Ore Reserve Estimation Research Articles

That BLUP is a Good Thing: The Estimation of Random Effects

In animal breeding, Best Linear Unbiased Prediction, or BLUP, is a technique for estimating genetic merits. In general, it is a method of estimating random effects. It can be used to derive the Kalman filter, the method of Kriging used for ore reserve estimation, credibility theory used to work out insurance premiums, and Hoadley's quality measurement plan used to estimate a quality index. It can be used for removing noise from images and for small-area estimation. This paper presents the theory of BLUP, some examples of its application and its relevance to the foundations of statistics. Understanding of procedures for estimating random effects should help people to understand some complicated and controversial issues about fixed and random effects models and also help to bridge the apparent gulf between the Bayesian and Classical schools of thought.

An interactive microcomputer application for ore grade interpolation

Following on from an earlier publication on Localized Trend Analysis (LTA), this paper addresses some of the more important issues that have since arisen. Questions ranging in emphasis from details of the fundamental theory to the hardware configuration and the software necessary for using LTA are answered here. The estimation of block grades for an ore panel is illustrated starting from first principles. An interactive microcomputer application for such an estimation exercise is presented. Finally the areas of use and some characteristics of LTA are discussed. Conclusions drawn reflect two important implications, among others. Firstly, LTA as a technique does not have all the answers to questions concerning ore reserve estimation. Secondly, the fact that the method is simple to understand and implement on microcomputers, makes it quite attractive for widespread use.

Effects of search parameters on kriged reserve estimates

Reliable ore reserve estimates for deposits with highly skewed grade distributions are difficult tasks to perform. Although some recent geostatistical techniques are available to handle problems with these estimations, ordinary kriging or conventional interpolation methods are still widely used to estimate the ore reserves for such deposits. The estimation results can be very sensitive to the search parameters used during the interpolation of grades with these methods.

Towards intelligent systems for geostatistical ore reserve estimation

Abstract Geostatistical techniques have been successfully employed in ore reserve estimation for more than two decades. It remains however, that the application of these techniques is not straightforward. To provide the means for the transferring of the knowledge and expertise involved, expert system technologies may be integrated with geostatistics. As a result intelligent geostatistical systems may be build to assist the industry in ore reserve estimation. Two experimental geostatistical expert systems developed, demonstrate that such systems are technically feasible, compatible to geostatisticians, simple to use, expandable, and educative for the user.

Ore reserve estimation using localized trend analysis

The techniques used in ore reserve estimation vary from the simple method of polygons through heuristics such as distance weighting methods to quite sophisticated kriging procedures of geostatistics. The results from the method of polygons are usually inferior to those of both the heuristics and geostatistics. This paper discusses a heuristic: Localized Trend Analysis (LTA). Most reserve estimating techniques start off by characterizing the deposits as a whole by means of frequency distributions, general trend surfaces or semi variograms. This is then followed by estimates of grades for smaller mining blocks. LTA starts off by exploiting local grade variation in deriving estimates for smaller mining blocks before proceeding to consider estimates for a deposit as a whole. The derivation of the basic formulae employed in LTA is presented and the estimation procedure is illustrated by means of an example.

Underground mapping and computer estimation of ore reserves

Abstract This paper traces the involvement of the mine surveyor with ore estimation procedures from the days when the art was simply a matter of sample lengths and assays being converted into tonnage and grade to the present time where an apparently highly sophisticated programme approach is used. The author suggests that there is a tendency to accept that these computer-based methods have resolved all the problems of resource evaluation. It is easy to gain the impression that such programmes have already taken into account errors in geological input, drill core data, sampling methods, volumes, assays, etc..

Geostatistics applied to short-term mine planning

Abstract Geostatistics is being used today for long-term mine planning (e.g., ore reserve estimation and mine model development) and for production scheduling (e.g., ore-waste selection) at many of metal mines in the U. S. Geostatistics is not as yet used for short-term mine planning, although geostatistics provides ideal tools to satisfy several goals of short-term mine planning. This paper reviews the probable reasons for the lack of geostatistical applications in short-term mine planning and demonstrates the practicality of routine implementation of the University of Arizona's short-term mine planning system, if there exists either an economic or a political incentive to do so.

