Here is a summary of the responses I received w.r.t. my question on

indicator kriging.

Hi Jon,

Indicator Kriging can work with as many classes as you want. At each grid

node, it

will give the probability for each class. You would then need to extract the

most

probable

class for each node, if you are after a categorical model. For the same

amount of

modeling

efforts, Sequential Indicator Simulation can give you the categorical model

by

sequential

Monte-Carlo sampling from those local probabilities.

Both algorithms require a variogram model for each class and both are

available in

GSLIB.

Gilles

Hello Jon,

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

like

to

analyze, e.g.

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)

3.? etc

If you want to get a picture of the subsurface only then the relation

of scientific result/expenditure tends to zero.

Regards,

Heinz Burger

Jon,

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.

2.0.

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).

Regards,

Chris

Hi Jon,

as I see it, your problem is primarily a problem of geometrically modeling,

and

not of estimation/prediction. Therefore, I would skip GeoStats and start

with some

interactive tool for 3d geometrical design like gOcad from ENSG Nancy,

France

(http://www.t-surf.com/).

Good luck,

Helmut Schaeben

Hello,

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.

Regards,

Jon Paul Jones

University of Waterloo

Department of Earth Sciences

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