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By K. Wangerud, B. S. Caruso

A water balance model with deterministic and stochastic components was developed and used for the Gilt Edge Mine Superfund Site, South Dakota, to evaluate risks of contaminated runoff discharging to surface waters based on assumed water treatment plant (WTP) rates for different remedial alternatives. The objectives of the modeling were to use a stochastic approach for analysis of precipitation based on historic records, and for probabilistic estimation of annual and monthly runoff from primary disturbed/mining activity areas that currently requires, or will need, treatment at the WTP, water storage and changes in a major pit, and risk of contaminated water bypass of the WTP to a downstream drainage. Subareas/source areas generating contaminated runoff requiring treatment were delineated. A simple water balance model was used based on precipitation inputs and evapotranspiration and groundwater losses. Annual and monthly precipitation records for Lead, South Dakota were used to estimate precipitation at the mine site. A lognormal distribution was estimated for monthly precipitation. The stochastic software package/Excel add-in “@Risk” was used to generate random monthly precipitation values using a Monte Carlo method based on the distributions. The average annual and monthly distribution of pan and lake evaporation, and groundwater losses were also estimated for the site. Stochastic outputs from the model for the end of each month and year included contaminated runoff requiring treatment, water storage in mine pits and the risk of WTP bypass given different assumed WTP rates. The probability of the time required to dewater the pits was also modeled.

Jan 1, 2002

By P. D. Chamberlain, R. M. Nadkarni, D. J. Kinneberg

Introduction The relationship between precious metal miners and gold refiners has been uneasy over the years. Reasons for this uneasiness and lack of trust include technical factors, economics of scale, and cultural differences. Technical factors take two forms. First, concentrates, precipitates, and sponge produced at the mine site are notoriously difficult to sample. A nonrepresentative sample can be the cause of misunderstanding and distrust. Dote, however, is relatively homogeneous and can be correctly sampled and analyzed with greater reliability. Second, the technology and chemistry of fine gold and silver production is complex and quite different from dote production. Most mining companies are content not to be involved with additional processing steps. From the standpoint of process economies, it is easy to see why miners and refiners are separate groups. Mine location is dictated by the natural occurrence of ore bodies. Heavy capital investment requirements for infrastructure in remote locations usually limits companies to produce the first marketable product from a mine. Beyond that point, the economies of scale and large capital investments for refineries generally dictate that the outputs of several mines be combined to feed a single refinery. The refin¬ing process is so complex that refineries are generally built in larger cities with a skilled labor pool. Therefore, only the largest mines can afford to refine their own output. Lastly, there are cultural differences between the miner and the refiner. The miner, particularly the small gold miner, is by definition a risk taker in a risky business. Refineries, on the other hand, have historically been operated under legal or implied monopolies approved by the government. The government is interested in owning gold, either for currency reasons or because many national mints are major users of gold coins. It is not surprising, then, to find that miners may regard refiners as part of an unresponsive government bureaucracy or, worse, as "city slickers." It is easy for the two groups to distrust each other with these different backgrounds. The interface between miner and refiner does exist and affects nearly all precious metal mining companies and most refineries. This paper discusses the technical and economic aspects of the interface. It points out how both parties can improve the relationship. Technical interface Precious metals selectively dissolve to produce a pregnant solution. They are then recovered from solution by zinc precipitation (Merrill-Crowe process) or by absorption onto activated carbon. This is followed by stripping and electrowinning. At this point, the mining company must decide whether to ship precipitates (or sponge) to refiners or to produce a dote. Some factors the company must consider are the ability to sample precipitates, concentrates or sponge, security of storage, and production rates. An important factor is the incremental cost (capital and operating) of converting precipitates or sponge into dote at the mine. Generally, mines prefer to melt precipitates or sponge to dote to avoid prob¬lems associated with sampling them. There are three types of fur¬naces used by mining operators to melt precipitates to dote. The first and most widely used is a sil¬icon carbide crucible heated ex¬ternally with a gaseous liquid fuel. The crucible is easy to use and slag can be skimmed before pouring dote. This simple system is capable of handling 1 t/a (32,000 oz per year) gold. It could cost as little as $20,000. More complex systems could cost up to $200,000. The second type of furnace is the gas- or propane-fired rever¬beratory furnace. This is usually used only by large-scale opera¬tors in the silver business. Precip¬itates in reverberatory furnaces come in direct contact with the flame. The large volumes of flue gas can carry significant amounts of dust and fume that must be re¬moved from the gas before dis¬charging it to the atmosphere. In the days when the Rand re¬finery in South Africa used reverberatory furnaces, the silver leaving the furnace in the form of vapor and fume was estimated at 2.2% of the total silver charged to the furnace. The gold in the gases was about 0.03% of the gold charged. Most of this silver and gold was recovered in the exhaust gas scrubber system. These scrub¬ber systems can be more costly than the furnace itself.

