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GEOSTATS: Modeling Spatial Distribution of Landmines

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  • McKenna, Sean A
    In response to Edith Wilkinson s request: Edith, sounds to me like you will end up trying to characterize an almost pure spatial Poisson distribution of small
    Message 1 of 6 , Feb 3, 2000
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      In response to Edith Wilkinson's request:

      Edith, sounds to me like you will end up trying to characterize an almost
      pure spatial Poisson distribution of small size samples (the mines) over an
      extremely large area (if I understand the problem correctly).

      Applications to sampling of spatial Poisson processes (SPP's) that I am
      familiar with have used spatial statistics to model the intensity (mean) of
      the Poisson process as spatial variable. If the mean number of landmines
      left behind for any subdomain varies spatially, geostatistical techniques,
      such as kriging, could be used to model the mean, and more elaborate models
      (e.g., clustering models) can be used to describe the actual distribution of
      the mines within each subdomain. SPP's with variable intensities are a form
      of "Cox" processes and also referred to as "double stochastic Poisson
      processes". Ideally, you may be able to find some ancillary (soft)
      information that can be correlated to the intensity of the SPP and
      incorporate this info through a cokriging procedure.

      A good example of modeling SPP's with geostatistics is:

      Caers, J., J. Gelders, A. Vervoort and L. Rombouts, 1997, Non-Conditional
      and Conditional Simulation of a Spatial Point Process, in: Baafi and
      Schofield (eds.) Geostatistics Wollongong '96, Kluwer Academic Publishers

      There is good info on Poisson processes in the book: "An Introduction to
      Stochastic Modeling" by Taylor and Karlin


      If, in fact, the left over landmines are located in a purely random fashion
      through the sample area, spatial statistics won't be much help and your
      sampling costs to get to the required confidence of an area being clean will
      be astronomical.

      I'm curious as to what other folks out there think about this problem

      Sean

      Sean A. McKenna
      Geohydrology Department
      Sandia National Laboratories
      PO Box 5800 MS 0735
      Albuquerque, NM 87185-0735
      ph: 505 844-2450
      fx: 505 844-4426

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    • srahman@lgc.com
      ... I am loath to think that landmines should follow some spatial process, other than being purely coincidental, and subject to the whims and fancies of a
      Message 2 of 6 , Feb 3, 2000
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        >If, in fact, the left over landmines are located in a purely random fashion
        >through the sample area, spatial statistics won't be much help and your
        >sampling costs to get to the required confidence of an area being clean will
        >be astronomical.

        I am loath to think that landmines should follow some spatial
        process, other than being purely coincidental, and subject
        to the whims and fancies of a human being with questionable
        motives (apart from blowing up the enemy). Just as with any
        "geostatistical" problem, I would first attempt to get an understanding
        of the genesis of such a process, i.e. why would some landmines
        be planted at certain locations of a particular terrain, taking
        into account such factors as altitude, access to main supply
        routes, distance from munitions base, enemy population, etc.

        In other words, would such a landmine distribution involve some
        sort of spatial component, and if yes, should I be modeling it?

        This can be as futile an exercise as the prediction of oil prices
        over time, what with such variables as political instabilities,
        worldwide demand, technological advances, etc. Likewise,
        stock market performance..

        Syed


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      • Joel Olson
        Ms Wilkinson stated:
        Message 3 of 6 , Feb 4, 2000
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          Ms Wilkinson stated:
          <<
          I am currently working on a project to evaluate the safety of landmine
          fields. I am therefore mainly interested in the estimation of the completely
          unknown "contamination" level of the field. The variable of interest is
          discrete (landmines) and the populations I will study range from 1000 m2 to
          100 million m2.

