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Re: GEOSTATS: Variogram Modeling

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  • roswell marjorie
    While we re at it, are their any errata for the Applied Geostatistics book by Isaaks and Srivastava? I m trying to tackle it on my own, but I was pretty
    Message 1 of 7 , Jan 9, 1997
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      While we're at it, are their any errata for the Applied Geostatistics book
      by Isaaks and Srivastava? I'm trying to tackle it on my own, but I was
      pretty certain of at least one error.

      (I tried reading it on my Carribean trip: I succeeded in completing only
      the review chapters...) (I'll get through it eventually. Does anyone give
      you any "credit" if you learn this stuff on your own?)

      Margie


      On Wed, 8 Jan 1997, Mohammad J Abedini wrote:

      > of the book written by Isaaks and Srivastava, it reads:
      >
      > 4- Is there any ERRATA being written for GSLIB manual? I need to confirm
      > some of the mistakes that I encounter in using the manual.



      _________________________________________________________
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    • Dubois Gregoire
      ... So as mentioned by Prof. Roberto Bruno, this decrease is often refered as hole effect . Here is an attempt to show a semivariogram with this hole
      Message 2 of 7 , Jan 9, 1997
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        Mohammad J Abedini wrote:
        >

        >
        > 3- If variogram value start to decrease after reaching the sill, what is
        > the physical meaning of that?
        >


        So as mentioned by Prof. Roberto Bruno, this decrease is
        often refered as "hole effect" .

        Here is an attempt to show a semivariogram with this "hole effect"


        (gamma)
        |
        | B
        | + + +
        | A + + C +
        | + + + +
        | +
        |+
        |______________________
        A B C Distance



        This suggests you that the samples separated by the distance C
        are more similar than those separated by the distance B, even if
        the distance C is greather that B. So you are in a non stationnary
        as you have a repetition of your structure (the behaviour in A
        is similar in C)

        This case appears if you have repetitions of the spatial pattern
        you are analysing. As an example, it is often the case when analysing
        chemical components in sedimetary rocks (because of the possible repeated
        periodic layers) or in environmental pollution if the pollutant is
        contaminating soils through rainfall. In radioecology, the field I'm
        involved in, we refer to this phenomenon by "hot spots".

        This is another reason why a semivariogram should be calculated at
        different lags and/or on the ranks in order to try to model first
        the very general spatial pattern of your variable.


        Hope this helps,

        Gregoire


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      • John Kern
        Additional comments: When the variogram starts to decrease from some sill value this is an indication of periodicities in the data. If periodic behavior is
        Message 3 of 7 , Jan 9, 1997
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          Additional comments: When the variogram starts to decrease from some sill
          value this is an indication of periodicities in the data. If periodic
          behavior is high frequency, then you see the oscilatory behavior in the
          variogram associated with a hole effect model. If the periodic behavior is
          low frequency relative to your study area (sampling window) then it is seen
          as just a decreasing variogram at long lags. This is a good indicator that
          there are large scale trends (relative to the sampling window) in the data
          which could be modeled as linear or quadratic or more complex response
          surfaces with correlated residuals.


          On anisotopy, Borgman and Li 1994 Math Geology give a nonparametric
          technique for estimating the axes of anisotropy. The procedure allows one
          to then use a linear transformation of the lag domain into a single
          direction in which the model fitting is conducted. This allows the use of
          all lag pairs in the model fitting procedure and ensures constant sill in
          all directions and the same set of nested structures in each direction
          provided you have enough data to detect multiple structures. In my
          experience it takes a lot of irregularly spaced data to estimate the shape
          parameters of a single structure let alone more than one structure. Good
          luck, John Kern

          >My 2cents worth on some of the following posted questions.
          >
          >>
          >> 1. On page 377 of the book written by Isaaks and Srivastava, it reads:
          >>
          >> "The most useful guideline for choosing weight coefficients is to remember
          >> that their sum must equal the sill of the sample variogram"
          >>
          >> The above condition is not satisfied by neither of the variogram shown on
          >> page 27(Figure II.5) and page 28 (Figure II.6) of GSLIB manual. If these
          >> variogram are generic, that is fine otherwise what is the cause of the
          >> discrepancy?
          >>
          >
          >My calculation of the sum of the weight coefficients for Fig 11.5 is
          >0.22+0.53+0.25=1.00 for both the NS and EW directions. This appears
          >pretty close to the sill values.
          >
          >For Fig. II.6 i get 0.40+0.40+0.95+0.9=2.65 for both directions. This
          >matches OK the higer sill direction. I presume the question is for the
          >other which has a sill around 1.7 or 1.8. The text notes that the
          >last spherical structure has a range of 80K and does not practically
          >contribute. Take away the weight coefficient of 0.90 and viola you
          >get 1.75.
          >
          >> 2. On page 383 of the same book at the bottom of the page, it reads:
          >>
          >> "To Summarize, the geometric anisotropy requires some foresight in
          >> modeling the directional sample variograms. All the directional variogram
          >> models must have identical sill values. Each nested ..........
          >> with the same coefficient."
          >>
          >> By the last sentence, I am assuming they mean the contribution coefficient
          >> of each structure (i.e., cc value). First of all, why that should be the
          >> case? etc etc etc [snip]
          >>
          >
          >Your on you own there. I cheat and assume everythings nice and isotropic.
          >Bad boy, I know......
          >
          >> 3- If variogram value start to decrease after reaching the sill, what is
          >> the physical meaning of that?
          >>
          >
          >Dont know the technical reason, but I found a similar thing when calculating
          >a variogram from output from a numerical model. My dip was due to the
          >boundary conditions, same constant head at two ends of an aquifer, so that
          >head values at suitably large distances were magically similar and viola
          >variogram value goes down.
          >
          >> 4- Is there any ERRATA being written for GSLIB manual? I need to confirm
          >> some of the mistakes that I encounter in using the manual.
          >>
          >
          >I hear that a new and improved manual [2nd Edn] is due to be out in January
          >by Oxford Uni P for about 45 pounds.
          >
          >** Anyone else heard anything about the release??? **
          >
          >> With many thanks for your time and help.
          >>
          >>
          >> Best of luck.
          >> Abedini
          >> |__|__| Mohammad J. Abedini |__|__|
          >> |_____| School of Engineering |_____|
          >> |_____| University of Guelph |_____|
          >> |_____| Guelph Ont, N1G 2W1 |_____|
          >> |__|__| Tel.:(519) 824-4120 ext. 4321 (W) |__|__|
          >> |__|__| Tel.:(519) 821-1199 (H) |__|__|
          >> |_____| Fax :(519) 836-0227 |_____|
          >> |_____| e-mail: mabedini@... |_____|
          >
          >Andrew
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