]. I waited for part 2, but it didn't actually have anything that would overturn accepted survey theory either...
Since this may indicate a more widespread lack of understanding in the cave survey community, this is a basic tutorial. I don't think that any of it is really new (although it may be to cavers), and is just a rehash of what appears in older [mine] surveying publications.
I would like to thank the many people who have checked over this article (so far) before it became public. They've saved me (once again) from a number of public mistakes. I'd like to give particular thanks to Doug Bruce (a licensed surveyor), and Dr. M. K. McCarter (a mine survey instructor) who have both suggested significant improvements to the article. [...I'm still working on incorporating their changes...]
Note that the folk surveying at Lava Beds in California have been using an equivalent technique to correct for magnetic anomolies for many years. They've even done surveys down a tube making the corrections, and then out another entrance and closing, to compare the corrections in the tube with the full loop. [Thanks to Bill and Peri Frantz for the information on this.] I think this more than shows that such corrections are not only possible, but practical in the real world.
Table of contents.
There is an implicit assumption in some of what follows that your survey has some reasonable basis of bearing to start with. How to come up with this is covered later.
One has to assume that the survey we are looking at is the result of good survey practice. The normal sources of surveyor-induced anomalies (reading the compass with magnetic wire-framed glasses, helmet and light too close, etc.) have been avoided, so that the only magnetic anomalies are those of the stations themselves.
Consider two stations, A and B, and a foresight from A to B, and a backsight from B to A. In the absence of magnetic anomalies you would expect that the foresight and backsight would differ by 180 degrees. However, if magnetic north is different at the two stations (not that unlikely in a lava tube), the foresight and backsight will differ, and no amount of remeasurement or checking will change that.
What does this discrepancy mean? If, for example, the backsight is 5 degrees counterclockwise from what would be expected from the foresight, then that implies (with a good, careful survey) that magnetic north at station B is rotated 5 degrees clockwise from the orientation of magnetic north at station A. The foresights and backsights on the next leg of the traverse1.3. can similarly be used to compute the direction of the deviation at the next station with respect to the first, and this can be continued for the entire connected survey. (Although I know of no cave surveying software that does anything other than average foresights and backsights.)
Some folk might argue at this point that this means that the errors accumulate as one goes further and further down the survey. To some extent this is true, but one would expect that [with good survey practice] the errors are random and not systematic, which would mean that they, in the long haul, tend to cancel. Note that with any redundancy such drift can also be compensated for. I have noticed that such arguments (usually) falsely assume something like the following; "If the standard deviation of a shot direction is [for example] half a degree, then the standard deviation at the end of 100 shots is expected to be 50 degrees." (As elementatary survey books point out, the correct expectation for the 100 shot traverse just mentioned is closer to a standard deviation of 7 degrees.)
My Internal Angles Article, shows that if there are loops or other redundancy, it is straightforward to distinguish magnetic anomalies from blunders. So that topic will only be touched on lightly in this article.
So, let us take an example survey, and walk this all through. We'll assume you have a good basis of bearing for the initial point and walk through the rest.
The example survey is laid out as follows:
A--B E | | C--D
So that the difference between the original and processed data is actually visible I'll assume large anomalies. I'll also assume a totally flat survey, since the inclinations don't actually figure into anything that follows, and would just complicate the presentation.
In the tradition of math classes everywhere, I've set it up so that the "right" answers are right angles... although nothing in the method actually cares.
Contrived Survey Data: (In the form typically seen in a mine surveyor's fieldbook)
BS is Back Station (Sometimes written +S) IS is Instrument Station (Where you are standing, which makes it what cavers call the "From station") FS is Forward Station (Sometimes written -S) SD is Slope Distance (i.e., Measured distance) FS is what cavers would call the "To" station, and BS is what cavers would call the "From" station". BS IS FS AZIMUTH VERT-ANGLE SD ----------------------------------- A B 90 0 10.0 A B 250 0 B C 160 0 10.0 B C 10 0 C D 100 0 10.0 C D 255 0 D E 345 0 10.0 D E 175 0 -----------------------------------
The first step would be to gather together, for each point, all the angles measured from that point. In this case, the data starts out that way, so nothing need be done.
