Hi Samuel,
I have dealt with similar problems when analyzing the spatial
distribution of dioxin and other heavy metals in river sediments.
Core lengths can strongly fluctuate from one sampling point to the
next. The empirical approach I used was to weigh each sample
proportionally to its length both in the computation of semivariograms
(use of weighted semivariogram estimators) and in the kriging
procedure (rescaling of kriging weights to account for core length).
There was no publication on this approach and reports are confidential.
These days I would use a less empirical approach and capitalize on the
analogy with the treatment of cancer rates, where the reliability of rates
is a function of the population size. You could still use weighted
semivariogram estimator, but use a kriging with measurement error
approach, whereby an error variance term (here inversely proportional
to the length of the core) is added to the diagonal elemnts of the
kriging matrix.
Here is just a suggestion but I am sure that some mining geostaticians
will come up with a more elegant solution.. I also think that Jayme
Gomez presented a paper on this issue (and the downscaling or
disaggregation problem in general) at the last geostat congress in
Banff, but since I only caught the last part of his presentation I
might be wrong.
Pierre
Dr. Pierre Goovaerts
President of PGeostat, LLC
Chief Scientist with Biomedware Inc.
710 Ridgemont Lane
Ann Arbor, Michigan, 48103-1535, U.S.A.
E-mail: [EMAIL PROTECTED]
Phone: (734) 668-9900
Fax: (734) 668-7788
http://alumni.engin.umich.edu/~goovaert/
On Tue, 26 Oct 2004, samuel verstraete wrote:
Hi,
I have a 3D data set that has been sampled by a private company. They
lacked a complete knowledge of geostatistics so there is no sampling
strategy involved. Another thing is that the support of the samples is
strongly fluctuating. Horizontally the sampling support is constant and
can be considered as a point (about 70cm^2 compared to a few hectares)
Vertically the sampling support is not stable and rather huge in
comparison with the vertical scale... (sampling can be 0.10 to 1 meter
and maximum depth would be 5 to 6 meter or even less)
I've read in the literature that there is a possibility to correct for
such a things, through regularization. But none of the literature seems
to discuss the possibility that the samples themself do not always have
the same support, as stated before samples can have a support that is 10
times bigger than the smallest sample.
Question is... Is there any other literature that discusses this matter
and even more importantly is there any software out there that can take
this sampling support into consideration when I'm calculating the
variogram or when I start with estimation/simulation of the field.
Thanks in advance,
--
Samuel Verstraete
Ghent University
Faculty of Bioscience Engineering
Dept. of Soil Management and Soil Care
Coupure Links 653, B-9000 Gent, Belgium
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