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AI-GEOSTATS: Re: sparse data problem

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  • Isobel Clark
    Everybody (especially Gali!) Just to put the base case in perspective. Many half-billion dollar projects in Southern Africa have been evaluated and floated on
    Message 1 of 2 , Dec 5, 2003
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      Everybody (especially Gali!)

      Just to put the base case in perspective. Many
      half-billion dollar projects in Southern Africa have
      been evaluated and floated on the stock exchange on
      the basis of 5 or 6 holes. When a sample costs a
      couple of million dollars to acquire, there is little
      point in hoping for more.

      We use an extremely well sampled case in our (free)
      tutorial analyses. Look for the GASA data which has 27
      samples. An embarrassement of riches in the mid-1980s,
      I can assure you.

      Isobel Clark
      http://geoecosse.bizland.com/softwares

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    • Gali Sirkis
      Dear members of the list, Below is the summary of all answers for the sparse data problem (sorry for the delay, I was out of my email for a while). Thank you
      Message 2 of 2 , Dec 27, 2003
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        Dear members of the list,

        Below is the summary of all answers for the sparse
        data problem (sorry for the delay, I was out of my
        email for a while). Thank you all for interesting and
        meaningful answers. I'll let you know about further
        developments in the problem solution.

        Happy Holydays and season greetings to everybody.

        With much appreciation,

        Gali

        From: "Isobel Clark" <drisobelclark@...> Add
        to Address Book
        Subject: AI-GEOSTATS: Re: sparse data problem
        To: "Marcel_Vall�e" <vallee.marcel@...>
        CC: ai-geostats@...

        Everybody (especially Gali!)

        Just to put the base case in perspective. Many
        half-billion dollar projects in Southern Africa have
        been evaluated and floated on the stock exchange on
        the basis of 5 or 6 holes. When a sample costs a
        couple of million dollars to acquire, there is little
        point in hoping for more.

        We use an extremely well sampled case in our (free)
        tutorial analyses. Look for the GASA data which has 27
        samples. An embarrassement of riches in the mid-1980s,
        I can assure you.

        Isobel Clark
        http://geoecosse.bizland.com/softwares

        This message is not flagged. [ Flag Message - Mark
        as Unread ]

        Date: Fri, 05 Dec 2003 13:20:07 -0700
        From: "Donald E. Myers" <myers@...> Add
        to Address Book
        To: "Gali Sirkis" <donq20vek@...>
        Subject: Re: AI-GEOSTATS: sparse data problem






        Gali

        For you information

        There is no difference between RBF and kriging, the
        multiquadric is simply a particular choice of a
        generalized covariance. In the geostatistics
        literature, the RBF would be called "dual kriging".

        Donald E. Myers
        http://www.u.arizona.edu/~donaldm



        Date: Fri, 05 Dec 2003 14:11:42 -0500
        From: "Marcel_Vall�e" <vallee.marcel@...>
        Add to Address Book
        To: "Gali Sirkis" <donq20vek@...>,
        ai-geostats@...
        Subject: Re: AI-GEOSTATS: sparse data problem





        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 Vall�e

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

        Marcel Vall�e Eng., Geo.
        G�oconseil Marcel Vall�e Inc.
        706 Routhier St
        Qu�bec, Qu�bec,
        Canada G1X 3J9
        Tel: (1) 418, 652, 3497
        Email: vallee.marcel@...



        Date: Thu, 04 Dec 2003 18:52:47 +0100
        From: "Umberto Fracassi" <fracassi@...> Add to
        Address Book
        To: "Gali Sirkis" <donq20vek@...>
        Subject: Re: AI-GEOSTATS: sparse data problem




        Hi Gali..

        I got the info accessing the algorithm description in
        Surfer 7.0 help.
        That's the best reference I can offer:

        CARLSON R.E. and FOLEY T.A., 1991, Radial Basis
        Interpolation Methods on Track Data, Lawrence
        Livermore National Laboratory, UCRL-JC-1074238

        I found it launching a search on google...

