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AI-GEOSTATS: Estimation in caves

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  • McKenna, Sean A
    All, I have an interesting problem that is a bit off the usual geostat track. The problem is the estimation of the amount of tracer deposited in a cave
    Message 1 of 2 , Sep 12, 2003
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      All, I have an interesting problem that is a bit off the usual geostat
      track. The problem is the estimation of the amount of tracer deposited in a
      cave system. The cave system is composed of multiple rooms and passages
      connecting the rooms. Air flow and transport models can be used to model
      the deposition of the tracer, but are difficult to set up and calibrate and
      I'd like to pursue a more geostatistical approach to the problem (if
      possible).

      However, a straight forward application of kriging the amount of deposition
      based on a number of samples will not work for at least two reasons:
      1) Euclidean distance is not very meaningful as two rooms in the system may
      only be separated by a 10 meter thick wall, yet the tortuous air flow path
      from one room to the other may be over 500 meters. Therefore the
      connections between sample points resemble something like a connected graph
      ala graph theory. But perhaps it is possible to use this information to
      remap the cave system into some sort of "connection space" and build
      variograms and do kriging in that space before remapping to the actual
      coordiante system (?)
      2) If it were possible to develop a covariance matrix using the sample data
      in some transformed coordinate system, it would not be symmetric. Due to
      the air flow patterns in the cave system, point B may be "downwind" of point
      A and there is a B->A connection, but there is no A->B connectivity. In the
      parlance of graph theory, this would be a "directed graph".

      I've found work across several different fields where the "best" places to
      take a sample in such a system can be determined using graph theory coupled
      with linear programming and/or heurisitc optimization techniques. I have
      not come across any work where estimations are made in the system based on a
      finite number of existing samples, except for those that resort to physics
      based models (i.e., flow and transport).

      If anyone has pondered this problem before and can point me towards any
      publications, I would be very appreciative.

      thanks

      Sean



      Sean A. McKenna Ph.D.
      Geohydrology Department
      Sandia National Laboratories
      PO Box 5800 MS 0735
      Albuquerque, NM 87185-0735
      ph: 505 844-2450



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    • Pierre Goovaerts
      Hi Sean, Your problem seems to bear some similarity with modeling of river networks where meaningful distances cannot be defined in the Euclidian space and
      Message 2 of 2 , Sep 14, 2003
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        Hi Sean,

        Your problem seems to bear some similarity with modeling of
        river networks where meaningful distances cannot be defined
        in the Euclidian space and downstream/upstream relationships
        need to be fulfilled.
        A few days ago, Pascal Monestiez from INRA Avignon gave a
        talk on Geostatistical modelling of spatial processes on trees:
        applications to drainage networks, which might be of interest
        to you... and there should be other related papers in the literature.

        Cheers,

        Pierre
        <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

        Dr. Pierre Goovaerts
        President of PGeostat, LLC
        Chief Scientist with Biomedware Inc.
        710 Ridgemont Lane
        Ann Arbor, Michigan, 48103-1535, U.S.A.

        E-mail: goovaert@...
        Phone: (734) 668-9900
        Fax: (734) 668-7788
        http://alumni.engin.umich.edu/~goovaert/

        <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

        On Fri, 12 Sep 2003, McKenna, Sean A wrote:

        > All, I have an interesting problem that is a bit off the usual geostat
        > track. The problem is the estimation of the amount of tracer deposited in a
        > cave system. The cave system is composed of multiple rooms and passages
        > connecting the rooms. Air flow and transport models can be used to model
        > the deposition of the tracer, but are difficult to set up and calibrate and
        > I'd like to pursue a more geostatistical approach to the problem (if
        > possible).
        >
        > However, a straight forward application of kriging the amount of deposition
        > based on a number of samples will not work for at least two reasons:
        > 1) Euclidean distance is not very meaningful as two rooms in the system may
        > only be separated by a 10 meter thick wall, yet the tortuous air flow path
        > from one room to the other may be over 500 meters. Therefore the
        > connections between sample points resemble something like a connected graph
        > ala graph theory. But perhaps it is possible to use this information to
        > remap the cave system into some sort of "connection space" and build
        > variograms and do kriging in that space before remapping to the actual
        > coordiante system (?)
        > 2) If it were possible to develop a covariance matrix using the sample data
        > in some transformed coordinate system, it would not be symmetric. Due to
        > the air flow patterns in the cave system, point B may be "downwind" of point
        > A and there is a B->A connection, but there is no A->B connectivity. In the
        > parlance of graph theory, this would be a "directed graph".
        >
        > I've found work across several different fields where the "best" places to
        > take a sample in such a system can be determined using graph theory coupled
        > with linear programming and/or heurisitc optimization techniques. I have
        > not come across any work where estimations are made in the system based on a
        > finite number of existing samples, except for those that resort to physics
        > based models (i.e., flow and transport).
        >
        > If anyone has pondered this problem before and can point me towards any
        > publications, I would be very appreciative.
        >
        > thanks
        >
        > Sean
        >
        >
        >
        > Sean A. McKenna Ph.D.
        > Geohydrology Department
        > Sandia National Laboratories
        > PO Box 5800 MS 0735
        > Albuquerque, NM 87185-0735
        > ph: 505 844-2450
        >
        >
        >
        > --
        > * To post a message to the list, send it to ai-geostats@...
        > * As a general service to the users, please remember to post a summary of any useful responses to your questions.
        > * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
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        >


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