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Re: AI-GEOSTATS: sparse data problem

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  • Monica Palaseanu-Lovejoy
    Hi, I am not sure i understood correctly your question. Fist of all, do the interpolated data have come from your sparse data interpolation? What method of
    Message 1 of 6 , Dec 3, 2003
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      Hi,

      I am not sure i understood correctly your question. Fist of all, do
      the interpolated data have come from your sparse data
      interpolation? What method of interpolation did you use in this
      case?

      After Burrough and McDonnel, 2000, you need at least 50 points to
      have reliable results through kriging. Certainly you can do it on less
      data, but until now i never saw a study considering this problem in
      depth (maybe there is literature out there, and if it does and
      anybody knows about it - i would like to know it also ;-))

      Secondly, if you know the outlier is not an error, but you interpret it
      as representing a different combination of properties than the rest
      of your data - i am not very sure it is wise to use it together with
      your rest of the data in any interpolation exercise. The outlier may
      represent a different population and in this case i cannot see any
      "physical" reason to treat all your data together if parts of the data
      represent different things. At least this is my opinion.

      Besides, if your data is not only sparse (5 or 6 data points .... it is
      really very sparse i think) but also far away in space, they can be
      at distances grater than the spatial correlation range, and in this
      case i really don't think you can use kriging .... you will have either
      a pure nugget effect or a very high nugget value and not a too high
      spatial correlation.

      Monica

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    • Gali Sirkis
      Hi Monica, thanks for quick reply. The interpolated data is a different data set with is by its nature (speaking about geological properties) should be
      Message 2 of 6 , Dec 3, 2003
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        Hi Monica,

        thanks for quick reply. The interpolated data is a
        different data set with is by its nature (speaking
        about geological properties) should be correlated with
        the sparse one.
        This is a geological data over not huge area - around
        20x30 kilometers. It should have at least some spatial
        correlation. The variogram is not of striking beauty
        :) but it is not a pure nugget effect, though.
        The only other way meaningfully interpolate between
        those sparse points, it seems to use the simple linear
        regression between those two datasets.
        The literature about kriging/interpolating for very
        sparse data would definitely help, if anybody know
        about, please let know.

        Thanks,

        Gali


        --- Monica Palaseanu-Lovejoy
        <monica.palaseanu-lovejoy@...> wrote:
        > Hi,
        >
        > I am not sure i understood correctly your question.
        > Fist of all, do
        > the interpolated data have come from your sparse
        > data
        > interpolation? What method of interpolation did you
        > use in this
        > case?
        >
        > After Burrough and McDonnel, 2000, you need at least
        > 50 points to
        > have reliable results through kriging. Certainly you
        > can do it on less
        > data, but until now i never saw a study considering
        > this problem in
        > depth (maybe there is literature out there, and if
        > it does and
        > anybody knows about it - i would like to know it
        > also ;-))
        >
        > Secondly, if you know the outlier is not an error,
        > but you interpret it
        > as representing a different combination of
        > properties than the rest
        > of your data - i am not very sure it is wise to use
        > it together with
        > your rest of the data in any interpolation exercise.
        > The outlier may
        > represent a different population and in this case i
        > cannot see any
        > "physical" reason to treat all your data together if
        > parts of the data
        > represent different things. At least this is my
        > opinion.
        >
        > Besides, if your data is not only sparse (5 or 6
        > data points .... it is
        > really very sparse i think) but also far away in
        > space, they can be
        > at distances grater than the spatial correlation
        > range, and in this
        > case i really don't think you can use kriging ....
        > you will have either
        > a pure nugget effect or a very high nugget value and
        > not a too high
        > spatial correlation.
        >
        > Monica


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      • Marcel Vallée
        Gail Sorry for not responding earlier to your request. Your explanatory comment to Monica does not convince me as a exploration and mining geologist. I think
        Message 3 of 6 , Dec 5, 2003
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          Gail

          Sorry for not responding earlier to your request.

          Your explanatory comment to Monica does not convince me
          as a exploration and mining geologist. I think her comments are
          wise and should be considered.

