Hi Oriol, 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. 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. 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 7:28 AM To: [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED]; [email protected] Subject: Re: AI-GEOSTATS: Re: generalize kriging variance to average-basedestimators different than Hi all!. Isobel, Jan and Adrian, thank you for your useful suggestions. I have been studying the information you suggested me to read. Please, correct me if I am wrong: "It is possible to compute the estimation variance for any weighted average estimator. But in order to do this we need to know the semivariogram of the property". More things regarding estimation variance: Actually, I am working in the interpolation/estimation of categorical properties (i.e. facies). Categorical properties take discrete values which do not need to follow any ordering (i.e. from category A to category C a transitional step with category B may not exist). 1) A possible manner of generating interpolation maps of this type of properties would follow this procedure: 1st) Order categories (this can be difficult to justify in some cases). 2nd) Transform the orderd categorical property into a continuous property by assigning a numerical value to each category. 3rd) Interpolate the numerical values of the continuous property. 4) Truncate the results of the interpolation of the continuous property with a number of thresholds equals to the number of categories minus one (the thresholds should be located between the assigned values), to get the interpolated categorical properties (or facies map). The estimation variance (or kriging variance) refers to the results of the continuous property interpolation (3rd step) and not to the categorical property obtained after truncating the continuous property (4th step). And therefore I do not know if it would be correct to assign this estimation variance to the estimation variance of the categorical property results (probably not), any idea on that? 2) Another option for generating interpolation maps of categorical properties is indicator kriging for categorical variables. The following procedure is used: 1st) The categorical property is transformes into n new properties (one for each category) according to the indicator transform for categorical variables, the value of each new property corresponds to the probability of finding the related category (or facies) at a given position. 2nd) Each new property is interpolated over all the grid and the results correspond to the probabilities for each category to be present in a location. 3rd) In each grid cell the category with the highest probability is chosen to obtain the interpolated categorical properties (or facies map). In this case we have a number of estimation variances related to occurrence probability at each point (one for each category). It is intuitive to chose the one of the selected category, but again I am not sure of how this variances, which are originally related to probability of occurrence, can be transported into variances of the categorical property, any idea on that? And one more question: I would like to know if there is any relationship between kriging estimation variance and the variance of the actual kriging estimates, any idea? Thanks a lot! Oriol Falivene Isobel Clark wrote: Oriol Download for free, my old book Practical Geostatistics. Chapter 4 tells you all about calculating the variance for any weighted average estimator. Follow links from http://www.kriging.com Isobel Oriol Falivene <[EMAIL PROTECTED]> wrote: Dear Colleagues, I'm a PhD student working on interpolation of categorical variables (like facies). I would like to know if it's possible to generalize the kriging variance to other average-based estimators different than kriging, such as kriging with an areal trend, indicator kriging or inverse distance weighting?; if it's possible could you send me some references where I can find that?. Thank you. Best regards Oriol -- ______________________________________ 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/ ________________________________ No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.1.394 / Virus Database: 268.9.10/384 - Release Date: 10/07/2006 -- ______________________________________ 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/