Application of Geostatistics to Coal Exploration, Reserve Estimation, and Quality Studies: ABSTRACT

Application of traditional methods of ore-reserve estimations to coal-reserve evaluation, quality studies, and mine planning in many circumstances do not allow the accurate prediction of the quantity and quality of coal at different parts of a deposit. Conventional methods do not produce any information with regard to continuity of the variable of interest and range of influence of the samples to be used in drill spacing during development drilling. Geostatistical methods of ore-reserve estimation, however, produce information about continuity of the variable of interest, range of influence of the drill holes, and the trend of deposition. A combination of information obtained from variogram(s), and geologic data can assist in determination of the appropriate drill-hole spacing. The estimation variance and geologic data can provide assistance in decision-making with regard to additional drilling required to improve reserve estimation and quality evaluation. This method is especially helpful if specified sets of standards such as maximum level of sulfur and ash or minimum level of BTU contents need to be met. End_of_Article - Last_Page 625------------

Book Reviews

Abstract A Mathematical Theory of Evidence. Glenn Shafer. Princeton, N.J.: Princeton University Press, 1976. xiii + 298 pp. $17.50. (88.50 paperback). Reviewed by Persi Diaconis Nonparametric and Distribution-Free Methods for the Social Sciences. Leonard A. Marascuilo and Maryellen McSweeney. Monterey, Calif.: Wadsworth Publishing Company, Inc., 1977. xvii + 556 pp. $17.95. Reviewed by John F. Bassler Methods for Statistical Data Analysis of Multivariate Observations. R. Gnanadesikan. New York: John Wiley & Sons, Inc., 1977. × + 311 pp. $19.95. Reviewed by P. K. Sen General Statistics, 3rd Edition. Audrey Haber and Richard P. Runyon. Indianapolis: Addison-Wesley Publishing Company, 1977. xvii + 459 pp. $12.95. Reviewed by G. Barrie Wetherill Statistical Concepts and Methods. Gouri K. Bhattacharyya and Richard A. Johnson. New York: John Wiley & Sons, Inc., 1977. xv + 639 pp. $14.95. Reviewed by Peter B. Imbey Statistical Power Analysis for the Behavioral Sciences, Revised Edition. Jacob Cohen. New York: Academic Press, Inc., 1977. xv + 474 pp. $20.00. Reviewed by James C. Daly Basic Statistical Concepts in Education and the Behavioral Sciences. Albert E. Bartz. Minneapolis: Burgess Publishing Company, 1976. 401 pp. $12.95. Reviewed by William K.A. Agyei Multivariate Analysis in Behavioral Research. A.E. Maxwell. New York: Halsted Press, 1977. vii + 164 pp. $8.95 paperback. Reviewed by P.K. Sen Marriage and Divorce: A Social and Economic Study, Revised Edition. Hugh Carter and Paul C. Glick. Cambridge, Mass.: Harvard University Press, 1976. xxxi + 508 pp. $17.50. Reviewed by James F. McCarthy The Spectral Maximum Likelihood Estimation of Econometric Models with Stationary Errors. Antoni Espasa. Göttingen, Germany: Vandenhoeck & Ruprecht, 1977. 197 pp. $12.00. Reviewed by John M. Abowd An Annual Growth Model of the United States Economy, Volume 100. B.G. Hickman and R.M. Coen. Amsterdam: North-Holland Publishing Company; New York: Elsevier/North Holland, Inc., 1976. xix + 287 pp. $36.50. Reviewed by Stephen M. Goldfeld The Labor Force in Economic Development: A Comparison of International Census Data 1946–1966. John D. Durand. Princeton, N.J.: Princeton University Press, 1975. xv + 259 pp. $15.00. Reviewed by Albert Berry The Statistical Analysis of Spatial Pattern. M.S. Bartlett. New York: Halsted Press, 1976. ix + 90 pp. $9.75. Reviewed by Paul Switzer Applied Statistics for Science and Industry. Albert Romano. Boston: Allyn and Bacon, Inc., 1977. xiv + 513 pp. $17.95. Reviewed by John Petkau Parameter Estimation in Engineering and Science. James V. Beck and Kenneth J. Arnold. New York: John Wiley & Sons, Inc., 1977. xix + 501 pp. $24.95. Reviewed by James Keith Lindsey Geostatistical Ore Reserve Estimation. Michel David. Amsterdam: Elsevier Scientific Publishing Company, 1977. xix + 364 pp. $44.95. Reviewed by Geoffrey S. Watson Proceedings of the International Conference on Quantitative Genetics. Edward Pollak, Oscar Kempthorne, and Theodore B. Bailey, Jr. (eds.). Ames, Iowa: Iowa State University Press, 1977. xxiv + 872 pp. $18.50. Reviewed by M.J. Garber Of Acceptable Risk: Science and the Determination of Safety. William W. Lowrance. Los Altos, Calif.: William Kaufman, Inc., 1976. ix + 180 pp. $8.95 ($4.95 paperback). Reviewed by Adel Shamseldin Risk Theory: The Stochastic Basis of Insurance, 2nd Edition. R.E. Beard, T. Pentikainen, and E. Pesonen. New York: Halsted Press, 1977. xvi + 195 pp. $12.95. Reviewed by Richard Cohn Scientific Analysis on the Pocket Calculator, 2nd Edition. Jon M. Smith. New York: John Wiley & Sons, Inc., 1977. xii + 445 pp. $13.75. Reviewed by R.M. Dudley Computational Probability and Simulation. Sidney J. Yakowitz. Reading, Mass.: Addison-Wesley Publishing Company, Inc., 1977. xxii + 240 pp. $22.50. ($12.50 paperback). Reviewed by David Freedman Algorithms for the Computation of Mathematical Functions. Yudell L. Luke. New York: Academic Press, Inc., 1977. xiii + 284 pp. $15.00. Reviewed by Christopher Bingham Selected Tables in Mathematical Statistics, Volume V. D.B. Owen and R.E. Odeh (eds.). Providence, R.I.: American Mathematical Society, 1977. viii + 263 pp. $16.80. Reviewed by Gus W. Haggstrom