Jan 10, 1986

By H. H. Schrenk

The purpose of respiratory protective equipment is to prevent the inhalation of harmful or objectionable atmospheres. Although constituents or contaminants that may render an atmosphere irrespirable or objectionable are numerous, they may be classified broadly as follows: I. Gaseous substance: n. A. Toxic. B. Inert (oxygen deficiency). II. Particulate matter (dispersoids). A. Solid. a. Dust (formed by disintegration). b. Pure (formed by condensation). B. Liquid. a. Mist (formed by disintegration). b. Fog (former by condensation).

Jan 1, 1940

By C. M. Wright

Siendo la veta principal San Cristóbal, una de las estructuras que atraviesan el Anticlinal Chumpe en la provincia de Yauli, su explotación ha sido limitada a las rocas volcánicas y filitas en el flanco sur-oeste del anticlinal. Por tal motivo, el texto señala que el análisis de la distribución de los metales y minerales dentro de la veta, revela un zoneamiento horizontal bien definido, que es compatible con el origen de las soluciones hidrotermales en el centro del anticlinal. Asimismo, este estudio cuantitativo determina las características de las partes ricas de la veta, trazando líneas de contornos de los cuatro tipos de metal en secciones longitudinales, como los controles de la distribución de metal y relaciona las áreas ricas de la veta con su medio geológico. De otro lado, en San Cristóbal, la distribución del metal presenta una característica zonal donde la paragénesis y el zoneamiento están íntimamente relacionados. Concluyéndose que con la aplicación de los resultados de este estudio, se permitirá una mejor exploración y desarrollo de las áreas ricas de la Veta Principal San Cristóbal y se proporcionará una guía útil para la exploración y desarrollo de vetas paralelas en esta área.

Aug 20, 1963

By Mark Colwell, Christopher Mark

This paper summarises the results of a research project whose goal was to provide the Australian coal industry with a rib support design methodology and software tool that could be utilised by suitably qualified colliery staff. The project was primarily funded by Australian Coal Association Research Program (ACARP) and further supported by several Australian longwall operations. The outcome of the project is a design methodology and software tool called, Analysis and Design of Rib Support (ADRS). ADRS is an empirical technique, which recognises that several geotechnical and design factors affect ribline performance and in addition that operational and safety issues essentially dictate the level of performance required. Therefore, the design recommendations associated with ADRS are specific to the Australian coal industry; however the procedure(s) for data collection and analysis could be applied to other countries' 'underground coal industries. Case history data were compiled from 34 longwall and two bord and pillar operations resulting in 204 case histories with each case history data set being defined by approximately 130 individual data fields. In addition monitoring (incorporating stress cells and extensometers) was undertaken at 10 collieries to assess and quantify the effectiveness of different rib support patterns and hardware on rib performance. The monitoring sites allowed for an improved understanding of the mechanisms of rib failure and degradation in terms of its interaction with the installed support and at the various stages of the mining cycle. The design methodology deals with both mains development and gateroad development specific to Australian longwall mines. This paper focuses on longwall gateroads subjected to abutment loading and in particular the travel road which becomes the tailgate of the subsequent panel. The statistical analyses associated with these cases suggested that the level of rib support should be based primarily on the development height and the pillar stress level. The ADRS software guides users through the design process, allowing them to develop rib support plans based on sound science and a broad base of in-mine experience To the best of the authors’ knowledge ADRS is the first systematic rib support design technique to be developed for any country’s underground coal industry. The development and use of empirical models in mining have substantially contributed to improving safety and productivity. ADRS further demonstrates that empirical techniques are particularly relevant and beneficial in dealing with the complexities of geotechnical design associated with underground coal mining.

