What is the usual amount of loop closure error

[Olly Betts]

On Tue, Aug 29, 2006 at 04:10:01PM +0100, Dr Footleg wrote:
> I am fairly new to cave surveying in practice, and am trying to plot up a 
> large cave system which contains much historical data plus some new data 
> from my own trips. I have found some loops closures are significantly out, 
> but have no idea what would be the normal expected amount of error. In 
> other words, when should I suspect that there are errors in the survey data 
> itself rather than just normal error in the instrument readings?

For BCRA grade 5, anything more than a few percent is definitely
suspect, though it depends on the nature of the passage - long legs
push the precision with which you can read the compass and clino.

Assuming you can correctly read to the nearest 0.5 degrees (which
is probably not really achievable), the sampling error will be 0.25
degrees on average which is 13cm for a 30m leg).  With short legs, it's
the station position error which will tend to dominate - it's easy
enough to get the tape on the station accurately, but sometimes harder
to read the compass and clino from the exact point.

The expected error goes up with the square root of the number of
legs (because random errors tend to cancel) so longer loops will
tend to look better.

If you're using Survex, the .err file shows 3 ratios which can
be very revealing.  Here's an example:

 131.part3.113 - 131.part3.114 - 131.part3.69 = 131.part2.69 - 131.part2.68 - 131.part2.67 - 131.part2.66
 Original length  30.64m (  5 legs), moved   0.76m ( 0.15m/leg). Error 2.48%
 3.284280
 H: 4.064168 V: 0.770105

Survex builds an error model using standard deviations taken from the
definitions of the BCRA grades (by default - you can specify other
values if you wish and these will be used instead).  We assume that
the standard deviation is half what the BCRA grade specifies for the
tolerance - so BCRA grade 5 says compass read to within 1 degree, so we
assume the standard deviation is 0.5 degress (so statistically 95.44% of
readings will be within 1 degree).  This is a little arbitrary, but it
only scales the ratios up/down.

The number 3.284280 is the ratio of the actual misclosure to what
Survex's error model gave for the expected error.  Assuming the
BCRA grades give realistic numbers for what is achievable (generally I
think the allowed tape and station position errors are more generous
than those for compass and clino), then anything less than 1 is fine.
The larger this number, the more likely there's a bad reading or
that a survey is connected in the wrong place.

The H and V values are similar ratios, but only consider the horizontal
and vertical components of the misclosure and error model.  Here the
horizontal ratio is high but the vertical ratio is very reasonable
which strongly points to there being a bad compass reading (or perhaps a
reversed leg with a small clino reading).  If H is small and V large,
that suggests a bad clino reading, or a reversed plumbed leg.

If you have historical and modern data, bear in mind that the magnetic
declination may have changed noticably between the different surveys.
Also they old and new data have probably been surveyed with different
instruments, so calibrating instruments in particularly important (sadly
if you don't have calibrations for the historical data you're a bit
stuffed...)

Hope the above is of some help.

Cheers,
    Olly