Block variance validation

Generally speaking, grade interpolation can be validated by VMS (visual assessment, mean assessment, swath plot validation) and block variance validation. These methods are easily understood and applied, except for the block variance validation.

When applying kriging to grade interpolation, the theoretical block variance adjustment ratio (f) and the actual block variance adjustment ratio (f*) can differ by a large measure that is not reflected in the VMS methods. Block variance validation is important for a kriging interpolation, but is not relevant to a non-kriging interpolation, so, the question is how to apply it?

One way is to examine which interpolation is most robust. As we know, the block variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean. Usually, different parameters produce almost identical global mean grades, but obviously different variances. This difference can produce different tonnage-grade curves. All the curves show the same level of confidence at the minimum reporting cut-off, but different levels of confidence at increasing cut-offs. Using a kriging method, the most robust choice is the one with the minimum difference between f and f*, which indicates that the estimated result follows well with the operator’s expectation. For a non-kriging method, the f cannot be calculated, so the confidence levels of f* and tonnage-grade curve cannot be assessed.

Another application is to find outliers in a borehole dataset. During grade interpolation, the smoothing effect happens inevitably as the support enlarges. The term support at the sampling stage refers to the characteristics of the sampling unit, such as the size, shape and orientation of the sample. At the modelling stage, the term support refers to the volume of the blocks. As support increases, the data is gradually distributed more symmetrically, and the spread of the data is reduced, as the variance shrinks. The only parameter that is not affected is the mean; it should stay the same regardless of support changes. Theoretically, the distribution presented by the sample data should vary more than that presented by the blocks. But in actual practice, the block variance is occasionally larger than the samples variance when all the reasonable interpolating methods and parameters are considered. Therefore, it is preferable to remove outliers that still exist in the borehole dataset before re-estimating the resources.

Finally, we can answer the question of how to apply block variance validation:

  1. Use it to decide which result is the most robust among kriging interpolations
  2. Ignore it in non-kriging interpolations
  3. Use it to mark the presence of outliers in the borehole dataset

Yonggang Wu: ywu@srk.cn

 


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