To account for the proportion p of the facies, just rescale the semivariogram by the quantity p(1-p).. hence the different semivariograms should be comparable. The fact that the dominant facies tends to be over-represented in the interpolated map is well-known and frequent when using a maximum likelihood classification, see * Goovaerts, P. 1996. Stochastic simulation of categorical variables using a classification algorithm and simulated annealing. Mathematical Geology, 28(7): 909-921.
* Goovaerts, P. and A.G. Journel. 1996. Accounting for local probabilities in stochastic modeling of facies data. SPE Journal, 1(1): 21-29. If you want to avoid the smoothing effect and reproduce target proportions for the different facies, you may want to use stochastic simulation as described in the aforementioned papers. 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: Oriol Falivene [mailto:[EMAIL PROTECTED] Sent: Sat 7/15/2006 10:45 AM To: Pierre Goovaerts; [email protected] Subject: Re: [Fwd: Re: AI-GEOSTATS: Re: generalize kriging variancetoaverage-basedestimators different than] Thank you, I will try with the variograms as you suggested, however as the proportions of each facies are different in the different maps to compare (because of the smoothing), also the sills of the indicator variograms will be different making the comparision non-straightforward. And what about using the proportions of each facies, this seams even more simpler measure of smoothing to me than computing the indicator variograms. For example; as the smoothing increases, the proportions of the dominant facies also increase from that of the original hard data, and the more smoothing the largest the increase. Do you think that computing the proportion of the dominant facies would be of any statistical sense in order to quantify the smoothing effect? Thanks again Oriol Pierre Goovaerts wrote: > 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 > + > + To post a message to the list, send it to [email protected] > + To unsubscribe, send email to majordomo@ jrc.it with no subject and > "unsubscribe ai-geostats" in the message body. DO NOT SEND > Subscribe/Unsubscribe requests to the list > + As a general service to list users, please remember to post a summary of > any useful responses to your questions. > + Support to the forum can be found at http://www.ai-geostats.org/ > > ------------------------------------------------------------------------ > Name: winmail.dat > winmail.dat Type: Surfer Worksheet > (application/x-unknown-content-type-Surfer.Worksheet) > Encoding: base64 > > ------------------------------------------------------------------------ > No virus found in this incoming message. > Checked by AVG Free Edition. > Version: 7.1.394 / Virus Database: 268.10.1/389 - Release Date: 14/07/2006 -- ______________________________________ Oriol Falivene [EMAIL PROTECTED] http://www.ub.es/ggac tel. (+34) 93 4034028 fax (+34) 93 4021340 Fac. de Geologia, Univ. de Barcelona + + To post a message to the list, send it to [email protected] + To unsubscribe, send email to majordomo@ jrc.it with no subject and "unsubscribe ai-geostats" in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list + As a general service to list users, please remember to post a summary of any useful responses to your questions. + Support to the forum can be found at http://www.ai-geostats.org/
