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Re: AI-GEOSTATS: log-normal kriging error

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  • Isobel Clark
    Marta I am not familiar with the software you are using, but it looks like your lognormal standard errors are being back-transformed into raw units. If this
    Message 1 of 6 , Dec 3, 2003
      Marta

      I am not familiar with the software you are using, but
      it looks like your lognormal standard errors are being
      back-transformed into 'raw' units. If this is the case
      part of the backtransform is to multiply the 'relative
      standard error' by the actual value of the estimate.

      That is, if your estimate is 0.52, the backtransformed
      standard error is multiplied by 0.52. If the estimate
      is 520, it is multiplied by 520. If you do a ratio
      between the standard error and the estimate, you will
      probably get equivalent 'relative' errors.

      We find it better to leave the standard errors in
      logarithms and use Sichel type confidence interval,
      using the lognormal model.

      Isobel
      http://uk.geocities.com/drisobelclark

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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 2 of 6 , Dec 3, 2003
        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 3 of 6 , Dec 3, 2003
          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 4 of 6 , Dec 5, 2003
            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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