          A 20x30 km area is a large one even when dealing with very
          uniform geology. Even in such conditions, different properties
          may be encountered, either as faults, vein or fracturation
          system, small intrusive bodies, mineral showings or deposits,
          pollution zones, etc.

          Such a small sample set as you have ["few (5-6) original data
          points + interpolated external data"] that covering whole study
          area] does not allow you to really appraise the validity and/or
          the geological cause of this "outlier." (There might be a
          sampling or assaying cause also). In such a case, it should be
          shown as an anomaly, not averaged out or kriged out.

          Excluding sampling/analytical problems, the outlier only has a
          "detection"value, meaning that the geology is not as uniform as
          expected and that additional geological observations and sampling
          in the vicinity is required to elucidate this problem.

          We should view geostatistics as an ancillary tool to understand a
          two or three dimensional "geological universe." Whenever data ara
          as sparse as in your exemple, kriged values should not replace
          and/or eliminate the potential meaning of sparse field observations.

          Sincerely


          Marcel Vallée

          ========================

          Marcel Vallée Eng., Geo.
          Géoconseil Marcel Vallée Inc.
          706 Routhier St
          Québec, Québec,
          Canada G1X 3J9
          Tel: (1) 418, 652, 3497
          Email: vallee.marcel@...





          =========================================
          Gali Sirkis wrote:
          > Hi Monica,
          >
          > thanks for quick reply. The interpolated data is a
          > different data set with is by its nature (speaking
          > about geological properties) should be correlated with
          > the sparse one.
          > This is a geological data over not huge area - around
          > 20x30 kilometers. It should have at least some spatial
          > correlation. The variogram is not of striking beauty
          > :) but it is not a pure nugget effect, though.
          > The only other way meaningfully interpolate between
          > those sparse points, it seems to use the simple linear
          > regression between those two datasets.
          > The literature about kriging/interpolating for very
          > sparse data would definitely help, if anybody know
          > about, please let know.
          >
          > Thanks,
          >
          > Gali
          >
          >
          > --- Monica Palaseanu-Lovejoy
          > <monica.palaseanu-lovejoy@...> wrote:
          >
          >>Hi,
          >>
          >>I am not sure i understood correctly your question.
          >>Fist of all, do
          >>the interpolated data have come from your sparse
          >>data
          >>interpolation? What method of interpolation did you
          >>use in this
          >>case?
          >>
          >>After Burrough and McDonnel, 2000, you need at least
          >>50 points to
          >>have reliable results through kriging. Certainly you
          >>can do it on less
          >>data, but until now i never saw a study considering
          >>this problem in
          >>depth (maybe there is literature out there, and if
          >>it does and
          >>anybody knows about it - i would like to know it
          >>also ;-))
          >>
          >>Secondly, if you know the outlier is not an error,
          >>but you interpret it
          >>as representing a different combination of
          >>properties than the rest
          >>of your data - i am not very sure it is wise to use
          >>it together with
          >>your rest of the data in any interpolation exercise.
          >>The outlier may
          >>represent a different population and in this case i
          >>cannot see any
          >>"physical" reason to treat all your data together if
          >>parts of the data
          >>represent different things. At least this is my
          >>opinion.
          >>
          >>Besides, if your data is not only sparse (5 or 6
          >>data points .... it is
          >>really very sparse i think) but also far away in
          >>space, they can be
          >>at distances grater than the spatial correlation
          >>range, and in this
          >>case i really don't think you can use kriging ....
          >>you will have either
          >>a pure nugget effect or a very high nugget value and
          >>not a too high
          >>spatial correlation.
          >>
          >>Monica

          Dear list members,

          Please advise what to do in following case:
          The sparse dataset for kriging inlcudes only few
          (5-6) original data points + interpolated external
          data, that covering whole study area. One of the original data
          points seems completly not to
          fit to the main correlation line between original and
          external data, however mostly probable is not an
          error, but might represent different combination of
          data properties. Is there is any chance to use this outlying point?
          Does is sound feasible for you as specialists in
          statistical analysis to use the kriging method in this
          case?

          Many thanks in advance for your help,

          Gali Sirkis
          >
          >
          >
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