## Re: AI-GEOSTATS: semivariogram for binary data

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• Dear Malin: The semivariogram of an indicator variable is always less than 1. Proof: The experimental semivariogram is (1/2) of the mean of the squared
Message 1 of 3 , Jan 16, 2001
Dear Malin:

The semivariogram of an indicator variable is always less than 1.

Proof:
The experimental semivariogram is (1/2) of the mean of the squared
differences Z(xi+h)-Z(xi) but the values of Z are 0 or 1, then the
semivariogram is (1/2) of the mean of the absolutes values of
Z(xi+h)-Z(xi). Now you use the triangular inequality and you get that
the semivariogram is less than 1.

Regards
Marco Alfaro

Malin Fahller wrote:

> Hi everybody, I feel confused and really need some help to straighten
> things out. I am currently working with geostatistical methods for
> marine geological mapping. My sourcedata consists of sediment samples,
> interpreted seismic profiles, bathymetric data and sonardata. In my
> first, and easiest, case I only use the sedimentsamples to get a rough
> picture of the sedimentary boundaries. So this question concerns the
> use of one single source of data, sedimentary samples. The source data
> is an ascii_file with three columns: (x_location, y_location, category
> (i.e soiltype)). What I have done so far is that for each category
> (i.e soiltype), I have done an indicator transform (for example:
> value 1 = sand, value 0 = not sand). Then I have used GSLIB, gamv, to
> make an omnidirectional semivariogram for my indicator transformed
> data. This has worked really nicely but I get semivariogram values
> that is larger than 1 and this troubles me. How can I possibly get
> semivariogram values that is outside the range 0 - 1 when I have
> indicator transformed data? Is there an error in the program or have I
> misunderstood the mathematics of semivariograms? Can someone PLEASE
> help me out. I reccon this is a basic question, but I just cant
> proceed if I dont get this straightened out. Many thanks in