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By W. K. Callaway

The need to increase ore recovery and pillar stability caused the Magmont Mine staff to investigate the use of sandfill to accomplish both tasks. The use of hydraulically stowed classified mill tailings as a subsidence preventative will be discussed as well as the use of sandfill in pillar recovery and as a part of the regular mining cycle.

Jan 1, 1986

By J. MacFadyen

The U.S. cement industry, including Puerto Rico, again set a record in terms of production and shipments. The increase in shipments came primarily from imports of portland cement as domestic production from produced and imported clinker gained only 1.9 Mt (2.1 million st). Clinker production as reported to the U.S. Geological Survey (USGS) was 88.6 Mt (97.6 million st), an increase of 1 percent. Gray and white portland cement production from domestic and imported clinker, estimated at 93.5 Mt (103 million st), was up 1.9 Mt (2.1 million st). Masonry cement shipments of 5.5 Mt (6 million st), which equates closely to production, was up 6.3 percent. Blended ce-ment shipments were up 35.9 percent from 2004 at 2.35 Mt (2.6 million st).

Jan 1, 2006

By Kasimcan Koruk, Julian M. Ortiz

A geological model accounting for uncertainties possesses important advantages for resource estimation. Machine learning algorithms (MLAs) employed on multivariate geochemical datasets open up ways to new methodologies for such geological models with ease in comparison to traditional geostatistical methods. This article proposes a two-step MLA with an ensemble implementation to define geological domains and their uncertainties based on geochemical data. The proposed workflow is applied hierarchically on a dataset from a porphyry copper deposit to perform binary classification that can be attributed to alteration domains.

Mar 1, 2024

By M. A. Reyes, L. Yan

Heat and humidity buildup withn refuge alternatives (RAs) may expose occupants to physiological hazards such as heat stress. The Mine Safety and Health Administration (MSHA) regulations require RAs in underground coal mines to provide a lifesustaining environment for miners trapped underground when escape is impossible. RAs are required to sustain life for 96 h while maintaining an apparent temperature (AT) below 95 °F (35 °C). The National Institute for Occupational Safety and Health (NIOSH) tested a 10-person tent-type RA, a 23-person tent-type RA, and a 6-person metal-type RA in its underground coal mine facilities to investigate the thermal environment over a 96-h period. The test results showed that mine air and mine strata temperatures surrounding an RA occupied by simulated miners (SMs) increased over the 96-h test period. The test results suggest that RA manufacturers should consider this increase in temperatures when calculating and evaluating RA components during surface and laboratory tests. The findings can equip stakeholders with additional considerations for calculating the interior heat and humidity temperature profiles for occupied RAs not tested in situ.

By L. R. Stoiser

The mineral resource potential of the Los Bronces deposit was successfully evaluated by an intense, coordinated program over a 37-month period (April 1978-May 1981) as part of an economic feasibility study. The program included more than 120 km of core drilling, 63 km of access road construction under adverse topographic and climatic conditions, detailed geological mapping, plus other related activities. This Tertiary-age copper-molybdenum deposit is composed of an earlier mineralized porphyry-type body intruded in part by a large complex of mineralized hydrothermal breccia pipes. Both intrusive and extrusive igneous rocks are present. Erosion, oxidation, leaching, and supergene enrichment of copper have resulted in a deposit now exposed at the surface that contains more than 368 Mt grading about 1% copper equivalent as sulfides.

Jan 1, 1982

By Zhian Liang, Xiong Huang, Weixin Wu, Lifeng Cui, Zhuanhua Wei, Guoyao Li, Xiao Ni, Junrong Wang, Shuiping Zhong

ZJ 201 (modified starch) is a non-toxic, odorless, and biodegradable polymeric depressant, which selectively depressed galena in batch flotation tests while chalcopyrite was not significantly affected. In a plant trial, copper-lead separation was successful for the first time without using dichromate. Moreover, the plant process could be changed to sequential Cu-Pb flotation using ZJ 201 for higher grade lead concentrate. A copper concentrate was obtained with a Cu grade of 24.91% and a Pb grade of 5.11%, which recovered 76.6% of the copper from the original ore; a lead concentrate was also obtained with a Pb grade of 21.90% and a Cu grade of 5.31%, which recovered 52.6% of the lead. In addition to the effective copper-lead separation observed in the plant trial, another improvement observed is that gold was recovered mostly in copper concentrate, which could be sold for higher prices. Au grade reached 230.64 g/t, and its recovery reached 65.8% in the copper concentrate. Au grade in lead concentrate was only 18.90 g/t.