English language publications on the French school of geostatistics

Some of the most important developments in this sequence of events have been in the field of ore reserve estimation. The single most outstanding contribution to this field in the last fifteen years must undoubtedly be credited to a group of French geomathematicians who pioneered and synthesized from several disciplines what has become known as "Geostatistics" but what could be called more explicitly the "Theory of Regionalized Variables and its Application to Problems in Estimation." Since the early sixties a number of contributions have been made to the geostatistical literature. Any prospective researcher wishing to develop expertise in geostatistics is confronted with the difficult task of finding some starting point and then wading through articles that can prove at times very difficult to obtain. It is this starting point that this compilation is intended to supply.

Automatic Kriging And Contouring In The Presence Of Trends (Universal Kriging Made Simple)

Abstract The main purpose of this paper is to present a new automatic interpolation and contouring technique which automatically recognizes the spatial structure of the dam to be contoured even when, trends are present and data are not regularly spaced. A brief relief of contouring problems is presented the idea of spatial structure and its characterization by a generalized covariance is then introduced and the POLYPAC program is described. Applications in various areas (oil shales, sulphide mines, coal field, cement industry, geophysical data) are illustrated and a detailed appendix covers the mathematical theory of the intrinsic random functions of order k, which is the basis for the program. References to other similar programs are included. Conceptual Background Introduction Attempting to survey everything that has been written on the subject of automatic contouring is a challenging task as ideas are generated in various fields with little communication between each other, such as coal reserves, ore reserve estimation or geophysical mapping, not to mention geography and meteorology. Also, the concern of contouring packages for high cosmetic quality like G.P.C.P., CSPL. Stampede, etc... tends to push people away from the fundamentals of the problem and its conceptualization, Most of the time the interpolation method used in a program is unknown to the map user, or he is left with the choice of up to 32 different interpolation subroutines in the same package, with no further hint at which method is adapted to his problem. It is our opinion that most mapping problems can be encased in the frame of a unifying theory which will allow the generation of the most adequate map for a given purpose. This theory has been known as kriging or simply geostatistics and was developed by Matheron, The full name of the most complete version of it is "theory of intrinsic random functions of order k", and all its intricacies have now been turned into another black box, which produces the best theoretical maps within the framework of distance weighted and trend-surface interpolation. It is one of the purposes of this paper to show which concepts are needed to understand why a given interpolation algorithm is good in certain cases and unacceptable in others. These concepts of spatial structure, drift, trend, high-frequency noise, estimation variance have been known for a long time, but we must admit that map users should be presented with something else than a truckload of equations. The contouring problem is easily split in two; the first problem is that of the generation of II. regular grid of points, the second being that of aesthetically contouring this fine grid. So far only the first problem retained the attention of geostatisticians, with few exceptions. Broken contours are not acceptable even if the theory behind the grid generation technique is faultless (Olea, 1972). There now exists a program matching the most sophisticated theory and superb contours.

