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AI-GEOSTATS: spatial point patterns

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  • Veerle Huvenne
    Dear List Members, With this email I would like to ask you 2 questions about spatial point patterns. I m working on a PhD, studying carbonate mounds at the
    Message 1 of 1 , Apr 2, 2003
      Dear List Members,

      With this email I would like to ask you 2 questions about spatial point
      patterns. I'm working on a PhD, studying carbonate mounds at the
      seafloor W of Ireland. We found a large province of these mound
      structures, where we estimate there are more than 1000 of them. In part
      of the province we could map the mounds accurately thanks to a 3D
      seismic data set. This resulted in 387 mounds in an area of about 300 to
      350 km2 (depending on where exactly we draw the boundary of the
      province), which I suppose is a nice subset of the whole province, on
      which we can do some statistical analyses. For example, I would like to
      study the spatial positions of the mounds : are they clustered, or
      rather regularly spaced?

      This brings me to the first point : I used Ripley's K-function,
      including edge correction, as described by Cressie (1993, Statistics for
      spatial data). However, it turned out that the calculated K-values and
      the resulting plots were very sensitive to the estimated 'intensity'
      (lambda). A difference in intensity of 1.21 mounds/km2 or 1.26
      mounds/km2 made a difference in interpreting the mounds to be clustered
      or completely randomly spaced. And although the province on the whole is
      quite sharply delineated, the 'exact' position of the boundary is
      subject to interpretation, which affects the province's surface area,
      and hence the estimation of lambda. (note that changing the postion of
      the boundary, but not the intensity value, did not affect very much the
      resulting K-values)
      When I tried to calculate the K-function in study areas inside the mound
      province, I received quite different results for the different study
      areas chosen. I have the feeling that part of this is caused by a slowly
      changing intensity. This would mean that the process is not

      * Therefore my question : is the K-function a good technique to study
      the spatial point pattern? (as I understood from Cressie (1993) it is
      one of the best ones?)? How sensitive is it to the estimation of lambda?
      And to non-stationarity? Any suggestions?

      The second point then goes one step further. Apart from the mound
      position, I also registered some morphological characteristics, such as
      mound height, cross-sectional area,... I could consider these data as a
      marked point process, is that correct?
      Now I would like to find out if there are zones with bigger and smaller
      mounds, which maybe could be related to depth, slope angle of the
      horizon on which they are seated etc. I made some plots already with
      different symbols for different height classes etc, but I could not
      really see a special pattern at first sight, and it would be interesting
      to put things in numbers, I suppose.

      * Hence my second question : should I consider these marked points as
      irregular lattice data? And then calculate a semivariogram, maybe
      interpolate a surface? I have the feeling there is quite a lot of
      variability in mound height over small areas. How do I express this

      I must admit that, although I obtained the basics of (geo)statistics,
      I'm not a (geo)statician at all, hence some of the derivations in
      geostatistical handbooks go a bit far... I am mainly interested in the
      application of the techniques in order to obtain information about the
      behaviour of the mounds.

      In any case, thank you very much for any help, and looking forward to
      your suggestions!


      Veerle Huvenne
      Renard Centre of Marine Geology
      University of Ghent

      Krijgslaan 281, S8
      9000 Gent, Belgium

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