GEOSTATS: Re: Non-colocated datasets. MUCK
> Hi. what is MUCK? I couldn't access theDeepest apologies. I was unaware that the geocities
> publications section of your web
> page. thanks. Brian Gray
sites were case sensitive!! Link is:
Just when I think I've mastered this Web stuff it
turns around and does something different! You can get
there and to my other pages from the base home page
Back in 1985 or so, when Bill Harper and I invented
non-co-located kriging we didn't know that was what we
were supposed to call it. At the time there was a joke
going round the community about the excessive use of
intials (IK, OK, DK, SK and so on) and there was a
rumour that someone was out there looking into Fuzzy
Universal Co-Kriging (work it out). To distinguish our
approach from the traditional co-kriging, we called it
Multivariable Universal Co-Kriging (MUCK).
The major difference between MUCK and traditional
co-kriging is simply in the definition of the
semi-variogram. We could not use the traditional
approach because we were looking at pressure heads in
water wells in two different aquifers. From the two
surfaces kriged individually, we could see that the
pressure surfaces were highly related. However, we
could not get a semi-varogram which demanded both
measurements at the same location. So we invented the
other one. For a more formal coverage, check out the
relevant section in Noel Cressie's book where he gives
the non-co-located as the standard approach and the
co-located as a historical background.
The kriging equations remain the same. The major
differences are these:
(a) you can use all of your data all of the time to
estimate the semi-variogram
(b) you get a positive definite shape like a normal
semi-variogram. there is no possibility to get
negative values as with the traditional one
(c) the intercept (nugget effect) is directly
analagous to the correlation coefficient which you
woul dget for co-located pairs
The drawbacks are:
(1) if the two measurements are of wildly different
scales, any structure in the semi-variogram would be
masked (same as with all covariance approaches)
(2) the difference between the means of the two
variables is a factor in the MUCK approach. We did not
have this problem in our application, because both
surface had a high degree of trend which had to be
removed, leaving the average for both variables
(residuals) as zero.
Both of these problems can be solved by using a
standardisation (say Normal score) or rank transform
on all of the variables. This will give the correct
model for the semi-variogram (theoretically) which can
then be scaled if necessary or desirable. In the
statistical world an auto-correlation approach such as
this is always given as preferable to a co-variance
approach such as that generally used in kriging.
Does this help?
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