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Re: GEOSTATS: Stationarity

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  • Syed.R.Syed@EXXON.sprint.com
    In addition to Dr. Myer s comments I would like to add the following as response to Konstantin s questions: 1) Some investigators have used combinatorial
    Message 1 of 2 , Apr 27, 1997
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      In addition to Dr. Myer's comments I would like to add the following
      as response to Konstantin's questions:

      1) Some investigators have used combinatorial optimization schemes such as
      genetic algorithms and annealing to honor different variogram models
      in different directions (in a stochastic simulation context, of course).
      This can be extended to the idea of a "best and optimal" map by averaging
      a large number of realizations, assuming you have the time. :)

      2) Use of moving neighborhoods is problem-specific. I would doubt that
      all datasets would result in the discontinuous artifacts that you mention
      in your posting. Generally, if there are less than 100 samples, all the
      data can be used in the kriging without too much computer cost, since
      you invert the covariance matrix only once (a 'unique' neighborhood).
      For more data than that, you might need to use search neighborhoods.

      Regards, Syed

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    • Costello, Oliver
      Dear All, I have a question regarding stationarity. Suppose I am dealing with a fluvial depositional environment with 3 different kinds of deposits: * coarse
      Message 2 of 2 , Nov 16, 1998
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        Dear All,

        I have a question regarding stationarity. Suppose I am dealing with a
        fluvial depositional environment with 3 different kinds of deposits:

        * coarse to medium grained sands in point bars and channel deposits
        moved and deposited primarily by traction;

        * sheetlike or splaylike overbank fine sand to silt levee deposits
        which are carried in suspension during flood events and then quickly drop
        out as currents subside and;

        * swampy or marshy clayey and fine silt floodplain deposits which are
        rained down vertically as stagnant muddy water slowly cleans itself up.

        As you can see the three types of deposits have very different grain sizes,
        the three dimensional shape of each facies is different and they were
        deposited by completely different mechanisms but they are all closely
        associated with one another spatially.

        The section I am looking at is 50 feet thick. The site is 700 acres in size
        with one linear channel belt roughly 1000 feet wide cutting across it. The
        parameter I am trying to describe with geostatistics is grainsize. I have
        500 borings with grain size measurements every 0.5 vertical feet on a
        regular spacing (250 horizontal feet) over the entire site.

        Here's my question. Does it make any sense to try and describe the grain
        size variogram for the entire site (all 3 facies lumped together)? It seems
        to me that each facies will have it's own area of stationarity and that it
        really only makes sense to model each facies independent of the others. It
        makes some intuitive sense to me that deposits deposited by the same
        mechanism with generally the same grain size could be stationary and could
        be reasonably described with a variogram. But lumping them all together just
        seems impossible.

        But this is what is commonly done, this is what I have done in the past.
        What are we really doing when we lump things together like this? What
        assumptions are we violating and what are the implications to the resulting
        interpretation? Does it even make sense to use the term variogram when
        lumping things together like this? Isn't this kind of a misapplication of
        the tool? Aren't we asking it to describe something it was never meant to
        describe?

        Thanks.
        Ollie Costello

        oliver.costello@...
        Fina Oil and Chemical
        14950 Heathrow Forest Suite 300
        Houston, Texas 77032
        281-986-6967

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