Jan 6, 2008

Sufficient time has elapsed since the enactment of the amendments to the mining legislation in 1981 to enable an examination to be made of the way in which the licensing system operates in practice. One of the most important decisions in resource management in New Zealand is whether or not rights of access to the resource should be conferred by the Crown upon an appropriate private sector participant. The licensing system is the means for allocating these rights of access. The manner in which the licensing system is administered, therefore, is crucial to natural resource management in New Zealand. What is the mining licensing system in New Zealand designed to achieve? This simple question admits of no easy answer. Is it the identification and development of the mineral resources of New Zealand? Are these objectives tempered by issues of resource conservation and environmental protection? Is a balance to be achieved among these competing factors? Does the legislation contain any priorities? Does the system respond in an ad hoc manner to particular facts and circumstances or does it operate within a more predictable framework? To what extent are decisions made on access to minerals with reference to the development or conservation of other resources? These questions may be summarised in the title to this paper which poses the question whether mining licences are instruments for resource management.

Jan 1, 1988

By G. Tamaro

The World Financial Center is situated on a 60,000 square meter site at Battery Park City at the southern tip of Manhattan Island. The foundations for the buildings and the related infrastructure posed difficult design and construction problems since the site was filled land in the Hudson (North) River. Foundation construction was made difficult by both the geology and the existence of two railroad tunnels which passed under the site. The soils at the site were unsuitable to support construction of heavy structures, and as a result, all of the foundations had to be carried down to bedrock, or the glacial till over rock. Two buildings were supported on piling and special battered caissons which provided lateral support against wind loading. The other two buildings were supported directly on rock, requiring excavation to depths of 19 meters (63 feet) below grade.

Jan 1, 1989

By T. Banerjee, D. Felsher, G. Leavoy

"Lake Shore Gold is engaged in commercial gold production at both the Timmins West and Bell Creek mines, located in Timmins, Ontario. Run of mine ore is processed at the Bell Creek mill which consists of a conventional gold mill flow sheet involving crushing, grinding, gravity concentration and carbon-in-leach (CIL) for gold recovery. Since 2009, the operating capacity of the mill has been upgraded from 2000 tpd tonnes per day (tpd) to over 3,000 tpd. The most recent expansion involved the installation of a low aspect ratio SAG mill to replace the secondary crusher. Without operational data on the low aspect mill, combined with a site team that was new to SAG milling, there were many challenges in achieving the target throughput from the circuit. Through the implementation of AwaRE advanced controllers, running in closed loop with PRC fragmentation cameras as well as embedded PARC modules within the Allen Bradley PLC, the site was able to rapidly develop a best operating practise and has been successful in creating a stable and consistent operational environment. The process, lessons learned and eventual solution will be reviewed in this paper.INTRODUCTIONLake Shore Gold is engaged in commercial gold production at both the Timmins West and Bell Creek mines, located in Timmins, Ontario. Run of mine ore is processed at the Bell Creek mill which consists of a conventional gold mill flow sheet involving crushing, grinding, gravity concentration and carbon-in-leach (CIL) for gold recovery. Since 2009, the operating capacity of the mill has been upgraded from 2,000 tpd tonnes per day (tpd) to 3,150 tpd. The most recent expansion involved the installation of a low aspect ratio SAG mill to replace the secondary crusher. This endeavor was split into two phases: the expansion of the back-end (Phase 1) and the front-end (Phase 2) of the mill. Phase 1 of the expansion was completed at the end of 2012 and involved enhancements and capacity addition to the leaching and adsorption circuits, which increased the mill’s capacity to 2,500 tpd. Phase 2 of the expansion commenced at the end of July 2013 and involved the expansion of the crushing and grinding circuits. The expanded front-end of the mill now has a capacity of 5,500 tpd, and processes ore from both Bell Creek and Timmins West mines. The updated flow-sheet, as shown in Figure 1, illustrates the replacement of the two-stage crushing and ball milling circuit with a single stage crusher and a low aspect ratio SAG mill."

