LETTERS TO THE EDITOR — Credentials, training essential for competent geostat evaluation

Geostatistics is rich with useful theoretical models. For example, the recipe for calculating optimal kriging weights can be found in projection theory. The ordinary kriging model is nothing more than the projection of the unknown on to the vectorial sub-space or linear manifold composed of all possible linear combinations whose weights add to one. The kriging set of weights is the unique set that minimizes the distance between the unknown and the projection on the linear manifold (Journel and Huijbregts, Mining Geostatistics, 1978).

To those who say, “more geostatistical gibberish,” let me provide an analogy that illustrates the relevance of theoretical models to the solution of practical problems.

Consider the following problems that involve calculating the distance between two cities, namely Prince Rupert, B.C., and Seattle, Wash.

• A tourist rents a car at a rate of 15 cents per km and wishes to estimate the cost of driving from Prince Rupert to Seattle. The most appropriate model for calculating the distance is by a road map that shows the provincial and state highway systems between the cities.
• The tourist then wishes to re-calculate the car rental expense if he were to put the car on the ferry at Prince Rupert. Now, the distances provided by the road maps are only relevant to and from the ferry terminals. The distance via the provincial and state highways is irrelevant, as is the distance traveled by the ferry.
• A submarine captain planning a trip from Prince Rupert to Seattle uses for his distance calculations a map of the Pacific Ocean floor, the most appropriate model.
• An airline captain is planning a flight between the two cities. For his distance calculations, the most appropriate model is provided by a map showing the great circle route between Prince Rupert and Seattle.
• Finally, a terrorist is planning to send a Tomahawk missile from Prince Rupert to Seattle. For his distance calculations, the most appropriate model is a topographic map of the coastline between the two cities.

Clearly, models are necessary to the solutions of such problems. This is especially true for statistical and geostatistical solutions. However, not only must one select the appropriate model to obtain the correct solution, the appropriate model must also be applied correctly. The tourist planning to send his car on the ferry must select the proper model — a road map — to calculate the distance. He must also use the model or map correctly. He must calculate the distance between the car rental lot and the ferry terminal in Prince Rupert and remember to convert the distance between the ferry terminal and his final destination in Seattle from miles to kilometres. The point is that the geostatistical practitioner must not only be quite familiar with a number of theoretical models; he must also know how to apply them correctly, even though they may be somewhat esoteric.

Numerous case studies exist in which geostatistical ore reserve models, production schedules, optimized grade control procedures and the like have been validated historically by production records. In addition to prediction or estimation, geostatistical models are also used to quantify uncertainty. For example, several successful mining companies have reduced drilling costs on specific projects by using geostatistics to calculate the optimum drillhole pattern required to predict the annual production grade within 10%, with 90% confidence. There is little doubt regarding the usefulness of geostatistics in these mining camps.

However, in spite of the success stories, many geostatistical ore reserve assessments are poorly done and often inaccurate. Why is this so? Unfortunately, experience shows that geostatistical theory is not well-understood by many practitioners. Over the past 17 years, I have found that inaccurate geostatistical ore reserve assessments are generally the product of theory being incorrectly applied by practitioners who have little formal geostatistical education.

Admittedly, geostatistical theory is not easy, and many professionals find that four or five years of college are necessary to master the subject. (Evidently, some individuals struggle with the concepts for years, yet what they comprehend amounts to little more than gibberish.) Some of us encourage practitioners to bolster their theoretical knowledge by offering short courses and through project teamwork. However, in my opinion there are too many underqualified, self-taught geostatisticians in the mining industry who simply do not understand the fundamental theoretical concepts well enough to provide reliable ore reserve assessments.

How can you be sure of am accurate geostatistical study? Check the qualifications of the person who will direct your study. Ask for academic records. Make sure the person has at least a master’s degree, or preferably a doctorate, in geostatistics or applied statistics. Would you risk your health to a self-trained neurosurgeon whose formal education consists of nothing more than several short courses in surgery? Ask for a list of publications and recent project reports written by the practitioner. Finally, ask for references. If your prospective practitioner passes these basic requirements, you can be reasonably assured of a study based on a correct application of sound theory.

Edward Issaks

San Francisco, Calif.