There are two ways to proceed from here... One could compute the differences in magnetic north between pairs of connected stations in the traverse, and then go back and reference them to the starting station, or we can do as I do below and rotate stations to match the orientation of the original station as we go.
Starting with station A, the shots involved in going to B are (ignoring inclination and distance):
BS IS FS Azimuth -------------- A B 90 (foresight) A B 250 (backsight)
The foresight from A to B was 90 degrees, so one would expect (in the absence of magnetic deviations) that the backsight would be 270 degrees. It is actually 250, so it is 20 degrees less (counterclockwise) than expected, so we can assume that magnetic north is rotated 20 degrees positive (clockwise) at Station B compared with station A. [Discrepancy = 250 - (180+90) = -20 degrees]
So the shots from station B which were:
BS IS FS Azimuth -------------- A B 250 B C 160
Can now be corrected (adding in the computed deviation) to:
A B 270 B C 180
(One could also view this as subtracting the observed discripancy, and that's the same thing if you keep careful track of the signs.)
Now the shots from B have been rotated to match the orientation of the magnetic field at A.
Using the corrected information for station B, we can now proceed to get the deviation for station C.
B C 180 -- (foresight) Corrected value B C 10 -- (backsight) Value from the notes.
With a foresight of 180, we would expect a backsight of 0 (or 360) degrees. We have one of 10 degrees. The discrepancy is 10 - (180-180) = +10 degrees. This is 10 degrees off in the positive (clockwise) direction. So the computed deviation of station C (referenced to station A) is -10 degrees (i.e., 10 degrees counterclockwise.) So now the shots involving C:
B C 10 C D 100
Can be corrected:
B C 0 C D 90
On to the shots involving D...
C D 90 -- (foresight) corrected value. C D 255 -- (backsight) value from the notes.
Discrepancy = 255 - (90+180) = -15 (counterclockwise), so the deviation (compared to station A) is +15 degrees. So now the shots involving D are:
C D 255 D E 345
Which correct to
C D 270 D E 0 (or 360)
On to station E
D E 345 (foresight) D E 175 (backsight)
Discrepancy = 175 - (345-180) = +10, magnetic north at E is therefore - 10 degrees compared to station AOriginal E shots:
D E 175 (backsight)
D E 180 ( backsight)
SO, the final corrected survey is:
BS IS FS AZIMUTH VERT-ANGLE SD ----------------------------------- A B 90 0 10.0 A B 270 0 B C 180 0 10.0 B C 0 0 C D 90 0 10.0 C D 270 0 D E 0 0 10.0 D E 180 0 -----------------------------------
And the computed magnetic deviation at each point (with respect to point A) is:
B = +20 C = -10 D = +15 E = +10
Note that this process is equivalent (mathematically) to what would have been achieved had turned angles been used at each station. Note that just because a surveying term "turned angles" has been used, doesn't mean anything fancy had to be done in the cave (other than just shooting both foresights and backsights). And nothing particularly complex has to be done in processing other than the simple procedures above.
If you can get to a point by different routes, then you have loops, and can use the techniques from my earlier paper.
An obvious assumption being made with this technique is that all shots *FROM THE SAME POINT* have the same offset from magnetic north. This is generally true unless the anomaly is being caused by something the caver is carrying. This assumption is one reason that some early mine surveys were run with a tripod-mounted Brunton. It insured that both foresights and backsights were made from the same point.
*Usually* a slight displacement of the compass won't cause a noticible change of deviation, so the "same point" assumption is not going to cause much of a problem. And, of course, it is not going to be any worse than the procedure of not correcting for deviations at all. If you have a surveying tradition where all points have to be physical points on the wall, you will have problems trying to achieve this same point criterion, but there are standard techniques that can be used to have points offset from the walls.
Some arguments I've heard against fore- and backsights involve solo surveyors or crawlways. Even in those cases, although I don't recommend it, it is possible to shoot foresights on the way in and backsights on the way out from the same points.
If you were prone to averaging foresights and backsights no reasonable analysis would be possible. For shot AB this would give you a recorded number of:
(azimuth_A + anomaly_A + azimuth_B + anomaly_B) / 2
which hopelessly intermingles the shots and any magnetic anomalies.