Aug 27, 2021

By Drew A. Meyer

Magnetic metals are the granddaddy of products which may be recovered from municipal waste. Aside from hand-picking of newsprint and corrugated boxes, magnetic metals are usually the first items a resource recovery facility considers extracting from the solid waste stream. Magnetic metals from incinerator residues and from municipally mandated source segregation programs were first used in significant quantities by the Copper Industry. The ability of the Copper Industry to consume metals from the municipal solid waste stream raised everyone's hopes that there would be more markets for municipal scrap when more of it became available. Somehow something has gone wrong. It is widely acclaimed that scrap is an environmentally sound and economical source of iron. It is greatly in demand for Its contained energy. The prices that the steel industry has been willing to pay for the scrap during the past year are all the proof anyone should need that scrap Is desirable and sought after. But the very fact that I'm speaking today on the markets for magnetic metals recovered from municipal waste indicates that something Is wrong. Clearly the problem is not that we do not need the scrap. The problem is we have not produced the kind of scrap that consumers are willing to buy - either through ignorance of what the consumers wanted or through a conviction that ferrous scrap is so obviously a good thing somebody will surely want it no matter what. Dr. Harvey Alter of the National Center for Resource Recovery has said "You can't sell garbage". In a sense that is only partly true. It really should be "You can't sell garbage for very long". The Steel Companies, in an effort to prove that steel is an environmentally desirable packaging medium, have bought some scrap that can only be described as garbage. They are to be commended for doing so. The fault lies not with the Steel Company for taking and paying for "garbage" but with the producer of that poorly prepared scrap. Far every instance where the steel industry has purchased the often undesirable product from resource recovery facility there are several magnetic installations sitting Idle because someone forgot the most essential part of producing the magnetic product - selling it to someone.

Jan 1, 1975

By V. T. McLemore

Deposits of rare earth elements (REE) are found in NM, but they have not been important exploration targets in past years because demand has been met elsewhere. However, with the projected increase in demand and potential lack of available production from China, the New Mexico deposits are being re-examined for their potential. REE-Th-U veins are found in the Gallinas, Caballo, Capitan, and Cornudas Mountains and Laughlin Peak-Chico Hills. Past production of bastnaesite has come from the Gallinas Mountains. Carbonatites are found in the Lemitar and Chupadera Mountains, Laughlin Peak-Chico Hills, Lobo Hill, and Monte Largo (Sandia Mountains). Although carbonatites have not been found in the Gallinas Mountains, they are suspected to occur in the subsurface based upon mineralogy/alteration. Disseminated Y-Zr deposits in syenite are found at Pajarito Mountain, Mescalero Apache Indian Reservation near Ruidoso. In 1990, Molycorp, Inc. reported historic resources of 2.7 million short tons grading 0.18% Y2O3 and 1.2% ZrO2 as disseminated eudialyte. Two additional deposit types have potential for REE in New Mexico: Cretaceous heavy mineral, beach-placer sandstone deposits and pegmatites. Exploration is ongoing in the Lemitar, Gallinas, and Cornudas Mountains.

Jan 1, 2012

By Debbie Laney

DOUG HALBE: Second in our quick run-through on "Operating Ideas That Have Saved Me Some Bucks," was Debbie Laney of Rayrock Mines. Debbie apologizes. She can't be here. But she said, "Doug, don't worry. I've asked Mary Korpi to present the paper. We're both short, blond, and wear glasses. Nobody will know." [laughter] Mary, I caught it right away. You ladies can't fool us. Debbie, who wrote the paper, has spent almost her entire career in operations. She is currently metallurgical manager of Rayrock Mines in Valmy, Nevada. Mary Korpi is also a real operator (that doesn't sound right). She has been responsible for a number of operating areas at Newmont's Nevada operations, and she is currently taking a break from operations as manager of public relations/employee communications for Newmont Gold in Carlin. MARY KORPI: They told us this year at Newmont that we were going to have to work twice as hard. I had no idea it meant I would have to work for another company, too. Over the years, and many times in association with work for mid- to small-size mining companies, there have been two areas that seem to have been the focus of cost savings when looking at new facilities or new processes.

