Hello,
 
If you want to quantify the smoothness of an interpolated map of facies,
you should use measure of spatial connectivity. For example, the indicator
semivariogram provides information on the probability of transitioning
from one facies to another, as a function of the separation distance.
Superimposing the variograms computed from different interpolated maps 
would allow a quick visual comparison of the degree of smoothness of the
different maps.
 
Pierre
 
Pierre Goovaerts
Chief Scientist at BioMedware Inc.
Courtesy Associate Professor, University of Florida
President of PGeostat LLC
 
Office address: 
516 North State Street
Ann Arbor, MI 48104
Voice: (734) 913-1098 (ext. 8)
Fax: (734) 913-2201 
http://home.comcast.net/~goovaerts/ 

________________________________

From: [EMAIL PROTECTED] on behalf of Oriol Falivene
Sent: Sat 7/15/2006 10:07 AM
To: [email protected]
Subject: [Fwd: Re: AI-GEOSTATS: Re: generalize kriging variance 
toaverage-basedestimators different than]






Hi Dr Goovaerts,

> It is not clear what you want to do with the kriging variance you obtain...
> Probably you want to quantify the degree of reliability of the allocation
> of a particular location to a given facies. This could be measured by the 
> variance
> or entropy of the distribution of probabilities of occurrence of facies at 
> that
> location, see my book page 354. This probability distribution is easily 
> computed
> by indicator kriging or you can use truncated Gaussian simulation if there is
> any physical ordering of your facies.

I'm trying to get a measure of the smoothing effect related to a
particular algorithm (truncated kriging, truncated inverse square
distance, indicator kriging,...) and a particular algorithm set up
(searching conditions or number of neighbours used to obtain each facies
estimate), applied to interpolate facies distribution in a dense coal
mine dataset.

A good measure would be the variance of the estimated property, but
since I am working with a categorical property (i.e. facies), it is not
direct to get this variance (one must assume a certain facies ordering
and attribute values to facies, and I'm not sure which would be the
effect of this assumptions int the variance of measures). And therefore
I was looking for other options like kriging estimation variance.

>
> For your last question, look at Journel and Huijbregts "Mining Geostatistics"
> page 451 for the "smoothing relations" that link the average kriging variance 
> to the
> variance of observations and the variance of kriging estimates.

thank you, I will take a look to this.

Oriol
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