Note that if you automatically compute coordinates directly from your input shots, and then hand those coordinates off to a least squares routine, you don't get the right result. This is because the step of computing the coordinates or coordinates loses information. (And the output basicly becomes what you would have had if you had averaged foresights and backsights.) This is not a weakness of least squares, this is a weakness of the technique of computing the coordinates (or vectors) before compensating for known data problems.
Without loops you have no redundant information to check against, so detecting blunders this way is not possible. HOWEVER, a survey with fore-and backsights does have SOME information that can be used to help tell what's going on even in those cases.
[Example of what you can pull from traverse satistics from a traverse goes here... This should elaborate on the prior paragraph.]
[??? Should this be a separate article ???]
The article above covers how to compute the orientation of the points of the survey relative to each other. But it has to this point ignored the issue of how to orient that collection to the "real world". (Or, alternately, how to orient that first point to the real world, so that you can orient the remaining ones as above.)
Well, it is time to address that issue. There are a number of ways to get a good basis of bearing1. for the survey.
What can be done to orient the origin(s) of the cave survey?
Star shots: If you don't mind staying out at the site some night, and have patience, and have read up on it, star shots are a possibility. (But overkill for most cave surveys.) Details can be found in most elementary surveying books. [Warning, the north star is on the order of a degree out... If you are going to do a star shot, learn to do it right. (Or get an ephemeris, and do your measurement at upper or lower culmination], which are the times it is exactly north.) For most of the U.S. Polaris is high enough that it is probably difficult to shoot it accurately.
Sun shots: If you know the location of your cave, an accurate time, and you record the direction to the sun as viewed from the cave, you can go home and compute what direction that really was. It is most accurate around sunrise or sunset; 30 seconds of error in time gives you about one degree in angle error around noon (depending on the sun's declination and the observers lattitude). Details can be found in most elementary surveying books.
Winging it from the map: Out here in the west there are usually mountains visible (particularly from our lava tubes). Most ranges have a mountain or two (or ten) with a benchmark that has known coordinates. You can inverse4. the coordinates of a line from the cave to the mountain and get the actual direction much more accurately than needed for your average cave survey. You can then shoot the same line, and compare the results for a good magnetic north correction. Often the government has already helped you out by providing a nearby benchmark with known coordinates. [For example, here in Utah at Tabernacle Hill Lava tube there is a USGS benchmark within sight of the cave and only a few minutes walk away. Its coordinates are known, and the coordinates of many of the visible mountains in the distance (10+ miles) are are also known. [...Need error analysis here...]
GPS; [...Need error analysis...] Nothing could be easier. Get the coordinates of the initial point, and the coordinates of some point visible from it and a goodly distance away, and inverse the coordinates to get the "real" bearing of that line of sight.
Proper use of foresights and backsights, and care in processing the data, allow you to handle surveys where there are magnetic anomalies. Even without a good basis of bearing you can get the magnetic deviations of the points (with respect to the starting point), and with a good basis of bearing you can get them with respect to north. If one doesn't have both foresights and backsights, proper processing isn't really practical without loops or other redundancy. These techniques don't involve anything particularly fancy in the field, but do require a careful survey religiously recording foresights and backsights.
1. It is just too much work to try to figure out what Cave-Survey specific terminology is at the moment. [Insert my standard objections to cave surveying having terminology other than that of standard surveying.] This paper will unappologeticly try to use standard mainstream surveying terminology in most cases.
2."Basis of Bearing" is what you have used to determine the actual north at the starting point of a survey instead of just the assumed magnetic directions.
3."Traverse" is a collection of points connected by survey shots to only the preceding and following points. Junctions connected by traverses (most cave surveys) are called "Traverse Nets".
4."To inverse" is to compute, given two coordinates, a bearing or azimuth between them. (This is the inverse of the problem of computing coordinates from a bearing or azimuth, and a distance.
This page is http://www.cc.utah.edu/~nahaj/cave/survey/internal-angles-example.html © Copyright 2005 by John Halleck, All rights reserved. This page was last modified on July 12th, 2005