          I am studying landmine fields after clearance. Therefore there should not be
          any patterns in the "missed" landmines I am trying to evaluate. Their
          density is totally unknown as their presence is a result of a clearance
          process which can not be guaranteed to 100 %.
          >>
          Syed noted:
          <
          Just as with any "geostatistical" problem, I would first attempt to get an
          understanding of the genesis of such a process, i.e. why would some
          landmines
          be planted at certain locations of a particular terrain, taking into account
          such factors as altitude, access to main supply routes, distance from
          munitions base, enemy population, etc.

          In other words, would such a landmine distribution involve some sort of
          spatial component, and if yes, should I be modeling it?
          >

          This location of remaining landmines appears to be the the sum of three
          processes: 1) putting in the mines, 2) their detonation, and 3) their
          removal.

          1) would seem to be a combination of military doctrine (strategy - where to
          put them and desired local pattern) - and tactical result (actual locations,
          methods used to place the mines.)

          2) would perhaps have eroded the outer portions of (uniform) areas. More
          recent data are presumably what you have to work from.

          3) The strategy here may have fewer options, but the tactics may be better
          known, and there should be more information. Do (did) the clearers see any
          patterns during their work?

          It may be feasible to set up a classification of areas, based on information
          of 1 & 3, that relate to parameters of the distribution.



          --------
          Amateurs discuss strategy, professionals discuss logistics. - anon.
          --------

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        • Frank Breen
          However, in one sence, the placement of the mines could be a function of terrain or geology as I suggested earlier. Let s face it, landmines are used to kill
          Message 4 of 6 , Feb 4, 2000
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            However, in one sence, the placement of the mines could be a function of
            terrain or geology as I suggested earlier. Let's face it, landmines are
            used to kill people, so therefore, there is likely a higher probablity that
            they will be placed in areas where people are likely travel. For example,
            near roads or along terrain that is easily traversed. They might be less
            likely in areas where bedrock is near the surface or areas of heavy brush,
            wetlands, or rocky terrain. Using parameters such as this, you could define
            areas of probable mine locations based on a number of independent variables
            (as previously stated). Geostatistical analysis could certainly be done
            with reasonable certainty for topographic elevation and near surface
            soils/geology etc. For example, would not areas that are relatively flat,
            between a road and say a river have a higher probability of having landmines
            than say a rocky area with heavy brush away from main traffic zones???? If
            you feel this is a feasible approach, then a variation of coKriging relating
            a number of independent variables with possibly a stochastic approach might
            be a reasonable way of determining high "danger" areas.

            Hope this helps. Let me know how it goes.
            Regards,
            Frank
            *************************************

            Frank Breen
            Breen GeoScience Management, Inc.
            25116 W. Catherine Drive
            Plainfield, Il. 60544

            phone/voicemail: 815.254.3834
            fax/voicemail: 800.471.4855

            fab@...

            *************************************

            > -----Original Message-----
            > From: owner-ai-geostats@...
            > [mailto:owner-ai-geostats@...]On Behalf Of srahman@...
            > Sent: Thursday, February 03, 2000 11:58 PM
            > To: McKenna, Sean A
            > Cc: 'Wilkinson Ms E'; 'ai-geostats@...'
            > Subject: Re: GEOSTATS: Modeling Spatial Distribution of Landmines
            >
            >
            >
            > >If, in fact, the left over landmines are located in a purely
            > random fashion
            > >through the sample area, spatial statistics won't be much help and your
            > >sampling costs to get to the required confidence of an area
            > being clean will
            > >be astronomical.
            >
            > I am loath to think that landmines should follow some spatial
            > process, other than being purely coincidental, and subject
            > to the whims and fancies of a human being with questionable
            > motives (apart from blowing up the enemy). Just as with any
            > "geostatistical" problem, I would first attempt to get an understanding
            > of the genesis of such a process, i.e. why would some landmines
            > be planted at certain locations of a particular terrain, taking
            > into account such factors as altitude, access to main supply
            > routes, distance from munitions base, enemy population, etc.
            >
            > In other words, would such a landmine distribution involve some
            > sort of spatial component, and if yes, should I be modeling it?
            >
            > This can be as futile an exercise as the prediction of oil prices
            > over time, what with such variables as political instabilities,
            > worldwide demand, technological advances, etc. Likewise,
            > stock market performance..
            >
            > Syed
            >
            >
            > --
            > *To post a message to the list, send it to ai-geostats@....
            > *As a general service to list users, please remember to post a summary
            > of any useful responses to your questions.
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            >

