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In 2002 the authors updated the MFire model developed by the US Bureau of Mines. MineFire, developed by Mine Ventilation Services, Inc. (MVS), uses the MFire model to perform mine fire simulations on typical mine ventilation networks. The MineFire program is capable of producing visual schematics and other analysis tools for input and output of the MFire model. The MFire model, however, was limited to 500 branches and 10 fans. This paper discusses the newly modified MFire model that is now capable of modeling over 5000 branches and over 400 fans among other expansions and improvements. Given the long history and proven track record of MFire, the expansion did not modify the core calculation methods or results. This paper focuses on a general discussion of the MFire program and issues encountered in expansion of the algorithm. An example large network with simulation results is discussed.

Jan 1, 2011

By Charles S. Robinson

INTRODUCTION Geology, the science of the earth, is the fundamental science in the construction of a tunnel. The approximate site of a tunnel is determined by its purpose. The geology of the tunnel site will determine the cost--or feasibility of a tunnel--the specific alignment to accomplish the purpose of the tunnel, the design of the tunnel (within the limits of the purpose of the tunnel), and the methods of construction. The more accurately the geology of a proposed tunnel can be depicted, the more accurately can the cost of a tunnel be estimated. The factors that should be defined for tunnel design and construction are the physical characteristics of the material in which the tunnel is to be constructed. The physical characteristics of the material are determined by the genesis of the material, and subsequent geologic processes that have affected the material. The geologic materials in which tunnels are constructed can be broadly classified as unconsolidated and consolidated. The unconsolidated materials include chiefly deposits of recent geologic time that occur near the surface. Because these deposits occur near the surface, and tunnels constructed in them will be at shallow depth, methods of physical exploration such as geophysical methods, trenching, and drilling will give more data at relatively low cost--therefore the physical exploration is generally, or should be, quite extensive--and the

Jan 1, 1997

By J. B. Gwiazda

S.S. Peng The highlights of this paper are : • The shield supports with lemniscate links will exert a tangential force on the roof strata, causing unnecessary and harmful roof movements, thus damaging the roof structure. The principal source of the tangential force is the horizontal movement of the point O, the pivotal joint between the canopy and the caving shield. When the support height is changed during setting, the point O will move along a curve upward and rearward toward the gob. As a result, it produces a vertical movement, causing the roof to move up a distance of ?d, and a horizontal movement toward the gob, creating vertical fractures in the roof. • The major purpose for employing the lemniscate-link system is to protect the hydraulic legs against the action of the bending moments induced by the tangential force that causes deformation or destruction of the legs. • Based on these two points, the author suggested that, in order to eliminate the harmful effects of the lemniscate-link system and strengthen its advantageous features, a shield support with a new design of that mechanism has been developed. With the new design, the conventional rigid lemniscate links are replaced by hydraulic rams. When the pressure inside the rams reaches a certain level, the ram will yield.

Jan 12, 1986

By James A. Madonna

Several universities and colleges in Australia, Canada and the United States, recognized the need to establish or reorganize geoscience programs at the vocational and two-year technical levels. To accomplish this, a cooperative study with industry in one state or province from each country was initiated. These include Tasmania in Australia, British Columbia in Canada and Alaska in the United States. The objective of this work was to develop a diversified geoscience educational model at the two-year technical, vocational and continuing education level that provides the source from which any nation can draw the proper educational tools to create a new geoscience program, modernize an existing program or strengthen a weak program. More than 100 mineral industry organizations provided information regarding their specific training needs for support personnel. The data gathered have been used to identify training areas for semi-skilled, skilled and technical personnel in geochemical mineral exploration. These included geological, geochemical, environmental and computer skills. With the areas of major educational need defined for geochemical exploration, an educational field skills model was developed for the three levels of training. The international need for a study of this type was recognized as early as 1980, following numerous contacts from domestic and foreign geoscience educators regarding the structure and success of training within the University of Alaska Fairbanks Mining Extension program, located in Fairbanks. Contacts, correspondence and visits included educators from Australia, Brazil, Canada, Mozambique and the conterminous United States. The need was magnified between 1985 and 1989 at the University of Alaska Fairbanks, when an attempt failed at initiating and developing a two-year geoscience vocational-technology program leading to an Associate of Science degree.