Jan 1, 2015

By Cameron J. Clayton

Cumberland Resources Ltd. is currently planning to develop the Meadowbank Gold Project located some 70 km north of Baker Lake, Nunavut in the eastern Canadian Arctic region. The Meadowbank Gold Project currently consists of up to 6 main gold bearing deposits within relatively close proximity to one another which are planned to be mined primarily as a truck-and-shovel open pit operation and using conventional gold milling and extraction. The mining plan indicates that approximately 20 million tonnes of ore will be mined over a mine life of 8 to 10 years. The operation will generate approximately 160 million tonnes of mine waste rock and about 20 million tonnes of tailings. The site is located in an area of continuous permafrost with mean annual average air temperature of -11 °C and average annual precipitation in the range of 100 to 200 mm. Lakes cover a large portion of the site, including some of the ore deposits. The location of the site, and the physical environment, pose challenges to development. This paper presents some of the designs considered to effectively manage and utilize the waste products of mining at the project.

May 1, 2004

By F. V. Lenel

This discussion is concerned with the method of manufacturing, the design possibilities, and the properties of pole pieces for direct-current electric . motors and generators made from iron powder. In such applications as pole pieces, the electric and magnetic properties of the material are of major importance, therefore they are discussed somewhat more fully. However, the main advantage in making pole pieces from powders lies in the rapid and inexpensive method of manufacturing these pieces, and in the flexibility of design, rather than in their superior electrical properties. As a matter of fact, pole pieces from iron powder have found their principal field of usefulness in small electric motors for controls and similar applications where the highest possible flux density in a given design is not required. Fig. I shows a number of different designs for pole pieces made from iron powder. The steps involved in fabricating them are: (I) briquetting—with each stroke of the briquetting press a complete . pole piece is produced; (2) sintering, and (3) sizing, which is a one-step coining operation in a hand-operated punch press. Conventionally small pole pieces are made from laminated electrical sheet steel stock by punching out the laminations and riveting them together (Fig. 2). The powder method has the advantage of being rapid and inexpensive; also, it makes possible the molding of pole pieces with a round hub, which are better from a design standpoint, as will be shown later. It is difficult to make such round-hubbed pieces from laminated stock. The pole pieces could, of course, be machined from solid stock, but this method is not widely used. The raw material for making pole pieces from powder is straight iron powder without the addition of any alloying ingredients. However, the grade of powder used is of considerable importance, as will be shown later when the influence of the grade of iron powder upon the magnetic properties is discussed. Pole pieces are briquetted in the same way that other iron-powder machine parts are made. Because the pole pieces are flanged—i.e., they have a hub and a wing section—they are made in presses that apply pressure from both ends. For best mechanical and magnetic properties, the density throughout the piece should be even and also should be constant from piece to piece. For that reason a powder of constant compressibility from batch to batch is needed for briquetting pole pieces. One method of obtaining the required magnetic properties is to sinter the pole pieces at temperatures higher than are used for most iron-powder parts. A temperature of 2400°F. and an atmosphere of hydrogen has been found satisfactory. No automatic furnaces of the roller hearth or mesh-belt type have yet been developed for such high temperatures. A box-type furnace heated with Globar heating ele-

Jan 1, 1945

By D. Ksinsik, R. Boisvert, D. Leblanc

Casting, cooling and crushing/sieving of ferroalloys has followed a well-established pattern in the whole ferroalloys industry for many years. Usually liquid metal or alloys are cast into flat open moulds of various shapes and forms, and after solidification the product is removed from such mould to further cool down to a temperature where subsequent handling steps are feasible. Common to all mechanical product fractioning is the generation of dust and fine size material with lower product value. For almost 10 years, Bécancour Silicon has investigated alternative roads to improve technology and/or reduce or solve problems related to those disadvantages. Since 1995 Bécancour Silicon operates a special silicon granulation plant targeted to product for the chemical treatment/conversion of silicon for silicones production. Prior to the development of the granulation process, various systems had been evaluated, among others the vibrating casting bed, now in operation elsewhere but judged inappropriate because of the tapping volumes to be handled at Bécancour Silicon and other disadvantages. After evaluation of all aspects of heat transfer, radiation, and conductivity in relation to transfer media and within the product, a novel system was designed and built.