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          • Stephen R. Riese
            ... used to kill people, so therefore, there is likely a higher probablity that they will be placed in areas where people are likely travel.
            Message 5 of 6 , Feb 4, 2000
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              >Let's face it, landmines are
              used to kill people, so therefore, there is likely a higher probablity that
              they will be placed in areas where people are likely travel.<

              Actually, killing people is seldom a purpose of landmines. Most doctrines
              (again, for the armies advanced enough to follow doctrines) suggest that an
              injury is preferable to death. This is primarily because an injury is more
              of an immediate burden on the enemy's logistical system (takes two soldiers
              to carry one stretcher, etc.). Furthermore, mines are often used as an
              area denial weapon. Armies can put mines out where they don't want anyone
              (including themselves) to go. In most cases, mine warfare doctrine opens
              with something like "Mines are a weapon that attacks the enemy's ability to
              maneuver..." Antitank mines go after vehicles and antipersonnel mines both
              protect the antitank mines and go after walking personnel.

              Your fundamental observation that we should be able to assign probability
              based on known placement tactics is, however, a good one. In this case,
              domain knowledge should include mine warfare doctrine of the armies (or
              terrorists, or para-military, etc.) that placed the mines.

              Good luck,
              Steve Riese

              SteveRiese@...
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            • Frank Breen
              Well in response to ignorance regarding the use of landmine, I am happy to say I have had no experience with mines. I do, however, find the problem an
              Message 6 of 6 , Feb 4, 2000
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                Well in response to ignorance regarding the use of landmine, I am happy to
                say I have had no experience with mines. I do, however, find the problem an
                interesting one and hope you can find a reasonable approach to solving this
                problem.

                Regards,
                Frank

                *************************************

                Frank Breen
                Breen GeoScience Management, Inc.
                25116 W. Catherine Drive
                Plainfield, Il. 60544

                phone/voicemail: 815.254.3834
                fax/voicemail: 800.471.4855

                fab@...

                *************************************

                > -----Original Message-----
                > From: Stephen R. Riese [mailto:SteveRiese@...]
                > Sent: Friday, February 04, 2000 2:43 PM
                > To: Frank Breen
                > Cc: Stephen R. Riese; McKenna, Sean A; [unknown]; [unknown]; 'Wilkinson
                > Ms E'
                > Subject: RE: GEOSTATS: Modeling Spatial Distribution of Landmines
                >
                >
                > >Let's face it, landmines are
                > used to kill people, so therefore, there is likely a higher
                > probablity that
                > they will be placed in areas where people are likely travel.<
                >
                > Actually, killing people is seldom a purpose of landmines. Most doctrines
                > (again, for the armies advanced enough to follow doctrines)
                > suggest that an
                > injury is preferable to death. This is primarily because an
                > injury is more
                > of an immediate burden on the enemy's logistical system (takes
                > two soldiers
                > to carry one stretcher, etc.). Furthermore, mines are often used as an
                > area denial weapon. Armies can put mines out where they don't want anyone
                > (including themselves) to go. In most cases, mine warfare doctrine opens
                > with something like "Mines are a weapon that attacks the enemy's
                > ability to
                > maneuver..." Antitank mines go after vehicles and antipersonnel
                > mines both
                > protect the antitank mines and go after walking personnel.
                >
                > Your fundamental observation that we should be able to assign probability
                > based on known placement tactics is, however, a good one. In this case,
                > domain knowledge should include mine warfare doctrine of the armies (or
                > terrorists, or para-military, etc.) that placed the mines.
                >
                > Good luck,
                > Steve Riese
                >
                > SteveRiese@...
                >

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