Jan 1, 1994

By J. E. Kogel

Industrial minerals play a central and dual role in the sustainable development (SD) of natural resources. Over the past decade the mining industry has increasingly focused on sustainably extracting and processing industrial minerals. This trend has been driven by higher energy costs, diminishing water resources and sensitivity towards environmental stewardship. Industrial minerals have been used throughout human history as low cost, naturally occurring, materials. Today they are critical components of recycled packaging, energy efficient building materials, light weight paper coatings, and other products critical to the responsible utilization of global resources. As industrial minerals become more widely used in ?green? products, mining companies have established best practices for the sustainable management of industrial minerals mining and processing. These management practices include reducing energy consumption, minimizing water usage, increasing waste recovery through recycling and process optimization, and maximizing the amount of ore extracted per acre of disturbed land. With the commitment to SD principles, quantitative methods for objectively measuring SD performance have become increasingly important. Measuring sustainability impact is a valuable tool for effectively applying SD principles and for making choices that balance sustainable development against other business objectives. SUSTAINABLE DEVELOPMENT AND MINING Sustainable development is a term that has become a common part of our lexicon; however, it has multiple meanings and interpretations leading to a sometimes confusing and contradictory array of definitions. The absence of a single, precise definition reflects the fact that SD is a broad concept or paradigm that offers guiding principles as opposed to a specific set of criteria or regulations enforceable by government or other oversight agencies. While a principle based conceptual approach allows businesses to broadly apply SD practices that are tailored to their specific situation, it has also led the public to sometimes view voluntary corporate SD programs with a degree of skepticism (Walker and Howard 2002). This is particularly true in the mining industry. One reason for this skepticism is that the relationship between SD and mining is misunderstood and to many, sustainably developing non-renewable mineral resources is a contradiction (Rajaram et al. 2005). However, this view takes a very narrow interpretation of the tenets of SD. The second is that mining carries a legacy of poor environmental stewardship that does not accurately reflect current corporate environmental practices Many minerals companies have adopted the Brundtland Comission?s definition of SD (United Nations 1987): ?? development that meets the needs of the present without compromising the ability of future generations to meet their own needs?. This definition is very broad and can be interpreted in a number of ways. It provides a general context for sustainable development and is not intended to provide detailed guidelines addressing specific aspects of sustainable development. To fill this gap the following SD principles were drafted by the international minerals community in 2003 (ICMM 2003): 1. Implement and maintain ethical business practices and sound systems of corporate governance. 2. Integrate sustainable development considerations within the corporate decision-making process. 3. Uphold fundamental human rights and respect cultures, customs and values in dealings with employees and others who are affected by our activities. 4. Implement risk management strategies based on valid data and sound science. 5. Seek continual improvement of our health and safety performance. 6. Seek continual improvement of our environmental performance. 7. Contribute to conservation of biodiversity and integrated approaches to land use planning. 8. Facilitate and encourage responsible product design, use, re-use, recycling and disposal of our products. 9. Contribute to the social, economic and institutional development of the communities in which we operate. 10. Implement effective and transparent engagement, communication and independently verified reporting arrangements with our stakeholders. These guidelines insure that SD concepts are applied equally across the industry while setting a clear performance standard and benchmark against which to evaluate success. By adopting these principles and issuing the Milos Statement (http://www.sdimi.org/milos_decl_October%206_2003.pdf), which provides a more detailed vision for integrating SD into everyday business operations, the minerals industry has embraced SD as a core corporate value. The unifying and holistic approach embodied in SD principles impacts the entire mine to market life cycle and addresses the economic, environmental and social consequences of mining. INDUSTRIAL MINERALS The world economy relies heavily on minerals; they are essential to economic prosperity and the quality of life. Industrial minerals are non-metallic, non-fuel minerals that provide the raw materials for a vast range of products used in most every aspect of daily life. They are mined and processed worldwide and they span the spectrum from relatively low value, high volume commodities (e.g. common clay, crushed stone) that are usually mined locally to high value, low volume specialty materials that are sourced from unique one of a kind deposits (e.g. barite, talc, mica). High volume commodity mining operations are often located near the end use market which, in most cases, means areas of high population density where construction and other urban activities drive demand. In these situations the strict adherence to SD principles is particularly critical as these are highly visible operations that must meet the public?s demand for good corporate citizenship. These operations are similar to chemical or other manufacturing facilities that operate near population centers. In contrast, some mining operations are located in remote but environmentally sensitive regions of the globe where the pressure to mine sustainably is driven by the need to preserve habitats and other

Jan 1, 2009

By Joseph W. Siefke

The Kramer borate deposit is located in the western Mojave Desert at Boron, California, about 100 miles northeast of Los Angeles (Figure 1). The deposit derives its name from the district in which it lies. Borax (Na2 B407.10H2O) is being mined from the Boron open pit to serve a major portion of the United States and world borate markets. This paper deals primarily with those geologic factors which affect slope stability in the overburden at the Boron open pit. Discussion includes slope failure history, slope monitoring techniques and the results of a dipmeter survey of overburden structure. Open pit mining was begun at Boron in 1957. The initial pit was successfully excavated at the recommended 1.5:1 (horizontal to vertical) slope in the overburden. During pit expansion in 1962, excavation of the overburden exposed beds dipping into the pit at +15 degrees and numerous high angle fractures associated with two intersecting fracture systems, the West Jenifer and Portal fault zones. Ensuing south and east wall failures indicated the need for more structural information in the arkose to establish better wall design criteria. Barnard and Kistler (1963) recognized that the many facies changes, faults and other variables in the Boron overburden make it extremely difficult to reduce prediction of slides to a simple arithmetical formula. Despite the difficulties and uncertain¬ties, special programs such as surface resistivity, refraction seismic and core drilling were conducted in an attempt to predict slope stability conditions and to gather geologic information. These early efforts while helpful, did not provide the necessary details of bedding orientations and fault locations which are of paramount importance in our slope stability program. A dipmeter survey in 1974 successfully measured these variables and data from that survey are instrumental in the design of slopes currently being excavated.