Estimation of Ore Reserves for In-Situ Solution Mining Production Projects, with Emphasis on Uranium: ABSTRACT

Estimation of Ore Reserves for In-Situ Solution Mining Production Projects, with Emphasis on Uranium: ABSTRACT

Geostatistical Techniques in Distributed Parameter System Estimation Problems

Publisher Summary This chapter discusses geostatistical techniques used in distributed parameter system estimation problems. It provides an overview of some mining problems. A mineral deposit is a three-dimensional body buried underground and with fuzzy limits; the body may or may not be homogeneous, and if it is possible to recognize different zones within it, their contour is a priori unknown. Once such a deposit has been located, it is usually sampled by means of expensive diamond. The chapter discusses techniques that have been developed for solving distributed system estimation problems encountered in mineral exploration. These techniques are quite powerful and are increasingly used by the mineral industry for ore reserve estimation. Although well documented in the geostatistical literature, they are not well known to control engineers, and the terminology that has evolved is somewhat specialized.

Practical kriging in three dimensions

Little has been published to date on the practical difficulties of ore reserve estimation in three-dimensional deposits. Some authors have suggested condensing the problem into two dimensions, but this is not always practicable or desirable. A suggestion and a FORTRAN IV Function Segment are provided which may alleviate some of these difficulties.

The scope for materials recycling

The work of Meadows et al. in The Limits to Growth, although open to severe criticism on a number of points, has focused attention on possible future shortages of materials, but the short life-time then predicted for many materials may be shown to result from oversimplification of published estimates of ore reserves. In fact, the absolute tonnages of most metals in the earth's crust are such that, with few exceptions, supplies are practically limitless, and depend largely on market forces. Pressures are likely to come from the demand for basic amenities by the large population of the developing nations rather than from the incremental needs of the relatively sparsely populated developed lands. Shortages will probably arise from the increasing cost of energy and the higher speck energy input needed to extract from low-grade sources as richer deposits are progressively depleted. The dependence of all advanced industrial nations on a supply of relatively cheap energy, and their vulnerability to political and economic pressures through that dependence, have recently been demonstrated. Most materials may be recycled from their primary use with the expenditure of only a fraction of the energy initially required to extract from their ores; thus, they may be considered as an energy bank. This, together with concommitant benefits to the balance of payments and the improvement in environmental quality resulting from the-recycling, rather than the abandonment, of materials makes the case for recycling almost irresistible in many cases For valuable materials, such as most non-ferrous metals, the channels for recycling are already well-developed, but opportunities exist for separation and re-use of commodities whose value is less apparent. Domestic refuse may be separated into fractions rich in iron and steel, aluminium, other non-ferrous metals, glass, and combustibles. Other techniques produce saleable fractions from incinerator residues. Perhaps the largest scope is in the field of so-called ‘open loop recycling’ where the waste from one process is used as raw material for another; here the possibilities for development of reuse cycles increase in number with the size of the catchment area.

Preliminary estimate of iron ore reserves

Prognostic estimates of iron ore reserves are discussed on the basis of experience and published theoretical premises. A geologic classification of ore deposits is offered as a basis for prognostication. (Note: The Geological Classification of Iron-Ore Deposits (table 2) may be of interest to American economic geologists.).—C.E. Sears

Metalliferous Mine Surveying

THE fundamental problem in mine surveying is the connexion between the surface and underground surveys and their relations to the boundaries of the property. In this book, which, unfortunately, the author did not live to see published, a successful effort has been made to present clearly and accurately modern methods of mine surveying with special reference to the correlation of the various parts of the work involved. Careful and practical descriptions of the instruments used are given, followed by details of survey practice and methods of preparing plans and sections and written records. Later chapters deal with stope surveys, estimation of ore reserves, and borehole surveying. The whole treatment is well proportioned, clearly written, effectively illustrated, and copiously provided with examples and calculations. Colliery surveying is not specifically dealt with, but the metalliferous mine surveyor has here a thoroughly up-to-date guide to all the leading features of his varied profession. The work was written by an Australian surveyor who had a wide experience, and his book represents the successful accomplishment of a difficult task.

The Estimation of Ore Reserves

The Estimation of Ore Reserves