Jan 1, 1998

By W. F. Visser

The growing availability of information and data analysis capabilities of recent years provides new opportunities for improving the performance of mining operations. By using real-time measurements and artificial intelligence, it is possible to respond faster to changing conditions, while accurate and timely information permits rapid evaluation of changes and fast business improvement decisions. This article presents a blueprint for alignment of systems, organizational design, and management practices to leverage these developments in performance-driven operations management in mining and mineral processing. The first component of the blueprint is a performance framework with a system of key performance indicators for production control that can be used across organizational levels. This system places improvement at the core of management activities, giving greater importance to improvement skills at lower organizational levels, so companies can leverage available information for improving operational control. Secondly, the blueprint defines an organizational structure that strengthens performance improvement with technological and change management capabilities. Finally, the blueprint proposes alignment of management practices, covering the optimization of short-interval controls, the application of an improvement project portfolio management system that determines the ownership of improvement projects, and the coordination of controls across the organization. This combination of systems, organizational design, and management alignment supports rapid decision-making at the right organizational level. Introduction of the presented blueprint for operations management enables mines to leverage the developments in information and analysis capabilities to improve the performance of operations.

By John Chadwick

In the drive for faster development advance rates, railbound systems can be advantageous, in the right application. Skanska BS, the contractor to mine-owner VSK Mining, is driving an adit access deep into the Volouské Urchy Mountain in Slovakia to access the Gemerská Poloma talc deposit, some 70 km (43 miles) west of Ko?ice, the economic and cultural center of eastern Slovakia. Skanska began driving the Stolna Elisabeth drift in February 2007, extending 25 kg/m (50 lb/yd) rails (with 750 mm or 30 in. between sleepers) into the mountain to provide the main haulage to bring talc ore and waste out of the new mine once it gets into production. It will also be used for personnel transport, and is now almost complete. As a second egress and for ventilation, a 2.5-m- (8.2-ft-) diameter shaft of about 300-m (984-ft) depth will be sunk from surface down into the orebody. Stolna Elisabeth is a 4.2-km- (2.6-mile-) long drift mined at a cross section of some 11 m2 (118 sq ft). The finished profile is 3.2-m- (10.5-ft-) wide by 3.6-m- (11.8-ft-) high. It has been developed on a very slight incline so that water runs down it to the portal. The portal is 450 m (1,476 ft) above sea level and the end of the tunnel is 475 m (1,558 ft) above sea level. Much of the rock through which it has been developed is magnesite with a compressive strength of 150 MPA. The drilling jumbo is an Atlas Copco twin-boom Boomer 282 Raildrill drilling 42- to 45-mm- (1.6- to 1.7-in.-) diameter holes to a maximum length of 2.5 m (8.2 ft), depending on ground conditions. This is a drill jumbo that Skanska has used successfully on a number of projects during its life. The condition of the rock through which this drift has been driven is extremely variable. Five classifications of A1 and A2 and B1, B2 and [ ] B3, where A1 is the most competent rock and B3 is the worst, have been established. The amount of support used, of which more later is determined by the classification of ground conditions. At the time of the author?s visit, the project it was about 40 days ahead of schedule, thanks to high advance rates. For instance 6 m/day (20 ft/d) was the plan for the advance to be achieved in B1 rock, but sometimes the crews have achieved 8 m/day (26 ft/d) ? which is the average for the whole project ? in those conditions. In A1 the best advance rate achieved is 12 m/day (39 ft/d). The loading unit is a Häggloader 9HR-B on crawler tracks with a pony track to run on the rails. This allows the unit to be towed up and down the drift along the rails. To load from the face, the Häggloader lowers the foot of its onboard conveyor system to the floor and the backhoe pushes material on to it. This digging arm-conveyor combination produces uninterrupted, optimal volume loading of the haulage unit, without spill ? a technique offering load capacities as high as 180 m3/h (6,356 cu ft/hour). Further-more, as an electrically powered machine, it offers great

