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142               Well Logging and Formation Evaluation

          • Petrophysical properties (porosity, net/gross, saturation, permeability)
            or combinations of such (equivalent hydrocarbon column [EHC],
            NPV)
          • Paleography, environments of deposition, facies variations
          • Fluid properties (depth of contacts, fluid density, salinity)


          10.1.3 Methods of Contouring

            Based on well data alone, the structure of a particular horizon is known
          only in discrete locations. What happens in between must be estimated.
          Various mathematical algorithms are available to estimate the most appro-
          priate values of a parameter to use between locations where the values are
          known with certainty. These are:


          1. Triangulation. Straight lines connecting data well locations are
             created, and along these lines the data are interpolated linearly. The
             subsequent contours may be smoothed using a “spline fit,” which
             attempts to reduce the second derivative of the curve.
          2. Inverse distance. In this technique, the inverse of the distance from
             each known data point is used to establish a weighting to use for taking
             an average of the known data values. Hence, if there are  n known
             values (Z 1 to Z n), the value (Z) of the parameter at some intermediate
             location is determined by:

             Z = Â n i=1 (Z i  d i )  Â n i=1 (1  d i )             (10.1.2)

          3. Polynomial fit. Rather than taking just the inverse of the distance,
             a polynomial function may be used.  The coefficients of this poly-
             nomial function may be determined from the data itself by finding
             the set of coefficients that fits the data best for the known well
             locations.
          4. Kriging. Kriging is an advanced technique that involves using all the
             data available to determine the best combination of the available data
             points at a particular intermediate location. In order to do this, it is first
             necessary to mathematically describe how the parameter in question
             varies between the known data points. This is done by constructing a
             semivariogram of the data. A semivariogram may be constructed using
             the formula:
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