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Re: AI-GEOSTATS: Re: sparse data problem

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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 1 of 2 , Dec 27, 2003
      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,


      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

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      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


      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

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


      Sorry for not responding earlier to your request.

      Your explanatory comment to Monica does not convince
      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
      uniform geology. Even in such conditions, different
      may be encountered, either as faults, vein or
      system, small intrusive bodies, mineral showings or
      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


      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!


      Date: Wed, 03 Dec 2003 13:47:37 -0500
      From: "Yetta Jager" <jagerhi@...> Add to Address
      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
      one would need more than that for a regression. If
      you can get more
      say 25 points or so, that would be a feasible
      solution. However, since
      more common data is already interpolated, its not
      clear why a kriging
      would be substituted for it -- just use your
      regression directly to
      estimate the sparse variable.

      Don't shoot the messenger!


      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
      "original" data which was already krigged (but not the
      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.


      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
      > the sparse one.
      > This is a geological data over not huge area -
      > 20x30 kilometers. It should have at least some
      > 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
      > 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

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


      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

      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

      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.



      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
      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,


      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
      >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
      >Many thanks in advance for your help,
      >Gali Sirkis

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