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GEOSTATS: Variogram Modelling for Kriging with External Drift (limited hard data case)

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  • Kian.C.K.Chua@woodside.com.au
    Hello all geostatistian/netters, I learned geostatistics (using Sigmaview and Isatis) about 2 months ago and am now struggling to apply it to derive a velocity
    Message 1 of 3 , Jun 18, 1997
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      Hello all geostatistian/netters,

      I learned geostatistics (using Sigmaview and Isatis) about 2 months ago
      and am now struggling to apply it to derive a velocity map for depth
      conversion. I wish to seek advice on the following problem on
      structural modelling (for kriging with external drift):

      Hard Data: Average velocities from 4 wells.
      (The wells are in 2 pairs on 2 fields, which are 18km apart.
      One pair is at 2 km separation and the other at 9km.)

      Soft Data: Seismically derived average velocity - to be used as external drift.

      Variograms: There are too few hard data points. So I used the soft data (quite
      good correlations with the well data), after de-trending with 2nd
      order surface to ensure stationarity.

      Four experimental variograms generated in four directions: 0, 45, 90 and
      135 degrees

      Shapes of the variograms are similar in three directions 0, 90 and 135
      which have high sills but it is very different in direction 45 degrees which
      has a low sill. The three similar ones can be modelled with "hole"
      structures to cover long range (> 15km) or "gaussian" structure to cover
      only the short range (< 6km). The fourth experimental variogram has to
      be modelled with a "spherical" or "circular" structure and has a range of
      over 20km. The near range behaviours are very different indeed.

      Omni-direction variogram: In omni-direction analysis, the variogram
      shows "hole"
      effect. The structure can be modelled with a "hole" or
      "gaussian" structure with a range of about 6km.

      Questions: 1. What are the valid ways to model the structure in the above case?
      2. Are four wells too few for kriging with external drift?
      3. Should a collocated co-kriging be used instead?
      (I tried collocated co-kriging, but the st. dev. map has very small
      values which I thought are not reflective of the uncertainties.)
      4. Is it better to use conditional simulations?
      5. Are there any case studies or references on similar problems?

      Thank you,
      Chew Kian Chua
      Kian.c.k.chua@...
      ;>) Confucius: Wise men learn from others' mistakes; fools learn from
      their own. ;>)

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    • Johnston
      data case) Chew Kian Chua, Kian.c.k.chua@woodside.com.au stated ..... among other things... ....and am now struggling to apply it (geostatistics) to
      Message 2 of 3 , Jun 19, 1997
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        data case)

        Chew Kian Chua, Kian.c.k.chua@... stated ..... among other
        things...
        <clip>
        ....and am now struggling to apply it (geostatistics) to derive a
        velocity map for depth conversion. I wish to seek advice on the following
        problem on structural modelling (for kriging with external drift):

        Hard Data: Average velocities from 4 wells.
        (The wells are in 2 pairs on 2 fields, which are 18km apart.
        One pair is at 2 km separation and the other at 9km.)

        Soft Data: Seismically derived average velocity - to be used as
        external drift.
        <end of clip>

        Just a comment on your question 1. "What are the valid ways to model the
        structure in the above case?"

        The following comments are "in addition to" any geostatistical advice you
        may receive.


        You are modelling "the earth" , or more specifically, a thin portion of
        the sedimentary section on ?? the NW Australian shelf. Since you work for
        Woodside you are a geophysicist or geologist or "have a geologist next
        door".... what is your geological model.... how should you expect the
        velocities to vary....

        The only way to model is to utilize your four hard data points, ALL your
        soft data and iteratively evaluate whether your results are internally
        consistent and geologically and geophysically and geostatistically
        reasonable... and evaluate and iterate... and etc...

        1. Obtain data over "near-by" producing fields (i.e. with more wells) in
        a similar structural and stratigraphic setting. What are their spatial
        time/depth/velocity relationships, from sea-level to the marker that
        you're interested in depthing? Are these velocity maps geologically
        reasonable ... can you derive a structural/stratigraphic/velocity model
        that you can "apply" on your area/structures....
        Can you evaluate the validity of (similarly derived?) "Seismically
        derived average velocities" in an area with more wells - this is
        important if you're going to use these velocities with only four well
        ties.
        What about utilizing your "other soft data set - your seismic time
        structure... to help derive your velocity map.

        2. Perhaps an interval method (2,3,? layers versus one layer) may fit
        other similar fields and your structures better.... evaluate your
        geological model.

        3. If you want to use one layer, perhaps an "acceleration method" may be
        better...
        a) rate of change of velocity derived at the wells and mapped
        spatially (geostatistically?) ... based on your model (concepts).
        b) derive velocities from acceleration map and seismic time values...
        c) derive depths from velocity map and seismic time values...

        This method is often a more secure "blind method".

        4. Often it's better to split an area like yours into sub-units:
        a) structure 1
        b) structure 2
        c) regional relating the two areas

        and use different methods/concepts for a/b) and c)

        5. Your depthing will never always be correct...so are your results
        reasonable based on what you're trying to accomplish (reserve
        determination, well prognosis,?), and do you have a feel for your
        problems/errors/uncertainties so that you can "improve" your model AFTER
        the next well is drilled....

        cheers,

        Sam Johnston, Calgary
        johnstos@...
        http://www.cuug.ab.ca:8001/~johnstos/


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      • Syed Abdul Rahman
        Re: the above, some additional comments in addition to the two earlier comments: 1. Couldn t agree more with S. Johnstone s comments re: incorporating
        Message 3 of 3 , Jun 19, 1997
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          Re: the above, some additional comments in addition to the two
          earlier comments:

          1. Couldn't agree more with S. Johnstone's comments re: incorporating
          geological info. Again, as mentioned ealier, problem is non-stationarity;
          18 km is a large distance, one end could be a river channel system with
          the other being a marine sand. Some familiarity with the basin model would
          be crucial for successful modeling.

          2. Probabilistic reserves techniques would do well with conditional simulation,
          and if this is your goal, then simulate.

          3. Ensure averaging volume for well averaged velocities and and seismic values
          are most or less comparable; since you plan to use the seismically derived
          correlation structure for the well data.

          4. Hole structure indicates some sort of periodicty in the lateral direction; this
          might be significant (a channel belt system)?

          Good luck.

          Regards, Syed


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