Jan 1, 2009

Development of a permanent human base on the Moon for exploration requires a self sustaining system. This entails production and processing of limited amounts of raw material on the Moon. Any mining and construction activities on the Moon can only be performed by a robust excavation machine that can excavate a variety of material from loose surface regolith to consolidated (frozen) regolith with embedded rocks in the mixture. Meanwhile, limited amount of information on lunar regolith is available to develop and optimize a machine for given lunar ground conditions. Therefore, any excavator designed for use on the lunar surface should have the ability to adapt to a wide range of operating conditions. A prototype cutterhead for the lunar excavator was built and tested at the Kennametal facility in Latrobe PA A. This paper discusses the results of initial material characterization as well as full scale tests of a prototype cutterhead inrelevent material. A brief review of anticipated production rates under various assumed ground conditions will also be presented.

Jan 1, 2009

What is the preferred electrolytic cell design and why? Hall: Considerable research remains to be done on electrolytic cell design. Studies are presently being conducted to determine optimum voltage and amperage. Zadra cells, which were used in some of the first carbon plants, are efficient when properly installed. Gold and silver are deposited on large-capacity, cylindrical steel wool cathodes. At times high value sludge falls from the cathode to the bottom of the cell. Rectangular cells, which were developed at some smaller operations in Nevada, require less floor space and have some desirable features in that cathodes can be moved and sludge can be removed from cell bottoms without actually shutting down the circuit. In South Africa two types of cells using graphite and diaphragm configurations are being tested. Duncan: The rectangular cell has one problem it's easy for shortcircuiting to occur. If you don't have a good seal on the side of the tank and on the bottom, the solution is going to want to flow around the bottom and sides of the cathodes and you're going to get poor performance in the cell. That is the advantage the Zadra cell has over the rectangular cell. With good sealing, which is a must, you should be able to get a ratio of the value of the solution going in to the value of the solution coming out of 10 to 1. Ken, can you tell me what you're attaining on the Zadra? Hall: At the Homestake gold operation in Lead, the cathode in the No. 1 electrowinning cell is loaded to about 600 ounces when it is moved to the refinery. At this time the No. 2 cathode is moved to the No. 1 cell. The No. 3 cathode is moved to the No. 2 cell and a cathode with new steel wool is placed in the No. 3 cell. In rectangular cells this sometimes is not possible because the loading on the cathode in the last cell may be as high as that in the No. 1 cell. As Don has pointed out this can probably be prevented by good seal design between cathodes. Potter: At the risk of sounding as though I'm straddling the fence, I really believe that either the round cell, as developed by Jack Zadra, or the rectangular cell will do an acceptable job. The Zadra is a fine unit. Leaks are not unknown but there are not very many. However, the rectangular cell is very saving of floor space. Plastics have been greatly improved during the past year or two and there is a very efficient design for the rectangular cell. It would have six cathodes in it and contain about 25 ft of steel wool. The body of this rectangular cell would be reinforced fiberglass plastic but with an integral lining of a high temperature plastic. I think either cell is so efficient and reliable that I would almost be tempted to flip a coin depending on floor space requirements. Either cell can be used to pull a loaded cathode and to advance the lesser loaded cathodes. Don, what is the configuration of your cell? Duncan: The Pinson rectangular cell has dimensions 2 ft wide, 30 in deep, and 10 ft long-long enough to take a dozen cathodes and anodes. We are currently using six of each but are not up to full capacity as yet. It's a steel tank coated with rubber. We have copper bus bars, which brings to mind that the last cathode in the tank, in one instance, was loaded heavier than the first one. That was probably a function of poor contact between cathodes and the bus bar. You can have erosion of the bus bar and if you don't get current flowing into the anode and out of the cathode, the cells will not function properly. Kappes: Just a few comments on cell design. In an alcohol stripping circuit we are running in Beatty„ NV, we are using PVC pipes for all circuitry piping and a commercial polypropylene electrolytic cell. They seem to be working quite nicely. The cell itself has eight cathodes measuring 18 in2. At six gallons per minute flow into the cell, at an average gold content of about 500 ppm, we seem to get good loading on the first three to four cathodes and not much on the end cathodes. At 12 gallons a minute flow we seem to be seeing gold uniformly along all eight cathodes. We are running at quite a high amperage level, about 400 amps into that cell. Gene McClelland, US Bureau of Mines, Reno Research Center (from the floor): I was associated with a company where the packing density of their steel wool cathodes was much too high and created some short-circuiting problems in their electrowinning circuit. I would like to ask the panel if they can recommend a packing density for cathodes in pounds of steel wool per cubic foot. Hall: The weight of steel wool put on one of our cathodes is 10 lb and the dimensions of the cathode are such that density would be about 0.75 lb/ft3. Duncan: I made a rough calculation and I'm estimating about 2 lb/ft3. Potter: In checking over a number of electrowinning operations, I found apparently very satisfactory operation within the limits that have been mentioned. I have come to a figure of about 0.5-1.0 lb of medium grade steel wool per cubic foot packed as uniformly as possible, of course. One consideration in packing is the fact that there should be good contact between the steel wool and the conductor. Operators tend to compact the steel wool more than would be desirable just to try to maintain good contact.