        Hope it helps!
        Ciao,


        Umberto


        Date: Wed, 03 Dec 2003 13:47:37 -0500
        From: "Yetta Jager" <jagerhi@...> Add to Address
        Book
        Subject: Re: AI-GEOSTATS: sparse data problem
        To: "Gali Sirkis" <donq20vek@...>




        Hi Gali,

        I'd say 5 points isn't enough even for kriging with an
        external drift
        as
        one would need more than that for a regression. If
        you can get more
        data,
        say 25 points or so, that would be a feasible
        solution. However, since
        the
        more common data is already interpolated, its not
        clear why a kriging
        model
        would be substituted for it -- just use your
        regression directly to
        estimate the sparse variable.

        Don't shoot the messenger!

        Yetta


        From: "Monica Palaseanu-Lovejoy"
        <monica.palaseanu-lovejoy@...> Add to
        Address Book
        To: "Gali Sirkis" <donq20vek@...>
        Date: Wed, 3 Dec 2003 18:39:30 -0000
        Subject: Re: AI-GEOSTATS: sparse data problem




        Hi Gali,

        Now i have even more questions ;-) If the dataset from
        which you
        have the interpolated data and your own data set
        represent the
        same phenomenon, then why you don't add your data to
        the
        "original" data which was already krigged (but not the
        interpolated
        values), and use this new data set for kriging. Of
        course if you don't
        know these "original data" then ..... maybe you have
        also the
        kriging standard deviation data. You can probably
        safely hope that
        the points for which these kriging errors are minimal
        are your
        "original" points, or very close to the original ones.
        Now i guess
        you need to do some "digging" in the literature to be
        sure this is a
        feasible idea.

        Aside of that, you have to take into consideration the
        fact that does
        not matter which method of kriging you use, the
        extrapolated data
        have higher errors (usually) than the interpolated
        ones. In fact if it
        was used simple kriging the extrapolated data at
        distances greater
        than the range will tend to the distribution mean,
        while for ordinary
        kriging will tend to the local neighbourhood mean. If
        you used
        universal kriging then you may have very unrealistic
        results for
        extrapolated data because they depend heavily on the
        local trend
        modelled for that neighbourhood. So ... in any case
        there is not a
        happy situation.

        If i were you and have time in my hands i would use
        the first set of
        data (the interpolated one) and i would try to the
        best of my
        knowledge to extrapolate it over the area where you
        have your 6
        values, and after i would look to see what is the
        difference between
        the inferred data and the "real" ones. I am not sure
        how i will
        interpret that now, but i am sure it might be very
        useful to see what
        type of errors you may introduce. After i would
        "build" a new data
        set with the "real" data you have and the "original"
        data from the
        interpolated data (again not the interpolated data
        itself) and do a
        kriging on that, after which i would do a
        cross-validation for the
        sparse "real" data you have and see what you are
        coming up with.

        In either case i will do as much research as i can in
        the nature of
        your outlier to have some physical base on which you
        can decide if
        you want to include it in your data, or to consider it
        as being a
        member of a different distribution, or whatever.

        Monica

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


        This message is not flagged. [ Flag Message - Mark
        as Unread ]

        From: "Monica Palaseanu-Lovejoy"
        <monica.palaseanu-lovejoy@...> Add to
        Address Book
        To: "Gali Sirkis" <donq20vek@...>,
        ai-geostats@...
        Date: Wed, 3 Dec 2003 17:56:06 -0000
        Subject: Re: AI-GEOSTATS: sparse data problem




        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

        --


        Date: Wed, 03 Dec 2003 18:35:33 +0100
        From: "Umberto Fracassi" <fracassi@...> Add to
        Address Book
        To: ai-geostats@...
        Subject: Re: AI-GEOSTATS: sparse data problem




        Hi Gali,

        may you not try with Radial Basis Function
        (Multiquadric) instead of
        kriging? It's meant to be an exact interpolator,
        although sometimes it
        doesn't fully honor your data. However, it's based on
        the concept of
        track data which seems to me to suit the issue you
        mention. I employ
        RBF
        with macroseismic effects of historical earthquakes.
        Since these data
        are sparse (and scarce and scattered..!) by
        definition, this algorithm
        effectively pursues aligned pattern in the dataset.

        Hope this may help...

        Ciao and best regards,


        Umberto

        Gali Sirkis wrote:

        >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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