Here is a summary of the responses I received w.r.t. my question on
Indicator Kriging can work with as many classes as you want. At each grid
will give the probability for each class. You would then need to extract the
class for each node, if you are after a categorical model. For the same
efforts, Sequential Indicator Simulation can give you the categorical model
Monte-Carlo sampling from those local probabilities.
Both algorithms require a variogram model for each class and both are
if you are not familiar with geometrical a n d geostatistical 3D-modelling
then I would emphatically recommend to look for an alternative approach to
your problem, i.e. corresponding to the scientific problem which you would
1. is it possible to reduce to 2D
2. can you transform classes of materials into hydro-geological relevant
parameters (porosity, permeability or K-values) so that you can
work with a single parameter in 3D space (which is difficult enough)
If you want to get a picture of the subsurface only then the relation
of scientific result/expenditure tends to zero.
The GSLIB IK routines are all there is going to be (and all you need). I'm
not sure what you mean by "2-parameter." An indicator CAN only be one of
two values -- zero or one. Either, you have "sand" at location x or you do
not. What you will get out of IK is the probability of having "sand" at an
unsampled location. You can't krige the values 1 through 19 because that
implies a numerical "sequence" to the values, whereas they really are just
arbitrary class designations: "Fred" and "Mary" would do just as well.
Obviously you can run the IK exercise 19 time, once for each class vs. "all
others", but then you're going to need to confront the issue of how you
convert all the probabilities to actual facies maps (Pr > 1/19?) and would
it be consistent. The power of IK is that your spatial model (variogram) is
customized to the variability of the indicator in question. You need a
variogram for each class. The downside is that the indicator technique is
an either-or proposition. The other plus is that IK forces you to confront
the issue of uncertainty.
Did you check out the gslib 1.2 program sisimpdf? This is intended for
categorical variable (class) simulation. It will generate simulated maps of
your 19 categories, but again, you've got to deal with the uncertainty
issue. A simulation is only one of N possible alternative models, all
equally likely. Note: sisimpdf is now incorporated within sisim in ver.
You may need to do some thinking on what you're going to use the result for
-- if a flow model, then you may be interested only in knowing where "sand"
and "gravel" are, because that's where the water is going to flow.
There is some literature around on modeling facies distributions using
truncated gaussian simulation. I've never done it, but the technique has
the advantage of respecting facies relationships: shale can only occur next
to limestone and never next to sandstone -- that sort of thing. I'd
recommend cruising the SCRF web site http://ekofisk.stanford.edu/SCRF.html)
at Stanford and looking through their assortment of papers and look for
titles including "facies" or "truncated gaussian simulation". You can also
download gslib ver. 2 from there.
Note that I'm assuming that you're modeling these lithologies as facies
rather than as discrete layers (formations).
as I see it, your problem is primarily a problem of geometrically modeling,
not of estimation/prediction. Therefore, I would skip GeoStats and start
interactive tool for 3d geometrical design like gOcad from ENSG Nancy,
What do you want exactly to interpolate?
If it's just the probability of occurrence of each
of the 19 classes, IK is the way to go and in the
new Gslib version there is possibility to
perform indicator kriging of categorical variables.
Let me know if it's what you are looking
for and I could send you the source code.
Jon Paul Jones
University of Waterloo
Department of Earth Sciences
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