Jan 1, 2004

By Rolf B. Pedersen, Ana Filipa Marques, Ingunn H. Thorseth, Ingeborg Okland

"Deep sea mining of polymetallic sulphides will change the physical and chemical conditions at the seafloor by creating scars when sulphides are removed, and potentially also by deposition of mine tailings at the seafloor. These changes will impact the existing ecosystems at the seafloor in and around the mined areas. Seafloor Massive Sulphide deposits that have been exposed to oxic seawater weather into Fe-metal-oxyhydroxides. However, the rates of weathering and release of heavy metals and other toxic compounds to the environment from freshly exposed sulphides in a deep-sea environment are not well studied.During a cruise to the Arctic Mid-Ocean Ridge in the Norwegian-Greenland Sea in July 2014 we will initiate in-situ experiments investigating the microbiological and geochemical processes involved in the weathering of freshly exposed massive sulphides deposits in a natural environment. This will be done by creating scars in naturally occurring sulphide deposits and by deploying weathering experiments at the seafloor. The sites will be revisited and re-sampled in 2015. The mobility and fate of heavy metals will be one of the main concerns of the study as well as constraining the time it will take for exposed sulphides to return to the chemical state present prior to mining. In this presentation we will present the experimental framework and the preliminary results from the July 2014 cruise. This project is part of the EU funded MIDAS (Managing impacts of deep sea resource exploitation) project."

Sep 1, 2014

By I. W. Farmer

Weightings and water inflows into longwall workings often occur together, giving rise to discussions on their relative genesis. Case histories are introduced which indicate that most water inflows are associated with heavy weightings. Resultant large releases of energy can lead to extensive vertical fractures, which can drain water from aquifers or other sources, such as separation accumulations, onto the face. Effectively control of water inflows in these cases depends on face support and weighting control.

Jan 1, 1996

By Lee Sieng Kai

This paper presents the result of the analysis of strain-dependent concrete modulus from full-scale static axial compression load tests conducted on more than 200 instrumented cast-in-place barrettes and bored piles over the past 12 years, covering commonly adopted grades of concrete for heavy foundation construction in Malaysia and Singapore. The concrete modulus values, Ec, analysed were directly back-calculated from the material of the instrumented test piles by means of placing a layer of vibrating wire strain gauges near the pile head region. The best fit curve for back-calculated concrete secant modulus versus measured axial strain follows non-linear behaviour for both categories of test pile samples analysed. The result of the analysis seems to suggest that using average constant modulus value would generally lead to a significant error in load distribution computation, particularly at high stresses region.

Jan 1, 2006

By A. Korchevisky

Environmental self-monitoring is one of the advanced approaches for industrial sustainability programs. Organization for Economy Cooperation and Development (OECD) defines self-monitoring as ?the system of organizational and technical measures put in place and financed by [the] regulated subject? in order to ensure their compliance with regulatory requirements?1. Self-monitoring is beneficial for industrial operators, communities, and governments. Industrial companies use self-monitoring as a central element of their compliance management that allows them to fulfill their duties, obligations, and to avoid citations. When industries control their emissions and ensure workers are not exposed above the regulated limits, communities are better. It is impossible for an EPA, OSHA, or MSHA inspectors to be close to every emission source or workplace full-time. It is much more effective for industries to self-monitor, under due supervision. Occupational conditions are a very important part of industry and health and safety self-monitoring should be highly prioritized. In this paper we will research the regulatory basis and best practice of occupational self-monitoring. We will show that not only is self-monitoring a vital element of an occupational health & safety management system, but that you need a management system for affective monitoring.

Jan 1, 2012

By AIME AIME

THE twenty-second annual meeting of the Canadian Mining Institute was held at the King Edward Hotel, Toronto, on Mar. 8, 9, and 10, and was followed on the 11th by an all-day excursion to the International Nickel Refinery at Port Colborne. The meeting was very well attended and dealt with some of the most important matters, both technical and economic, that have ever come before the Canadian Institute. The question of licensing engineers is before the Canadian members as it is before our own in this country and the attitude of the mining engineers across the border is like that of the American mining engineers, opposed to the licensing of the mining. engineer, however they may feel toward the licensing of other branches of the engineering profession. It was well pointed out that such a law, had it been in existence in the last decade or two, would probably have prevented the rapid development of Canada's mines. Whereas one civil engineer can run a line of survey as well as another, perhaps, it is only a question in his case of whether he can or cannot survey. In the case of a mining engineer employed by a man with capital to invest in a development project, unless the man with the money has confidence in the judgment of his engineer the fact that he is a professional man would carry little weight in inducing a large investment toward the development of Canada's resources. It was also pointed out that although the Institute as a whole had not passed on the matter, it would probably be opposed to legislation aiming only for self-interest, but would be heartily in accord with legislation which could be shown to be for the service of the community at large.

