Backsights and default accuracy estimates

[John Halleck]

On Thu, 30 May 2002, Martin Green wrote:

> Date: Thu, 30 May 2002 22:24:52 +0100
> From: Martin Green <mjg54@cam.ac.uk>
> To: John Halleck <John.Halleck@utah.edu>, Olly Betts <olly@survex.com>
> Cc: survex@survex.com
> Subject: Re: Backsights and default accuracy estimates
> 
> ----- Original Message -----
> From: "John Halleck" <John.Halleck@utah.edu>
> To: "Olly Betts" <olly@survex.com>
> Cc: "M.J. Green" <mjg54@hermes.cam.ac.uk>; <survex@survex.com>
> Sent: Tuesday, May 28, 2002 11:06 PM
> Subject: Re: Backsights and default accuracy estimates
> 
> >
> > Forgive my slow reply, I've been out of the country for about 5 weeks...
> >
> > > On Thu, May 09, 2002 at 07:05:04PM +0100, M.J. Green wrote:
> > > > Strictly with the grade 5 BCRA limits, errors should be called for
> greater
> > > > than 2 degrees, for fore sight to back sight discrepancies.
> >
> >   Fore and back site discrepancies of much larger than that can be
> >   *CORRECT* for places with large magnetic problems.  Such data can
> >   be processed properly to distinguish errors from magnetic
> >   anomolies.  (As I've written up before.)
> >
> 
> Survex does not deal with magnetically annomalty problems, therefore it
> should call up an error, if such data is encountered.

  Which is what I have also said. 

  In fact, the message you are replying to had the following when I sent
  it:
     "However, if the program doesn't know how to handle such issues
     correctly (and it is a difficult issue to retrofit in) then
     I agree that descrepancies greater than (say) 2SD should be
     flagged."
  A pitty you didn't leave that text in when you edited the reply..

> In these senarios the error along a chain of reading increasing to the power
> 1.5 with no. of stations, due to the errors in each direction measurement
> adding to all the previous errors(to the power 0.5 as independant) and the
> errors of where the leg started( to the power one as dependant), rather than
> to the power 0.5 in the case of each leg being measured with respect to
> magnetic north. 

  Actually, it is not hard to get any arbitrary amount of error if you
  blindly assume that all readings are magnetic problems, and the error
  isn't in a loop, and you don't have fore and back sights, since it swings
  the entrire rest of the survey.
  That is why proper error analysis is very important in such cases.

  By the way, a number "to the power one" is just that number... I'm not really
  sure what you are trying to say here.  The comment about "to the power 0.5"
  seems to be refering to the rule for error propagation in an addition of a
  number of independent one dimensional measurements.  But note that we are
  doing a three dimensional problem here.  (And note that the vectors here do
  not have independent X, Y, and Z's, since they are a [non-linear]
  transformation of the observed values.)
  You've made an interesting leap from a rules for basicly distances
  to the claim it applies to directions.

> If anyone impliments code for magnetic annomily caves, they
> need to be careful because of this.  Places where fore sights and back
> sights are taken should not be treated in the special magnetic annomily way,
> unless there is evidence to suggest the magnetic field is doing funny
> things, otherwise the errors will unescesarily explode.

  Excuse me?  A good error analysis will tell you whether or not you
  have a problem.  And yes, if you do it in a less than carefull way
  you can have an analysis that models something notably different
  than what you have.

> Sorting out the errors may be tricky in terms of loop closurers.

  Not really...  See my paper on the topic, for example.
  If you have fore and back sights, and loops, that is the easiest
  case.  Fore and back sights, without loops is next easiest.
  And if you have neigher fore and back sights nor loops you can't
  do a good magnetic anomaly analysis anyway.

> How bad can magnetic variations get?

  I've seen 15 degrees between eye level and the floor.

> How quickly do they vary?

  I have no idea.  (Although I've seen reports of a degree a minute in
  high latitudes during a magnetic storm.)

> Do many caves suffer from this? 

  I can point to thirty or so here in Utah.  (All lava tubes.)

>  Are entire caves affected or only part of caves?

  Entire caves.

> It may be that if the magnetic fields are only devitated slightly, then the
> errors assosiated with the fore sight backsight method would become
> comparable to assuming that north does not change, over the size of a
> moderate cave system.

  See above.

>   Particularly if any pitches are involved, where the
> magnetic readings become rather poor in my experience.
> Perhaps you have already mentioned some of this in the article you wrote, I
> read it a while ago so can not remember.
> 
> > [...]
> >
> > > > Perhaps this could be defined so that 2 degrees is when it shouts.
> >
> >   If you are going to shout, then a figure based on the SD's that you
> >   expect seems cleaner.    For extreme example, if the instrument I'm
> using
> >   is my naked eyeball without an instrument, and I have (for example)
> >   10 Degree SD, then a 2 degree discrepancy is not remarkable.
> >   If I'm using a Total station then a few minutes of arc descrepancy
> >   might possibly be appropriate.
> >
> > > [...]
> >
> >
> 
> This remark was made with regard to when survex should complain about
> discrepancies when surveying to grade 5 and there are no magnetic
> annomilies.

  I can't find any mention of the "no magnetic annomilies" restriction
  in the part of the dialog I saved.  Forgive me if I missed it.

>   The problem being the definition of angle measuremnts to grade
> 5 standard, are that they are not greater than 1 degree out.

  I'm not familiar with what a "Grade 5" standard is (must be a cave
  survey thing, rather than a survey thing).  But as I stated above,
  it is not hard to find caves where magnetic north varies more than
  two degrees between stations.  It is still quite possible to do an
  accurate survey in those conditions.
  Mine surveyors in mines with magnetic problems routinely do surveys
  much more accurate than your average cave survey, in mines that have
  notable differences between magnetic north between stations.

  I'm surprised that a standard for survey accuracy would make a claim
  that fore- and backsights would have to agree within a degree.
  This would mean that some caves could never have an "accurate" survey
  since the physical situation doesn't match that specification.
  Can someone else verify for me that the grade 5 standard  really says that?

  Maybe Survex can't handle that, but that doesn't mean it can't be done.
  (And you are right, survex should complain about anything it can't handle
  Properly.)

>  It does not
> mention anything about gaussian distributions, so I was using a cyclic
> argument about how to determine how many standard deviations to complain at,
> given I am uncertain about how big one standard deviation should be if the
> only info is the survey said it was done to grade 5.  This would make the
> surveying software consistent with the grade 5 standard, in the fore sight
> back sight no magnetic anomily senario.

  And how, pray tell, can you tell the magnetic anomaly senario from
  a blunder senario if you don't do the analysys?  (A rethorical question.)
  
> Further E-mails that I wrote, mention other ways of deciding how to tell
> what 1sd in a grade 5 survey might be.

  I'll do my standard mumble under my breath about cavers re-inventing
  the wheel instead of following standard survey practice.

  If you want to know that the Standard Deviation is, take surveys that
  are of this "grade 5", and do the error analysis, and then you'll have
  your number...  independent of any theoretical arguments as to what
  it might or should be.  That will give you what it *is*.  (And if the
  number of surveys is too small to give a good statistical assurance,
  then the question is moot anyway.)

> Martin