Jan 10, 1981

By John J. Murray, Michael T. McRae, Michael A. Krulc, Kathy L. Schuler

The San Vicente Pipeline Tunnel Project involves the construction of an 8.5-foot-diameter water pipeline in an 11 mile tunnel in San Diego, California. The tunnel is located in extremely variable geologic conditions of strong granitic and volcanic rocks, weak sedimentary rocks, abrasive conglomerates, and mixed face conditions. One reach of the tunnel is a 5,200-foot mixed face reach that includes Friars Formation Conglomerate overlying granitic rock. Due to the variable ground conditions in this reach, the use of a TBM was deemed too risky and the contract documents required drill-and-blast and hand mining methods. Although it was not required, the contractor elected to construct this reach using NATM methods. This paper describes the geology of the 5,200-foot mixed-face reach, the design evaluation, and the construction challenges faced on this project.

Jan 1, 2007

By David K. Hylbert

This study investigated roof falls in room-and-pillar drift coal mines in eastern Kentucky and utilized geologic methods for predicting roof conditions in advance of mining. In the Highsplint mine, the roof was classified in four categories or conditions: Condition A and B (Laminated Shale), Condition C (Rolling Sandstone with Shale in Pockets) and Condition D (Zone of Major Sandstone Roll(s)). Structure contour and isopach maps of the Darby coal bed and associated immediate roof rocks were used to project axial trends of the sandstone roof. Trend mapping in the mine and on outcrop provided more detailed control for roof projections.

Jan 1, 1978

By E. Lee Bray

"Editor’s note: The editors thank those who make this annual issue possible. A special thank you goes out to the Industrial Minerals Annual Review editor, to the Industrial Minerals & Aggregates Division Technical Committee chair and vice chairs, and to the authors of the individual commodity profiles.Jim Norman, member SME, of Tetra Tech Geo, is the industrial minerals annual review editor. Edgar Blanco, member SME, of Freeport- McMoRan, is chair of the Industrial Minerals &Aggregates Division’s Technical Committee.The technical committee vice chairs include:• NickTushar Gupta and Sallie Gaillard, of the USGS, members SME, agricultural materials.• Abhishek Choudhuryand Xihui Yin, members SME, of Montana Tech and Kemira, repectively, ceramic and refractory materials.• Bobbi Strange and Riddhika Jain, members SME, of Outotec, Martin Marietta and Outotec, respectively, chemical raw materials.• Snehamoy Chatterjee, Alyssa Kendir and Alind Chandra, members SME, of BMT, Universityof Kentucky and Michigan Tech, respectively,construction aggregates.• Subham Verma, Gauran Soni and Freddy Sime, members SME, fillers and pigments.• Kaiwu Huang, Thomas Hilderbrand and Ricardo Santander members SME, of Virginia Tech, Thiele Kaolin and Carbo Ceramics, respectively, sorbents, filters and process aids.• Rhaghay Dubey and William Rapier, members SME, of Outotec and a consultant, respectively, specialty minerals.On behalf of ME readers, the editors thankTwo U.S. alumina refineries produced an estimated 1.5 Mt (1.65 million st) of alumina from imported bauxite in the United States in 2018. The 500-kt/a (550,000-stpy) refinery in Burnside, LA, owned by Almatis Inc. produced specialty alumina used in the abrasives, ceramics, chemical and refractory industries. The 1.2-Mt/a (1.32 million-stpy) refinery in Gramercy, LA, owned by Noranda Alumina LLC produced alumina mostly for use in aluminum smelters but also produced specialty alumina. An upgrade project at the Gramercy refinery to convert 200 kt/a (220,000 stpy) of capacity to produce more profitable specialty alumina was completed in the first half of 2018, and another project to increase capacity was started but a completion schedule was not available. The amount of new capacity was not disclosed, but it would be used to produce nonmetallurgical grade alumina. The 2.3-Mt/a (2.5 million-stpy) refinery in Point Comfort, TX, which was temporarily shut down in March 2016, remained closed throughout the year."