Jan 1, 1920

By Prince Lazarovich, Hrebelianovich

I WAS asked by the chairman of one of the Sessions on Employment Problems to talk about the viewpoint of the foreign workingman. I am not a workingman. I have never done what a work-hand might call an honest day's labor; that is, I have never been in a factory or manufacturing plant or in a mine, though in truth, hard work and I are well acquainted. I was a soldier, am an engineer, have long been actively interested in the most important waterway construction in the near East, have served politics and diplomacy, written books and lectured at universities. My knowledge of the foreign workingman in this country comes from the fact that my own compatriots here at various times came to me and appealed for advice and help, and last year I was asked by the employment manager of a corporation to undertake a welfare job at one of their plants. I went out, saw the plant, talked with the superintendent and outlined certain of my ideas which he personally heartily approved, but which did not find favor with those higher up. I approach the subject of the foreign workman's point of view with the understanding that the industrial employer's effort is for the maximum of efficiency. I am conversant with labor conditions abroad both in industry and agriculture. What I have learned of industrial conditions in America as they affect the foreign immigrant has been chiefly gathered from the cases referred to of foreign workmen who from time to time have come to me with their troubles. In the course of those investigations, in order to give whatever help or advice was possible, I have been impressed with the fact that the great United States industries evidently had- pot yet sufficiently recognized the value of studying the conditions of the workingman in the lands of his origin across the seas. A careful study of that which could be called the moral element in connection with its foreign labor would give industry a knowledge of the man's reason for coming, what' grievances he brings with him, his hopes for a future, and the peculiar character of his capacities. The employer would thereby be enabled to meet the man, to be helpful to him, to aid him and at the same time promote industrial efficiency, inasmuch as a workman who believes that he is being dealt with humanly and squarely is contented and satisfied and will give willingly, and even with pride, the best that is in him; justice and a fair deal is all the man wants.

Jan 4, 1918

By Norman G. Foster

The mass spectra of four tertiary butyl substituted thiophenes are reported. A comparison and contrast with earlier structure correlations made by API-RP48 mass spectroscopists is presented. The fragmentation routes of these types of molecules are discussed and explained in terms of existing theories in mass spectrometry. Low ionization voltage data are presented to support the mechanistic picture developed. Structures are inferred about some of the ions, and these are correlated with existing theories. Metastable peaks in the spectra are used to support the fragmentation paths. The presence of doubly charged ions in the spectra is noted and the possible implications toward mechanisms discussed. The general picture of simple, small fragments leaving the ion moiety upon further fragmentation is developed in detail. Some suggestions are presented for further work utilizing isotopically labeled molecules to establish firmly the general picture of fragmentations of the alkylthiophenes.

Jan 1, 1966

By G. R. Hopkins

According to reports received by the Bureau of Mines, Department of the Interior, as of January 1, 1934, there were 591 completed refineries in the United States, an increase of 86 ever the total reported at the beginning of 1933 and the largest total ever recorded. It should be noted that the 1934 total, although large, probably does not include more than half of the "pot-still" plants of 1 barrel to 50 barrels daily capacity which have sprung up within the last 2 or 3 years and about which very little information is available. However, the combined operations of these snail refineries are of negligible importance as altogether they refine less crude than one plant of average size. Of the completed plants, 454 were operating on January 1, 1934 and 137 were shut down. In addition, 13 refineries were under construction on January 1, 1934. Compared with the previous year these data indicate a marked increase in the number of operating plants, little change in the number of inoperative plants, but a decline in' the number being built. The material gain in the number of operating plants resulted primarily from the construction off approximately 25 refineries, averaging about 100 barrels capacity in the Kooky Mountain district, as well as from the addition of about 20 plants in the East Texas field.

