LETTER TO THE EDITOR — Team-work leads to reliable resource models

Geostatistics has become a topic of hot debate. Graham Clow discussed the issues of qualitative judgment and quantitative estimation, Edward Isaaks argued for geostatistical training, and Ben Whiting raised geological concerns about the use of geostatistics. Each author has raised valid points that merit consideration and comment.

The ultimate goal of reserve calculations is to predict recoverable reserves accurately, for these strongly affect a mine’s performance. Estimation of recoverable reserves involves many disciplines, such as geology, statistics, economics and engineering. Nevertheless, the establishment of an optimal resource model is critical for an adequate prediction of recoverable reserves. I agree with Isaaks in that the appropriate use of geostatistics requires necessary training. I concur with Whiting in that inadequate geological models have contributed to the failure of some geostatistical applications.

My view is that geostatistics rarely succeeds without the support of sound geological control. Adequate geological models are capable of preventing major failures, even without the use of geostatistics.

A successful estimation relies on the correlation of database quality, geological control, mineralization control and estimation procedure.

The first consideration in resource modeling is the adequacy of information from which such models are established. It is evident that resource models are less sensitive to the choice of estimation method when comprehensive data are available. All unbiased estimators yield similar estimates when a deposit is sampled exhaustively. To the contrary, no methods, including geostatistics, do well if the deposit is not drilled sufficiently. Hence, it is wise to assess the adequacy of information prior to a serious modeling effort. The amount of information dictates the accuracy of resource estimates.

The next condition for accurate resource modeling is the establishment of geological control. Almost every deposit has unique features that control the mineralization of interest. Geology is too complex to be accurately quantified by a mathematical wizard. Diverse geological conditions contradict the preconditions of uniformity assumed by geostatistical techniques.

In general, a deposit must be partitioned into several domains, each of which can be treated as a relatively uniform geological environment. The partition can be based on lithological unit, anisotropic feature, and distinct structural conditions.

The level of detail in geological control, however, has a limit. In the early days, many geostatistical applications lacked geological support, a cause for many failures. In more recent times, some modelers tend to use too much geological control because they fear criticism for not using enough geology in their model. History has shown that resource models will likely fail if adequate geological control is absent, but I would warn that introducing unnecessary geological details might also degrade the quality of resource models. Spatial heterogeneity of the deposit is a geological issue, but estimation of block grades is a geostatistical problem.

Geological control sets up geological boundaries for resource modeling, but they do not necessarily serve as mineralization constraints. Furthermore, geostatistical methods do not automatically provide mineralization definitions. A desirable resource model generally requires the definition of additional mineralization conditions. Some have mistakenly confused geological constraints with mineralization control.

In resource modeling, mineralization envelopes should also be established within the framework of geological domains prior to the interpolation of grades. The use of appropriate mineralization controls ensures that grade estimation takes place strictly within the mineralized bodies, rather than in broad geological domains. Furthermore, many deposits contain mixed grade populations, which must be appropriately separated by means of mineralization control.

Any interpolation method requires the definition of a spatial neighborhood around an estimation point or block. Besides the conditions discussed above, the design of search strategy is probably the most important factor affecting the quality of a resource model. Different search radii can produce vastly different tonnage-grade relations.

Unfortunately, variograms are not always capable of defining the best search strategies, since variogram models themselves are generally data dependent. It is my opinion that some geostatisticians have over-emphasized the role of variograms in the quality of estimation. An adequate search strategy should include the definition of anisotropic features, search radius, the maximum number of samples and search patterns, among others.

Relative to geology, mineralization and search control, selection of estimators is the smallest concern in resource modeling. Some geostatisticians have over-emphasized the importance of the choice of estimators. This does not mean that the selection of estimators is irrelevant. Indeed, many comparisons have shown that some estimators produced noticeably better estimates than others did. Geostatistical estimators (such as ordinary kriging), theoretically, are superior to other conventional interpolation methods (such as inverse distance), but the difference is less significant than other factors.

Is it always worthwhile to choose a complicated estimator over a simple one? The answer is no, since complicated estimators are generally error-prone, owing to increased complexity in implementation. In fact, simple estimators are always preferred. In estimating resources, it is wise to choose more than one estimator and to compare results. For example, nearest-neighbour assignment or inverse distance methods should be checked against geostatistical estimators.

Establishment of a resource model serves as a basis for the estimation of recoverable reserves, which requires the interaction of many experts from different disciplines. One is confident in arguing for his specialized field, but generally less confident in the fields beyond his expertise. Mining companies can only benefit from resource models established by collaboration between geologists and geostatisticians.

Guocheng Pan, President

GeoSight

Highlands Ranch, Colo.