[ai-geostats] Definition of standardize variograms
Title: Definition of standardize variograms Dear list, While playing around with different software, I encounter different definitions for standardized variograms. Surfer (which is using the terminology of Variowin), uses the term standardized semivariogram for variograms obtained by dividing the semivariance by the lag variance, while GS+ uses the total variance. While the function obtained in GS+ is only a matter of rescaling variograms, allowing so various variograms to be compared, those proposed in Surfer have the same pupose as the local, pairwise and/or general relative variograms (see Isaaks Srivastava, page 163-170), that is to reduce the influence of local means. Interestingly enough, one may note that very few software propose relative variograms while I, very personally, consider these functions as essential for detecting spatial structures of many environmental variables. I have thus here two questions about the use of standardized/relative variogram: 1) What is the correct terminology or definition for standardized variograms? (I personally do not like very much the use of standardized when the standardisation is only applied to each lag...) 2) The general relative variogram (lag divided by the mean of the lag) has properties that are very similar to the standardized variogram (lag divided by the variance of the lag) but both functions differ. How shall one decide what to use and what are the relative properties of these functions? Thank you in advance for any feedback. Gregoire PS: a few points here good be added to Tom Mueller's FAQ on Geostatistical Software Conventions. __ Gregoire Dubois (Ph.D.) JRC - European Commission IES - Emissions and Health Unit Radioactivity Environmental Monitoring group TP 441, Via Fermi 1 21020 Ispra (VA) ITALY Tel. +39 (0)332 78 6360 Fax. +39 (0)332 78 5466 Email: [EMAIL PROTECTED] WWW: http://www.ai-geostats.org WWW: http://rem.jrc.cec.eu.int The views expressed are purely those of the writer and may not in any circumstances be regarded as stating an official position of the European Commission. * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
[ai-geostats] Definition of standardize variograms
Gregoire Michel David coined the term relative semi-variogram back in the 70s for what I think you mean by general relative -- that is, each lag is divided by the square of the mean of the samples used at that lag. Gary Raymond proposed the pairwise relative soon after. I used the type you are describing where the whole semi-variogram is divided by the same mean-squared in my 1979 paper (Does Geostatistics Work) because I was analysing a line of samples where all samples are used at every lag. The term standardised in general statistics usually means dividing through by the variance or standard deviation (not a mean). This is the first time I have seen it in context with a semi-variogram. Seen with no other information, I would have taken this to imply standardised to total sill of 1. This would mean dividing by the variance, not the mean-squared. Relative semi-variograms help you avoid the proportional effect if you are trying to calculate a semi-variogram on positively skewed data. Noel Cressie wrote a paper in Mathematical Geology (early 90s?) which showed that the David relative semi-variogram was topologically equivalent to using logarithms. You data does not have to be lognormal to do this. Computationally, taking logarithms is faster and more stable than relative semi-variograms. Probably why most people don't bother. Gary Raymond provides software for the pair-wise and Geostat Systems will have relative semi-variograms. Don't know of any free stuff. Isobel http://geoecosse.bizland.com * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
RE: [ai-geostats] Definition of standardize variograms
Hi Gregoire, I agree with you regarding the merits of the standardized semivariogram as implemented in variowin software. In one of my last studies, the rescaling by the lag variance helped correcting the preferential sampling of wells with high arsenic levels, leading to a susbtantial decrease in random fluctuations of the experimental semivariograms. While the general relative semivariogram approximates the lag variance by the square of the lag mean, the standardized semivariogram uses the actual lag variance, hence makes less assumptions. Regarding the terminology, I guess we should used a term like lag-standardized to distinguish the global and lag-specific standardization or rescaling of semivariogram values. Cheers, Pierre -Original Message- From: Gregoire Dubois [mailto:[EMAIL PROTECTED] Sent: Tue 4/5/2005 9:48 AM To: ai-geostats@unil.ch Cc: [EMAIL PROTECTED] Subject: [ai-geostats] Definition of standardize variograms Dear list, While playing around with different software, I encounter different definitions for standardized variograms. Surfer (which is using the terminology of Variowin), uses the term standardized semivariogram for variograms obtained by dividing the semivariance by the lag variance, while GS+ uses the total variance. While the function obtained in GS+ is only a matter of rescaling variograms, allowing so various variograms to be compared, those proposed in Surfer have the same pupose as the local, pairwise and/or general relative variograms (see Isaaks Srivastava, page 163-170), that is to reduce the influence of local means. Interestingly enough, one may note that very few software propose relative variograms while I, very personally, consider these functions as essential for detecting spatial structures of many environmental variables. I have thus here two questions about the use of standardized/relative variogram: 1) What is the correct terminology or definition for standardized variograms? (I personally do not like very much the use of standardized when the standardisation is only applied to each lag...) 2) The general relative variogram (lag divided by the mean of the lag) has properties that are very similar to the standardized variogram (lag divided by the variance of the lag) but both functions differ. How shall one decide what to use and what are the relative properties of these functions? Thank you in advance for any feedback. Gregoire PS: a few points here good be added to Tom Mueller's FAQ on Geostatistical Software Conventions. __ Gregoire Dubois (Ph.D.) JRC - European Commission IES - Emissions and Health Unit Radioactivity Environmental Monitoring group TP 441, Via Fermi 1 21020 Ispra (VA) ITALY Tel. +39 (0)332 78 6360 Fax. +39 (0)332 78 5466 Email: [EMAIL PROTECTED] mailto:[EMAIL PROTECTED] WWW: http://www.ai-geostats.org http://www.ai-geostats.org WWW: http://rem.jrc.cec.eu.int http://rem.jrc.cec.eu.int The views expressed are purely those of the writer and may not in any circumstances be regarded as stating an official position of the European Commission. * By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