Jan 1, 1934

M.S. Azun I have many objections to the content of the author's paper. Before discussing it, however, I would like to repeat the property of semivariogram function. Second order stationary properties of regionalized variables (ReV's) such as semivariogram function y(h) are perfectly known in geostatistics. Also, the kriging equations in the language of mathematical statistics using second order stationary properties are well understood. However, the way to use the sample (estimated) semivariogram function in any one of the kriging procedures is vague. The sample semivariogram function is given as follows: [ ] where N is the total number of samples, Xi is the sample value at the i - th location, Xi+h is the sample value at the i + h - th location, and h is the distance among the samples. An estimation variance of sample semivariogram function of first lag is smaller than that of higher order lag. The theoretical semivariogram function reaches the variance of samples asymptotically. But this is not easily observable because of the larger variation involved in the estimate of semivariogram function. In general, an estimation procedure is done for h = 0, 1, 2, up to the greatest integer less than N/2, even though sample semivariogram function can be computable through N-1. After estimating semivariogram function, the critical question of how to model sample semivariogram function arises. As seen in the above equation, sample semivariogram function is discrete and can be smoothed by the model being selected. Therefore, modeling of sample semivariogram function is the most important step in geostatistics. It not only smoothes a discrete function but also affects the results of the kriging procedure. When the only aim is to model the semivariogram function, which is the basic point of the author's paper, one can employ any fitting techniques, such as curve fitting, or any arbitrary functions, which are called submodels in the paper. The term "arbitrary function" is used rather than "submodel" because there is no basic understanding of developing them. The author suggests that the sum of those submodels can also be used for the modeling of sample semivariogram function. The combination of any arbitrary functions brings many problems instead of giving an insight of the domain structure considered. The author used two arbitrary functions and the nugget effect in response to sample semivariogram function (Fig. 10). For the same example, he stated that the parameters involved in the mixed arbitrary function model can be accepted when the discrepancy between sample semivariogram function and the model is small visually. For verifying the fitting behavior of any selected model, one should not be contented with the visual satisfactory. Some statistical measure such as goodness of fit has to be used. The author's practice is no more than an exercise in curve fitting without any fundamental understanding or conceptualization of the underlying physical mechanism. Furthermore, the selection of any model is not an easy task if the purpose is the search for the "best" response to the observed second order properties of ReV's. I suggest that the Markovian model (Azun, 1983), on the basis of a theoretical understanding of underlying mechanism, which gives more information about the occurrence of regionalized variables, is used to respond all properties of ReV's. There are a lot of problems for modeling of one-dimensional sample semivariogram function. Thus, it is not appropriate to go to higher order dimensional sample semivariogram function modeling. In the meantime, I would recommend that one can connect the values of standardized sample semivariogram function rather than simple values of semivariogram function in the two-dimensional estimation. The standardized values can be computed in dividing the semivariogram function value by the number of sample pairs involved in each lag regardless of the directions. In conclusion, geostatistics is an interdisciplinary area in mining that uses the principles of mathematical statistics. Thus, it should not violate any probabilistic and statistical rules. When Matheron was developing the theory of geostatistical study in the early years of geostatistics, many mining people had a reservation accepting the geostatistical tools. However, this does not mean that we, the geostatisticians, might try to convince those people using some "strange" tools or rules as some authors implied (Baafi and Kim, 1984). Instead, we have to develop and explain the geostatistical tools staying only in the framework of statistical concepts and properties. References Azun, M.S., 1983, "Stochastic Process Modeling of Spatially Distributed Geostatistical Data," Columbia University, Ph.D. Thesis. Baafi, E.Y., and Kim, Y.C., 1984, "Discussion - Comparison of Different Ore Reserve Estimation Methods Using Conditional Simulation," Mining Engineering, Vol. 36, No. 3, p. 280. Reply by J.M. Rendu The interactive method proposed by Rendu allows practitioners to develop semivariogram models that take into account not only the numerical information obtained by sampling, but also highly significant additional information that often cannot be quantified. The geology of the deposit - including hypotheses concerning its genesis, sampling methods, assaying methods, and mathematical methods used to calculate the semivariograms - all have an influence on the numerical results obtained and on how these results should be interpreted. If all the information concerning the spatial distribution of values in a mineral deposit was contained in the sample values, it could be argued that statistical techniques alone would produce optimum models. However, this is rarely, if ever, the case. Methods that allow the user to take into account his experience and his geologic understanding of the deposit should not be rejected for the sake of theoretical statistical purity.

Jan 11, 1985