Jul 1, 2019

By R. L. Grayson, F. Giana, R. Aspinwall

Small-mine and contractor Fatal Incidence Rates have been a problem for over 20 years in the coal industry, and the rates persist as unacceptably high. This paper briefly retraces historical information and data on the continuing problem and recounts the many unsuccessful efforts and initiatives to address the problems effectively. Next the results of a review of international literature on addressing the problems are presented. After focusing on a method to pinpoint the trouble spots more specifically through a nested data analysis, suggestions are provided on how the problem may potentially be addressed more systematically and effectively in the U.S.

Jan 1, 2006

By James J. Meadows, Jason D. Pampena, Emanuele G. Cauda, Lauren G. Chubb

Exposure to respirable crystalline silica (RCS) can cause serious and irreparable negative health effects, including silicosis and lung cancer. Workers in coal mines have the potential of being exposed to RCS found in dust generated by various mining processes. The silica content of respirable dust in one single mine can vary substantially over both time and location. The current monitoring approach for RCS relies on the use of traditional air sampling followed by laboratory analysis. Results generated using this approach are generally not available for several days to several weeks after sampling, and this delay prevents timely and effective intervention if needed. An alternate analytical method is needed to reduce the time required to quantify the RCS exposure of mine workers. The National Institute for Occupational Safety and Health (NIOSH) has developed a new method using commercially available portable infrared spectrometers for measuring RCS at the end of the sampling shift. This paper will describe the application of the new field-based RCS analytical process for coal mines, including the use of the new method with the existing Coal Mine Dust Personal Sampler Unit. In a case study conducted by NIOSH with a coal mine operator in West Virginia, field-based RCS analysis was completed at a mine site to evaluate the new technique. The RCS analysis results obtained by the field-based method in this case study showed sufficiently strong correlation with results obtained by the MSHA standard laboratory analysis method to allow the mine operator to use the field-based method for evaluating process improvements.

By Andrew B. Cecala, Emily J. Haas, Jay F. Colinet

A sociotechnical system (STS) creates a framework that allows an examination of how social and technical factors affect organizational outcomes within a specific environmental context. STS has been rigorously studied with a primary research focus addressing worker-technology interactions. Although these interactions are important, the social processes and interactions that occur whenever any technical or environmental change is introduced into the system have been undervalued. If social processes are better understood, mining organizations could efficiently prepare and stabilize for such changes. With this goal in mind, we sought to extend STS theory through applying principles of meta-design to analyze the results of two case study interventions. Specifically, we studied the impact of an unregulated dust control technology (the Helmet-CAM) and a regulated dust control technology (the Continuous Personal Dust Monitor) on factors within an STS including employees’ knowledge of, communication about, and use of technology to mitigate respirable dust sources. The results are presented in a way that first, addresses the overarching principles of meta-design STS including organizational participation, flexibility, and communication and second, examines how technology implementation processes differ when the organization is complying with a formal, higher-level requirement. Results show that a prominent focus on the social factors within an STS framework could help reduce unpredictability on the technical side and may improve communication within the system to help reduce adoption time, especially if and when accompanying a new, formal work process.

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