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707AI-GEOSTATS: Lognormal Kriging Revisited

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  • ramanitharan.kandiah@tulane.edu
    Sep 13, 2002
      Dear all,

      Even after learning geostats for couple of years, I am not sure I got
      the concepts right. (My lame excuse, "Since I am a statistician, I have
      to understand a lot" does not help) Hence, pardon me if/since my
      questions are very fundamental to this group. Whenever I have
      geostatistical concept and implementation issues, I explore the
      ai-geostats (old & new) archives at yahoo!groups to clear clouds over my
      head. However, I haven't found any relevant threads deeply addressing on
      the following questions. Thus, I am posting here.

      1. Having normality in data always bothers me; I see the text books and
      papers comment on this issue, mostly saying, "Normality is not necessary
      for kriging, but having normal data distribution makes the prediction
      better." I am yet to understand this statement.

      2. On Lognormal kriging, I have two questions.

      2.1. If my (original) data shows a second order polynomial trend, while
      fitting a lognormal distribution, how to proceed further along variogram
      fitting & kriging?

      Removing the trend from the original data and fitting the variogram to
      the 'residual'? or, can this second order polynomial trend be directly
      incorporated into the lognormal OK or lognormal KT?

      [In the archives, I saw a post by Prof. Donald Myers touched this issue;
      'Dioxin contaminated site' paper by Dr. Goovaerts has touched the
      comparative studies among different types of kriging]

      Prof. Cressie's book ("Statistics for Spatial Data", pp. 135-137)
      discusses the lognormal kriging to an extent. However, I do not
      understand well how the 'Mean' discussed in the lognormal kriging is
      connected to the trend in the original data.

      2.2. How to do the lognormal cokriging? (as a matter of fact, is it
      anything called 'lognormal cokriging'?) I haven't seen any lognormal
      cokriging models in the books.

      I have to cokrige in two ways. In the first case, both cokriging data
      sets are lognormal. In the second case, while one is lognormal, the
      other is normally distributed. I would appreciate if anyone can give a
      short statistical methodology on how these problems can be approched.
      Even giving citations may be helpful for my reference. I am also
      searching for papers that talk about principal component kriging on
      non-normally distributed data & handling anisotropy in lognormal

      3. As the result of the complexity wrapped with the lognormal & the
      transgaussian transformations, is it alright "getting away" with the
      traditional OK/KT keeping a "blind eye" on the normality? [I do not know
      how scientific this question is. However, I could not resist the
      of asking it]

      Thank you very much.


      Ramantiharan Kandiah
      Graduate Student
      Department of Civil & Environmental Engineering
      Tulane University
      New Orleans, LA

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