Jan 1, 1976

By M. H. H. Mahmoud, T. A. El-Barbary, E. A. Abdel Aal, I. A. Ibrahim, A. K. Ismail

Fertilizer-grade phosphoric acid with a P2O5 concentration of 50% should contain less than 1.5% Fe2O3, otherwise, the P2O5 water solubility of the fertilizers prepared from high-iron acids will be low. High-iron Egyptian phosphate concentrates fromAbu-Tartur and Sebaiya- West were leached with sulfuric acid and recycled phosphoric acid to produce 50%-P2O5 phosphoric acids containing 4.0% and 2.7% Fe2O3, respectively. The high iron contents were reduced to the industrially accepted limit of 1.5% Fe2O3 by precipitation with potassium sulfate. The factors affecting the effi¬ciency of the precipitation process, e.g., temperature, time and K2O/Fe2O3 ratio, were systematically studied, and the optimum conditions were achieved. The clarification of the prepared phosphoric acid from iron-containing sludges was also investigated by varying the time and temperature. The utilization of the separated sludges as fertilizer and recovery of P205 by pulping in water were also evaluated.

Jan 1, 2000

By Leonard N. Hill

Cyprus Sierrita Corp. has 16 parallel 5.03 m-diam x 5.8 m long (16.5 ft-diam x 19 ft) primary ball mills, each operating in closed circuit with a nest of cyclones. Before the upgrade to 840 mm (33 in.) cyclones, each mill operated with a nest of five 660 mm (26 in.) cyclones - four in use and one on standby. In this configuration, the mill throughput was 88.5 kt/d (97,500 stpd). Flotation feed averaged 25.9% +212 pm (+65 mesh). The 660 mm (26 in.) cyclones normally operated at an inlet pressure of 34 kPa (5 psi), lower than the inlet pressure of 55 kPa (8 psi) recommended by the manufacturer. The circuit was typically operated with cyclone overflow densities greater than 40% solids to achieve the required throughput. This resulted in inefficient cyclone operation and excessive coarse oversize reporting to flotation. The apexes choked frequently. Larger apexes were tested but reduced the classification efficiency and resulted in circulating loads greater than 800%.

Jan 1, 1994

By Cherie H. Tilley

The possibility of drilling oil wells from underground locations is not a new concept. It bas not been cost effective for the oil industry in the past and therefore disregarded. Today's state of the art in tunneling and shaft sinking greatly improves the potential for this type of oil field development scheme. This report presents a plan for providing a aeries of drilling bases and the design of the drilling location. The design minimizes the amount of excavation needed to develop the oil field and maximizes the use of rapid excavation techniques.

Jan 1, 1983

By D. M. Abbott, H. J. Sandri

The geoscience matrix method has proven useful for valuing metallic mineral properties lacking delineated mineral resources or reserves. However, the method explicitly excludes commodity markets from the factors considered; marketability is assumed. When valuing industrial mineral properties, marketability cannot be assumed, it must considered. Market considerations may also significantly affect the standard weightings of geoscience matrix parameters such as the proximity to known deposits. In some cases, such proximity is desirable but in many cases it is undesirable. Application of the geoscience matrix method to industrial mineral properties therefore requires thoughtful, market-related adjustments to the basic geoscience matrix methodology.

Jan 1, 2000

By D. G. Klaren

Self-cleaning fluidized bed heat exchangers are conquering the world for reason that they are able to solve any severe fouling problem in indirect heat transfer due to the circulation of cleaning particles through the tubes of vertical shell and tube exchangers. In most cases, these particles consist of chopped metal wire. Moreover, self-cleaning fluidized bed heat exchangers perform with excellent heat transfer at very low liquid velocities, which makes completely new designs of shell and tube configurations possible. Further, self-cleaning fluidized bed heat exchangers show a strong shear thinning effect in non-Newtonian liquids. All the above characteristics make the self-cleaning fluidized bed heat exchanger an ideal tool for the indirect heating of laterite nickel slurry in High-Pressure-Acid-Leach (HPAL) plants. Preliminary tests and evaluations of these heat exchangers have shown that the performance and price of these heat exchangers used for the production of nickel and cobalt from a laterite slurry, cannot be matched by existing conventional heat exchange systems. This article explains the principle, design, lay-out and enormous advantages of the self-cleaning fluidized bed heat exchange technology in a plant suitable for an annual production of approx. 45,000 ton nickel and 4,500 ton cobalt from laterite slurry through high pressure'acid leaching.

Jan 1, 2002

By Richard Adsero

The Australian Bureau of Statistics and the United States Bureau of Labor Statistics publish data for a range of industries, allowing a measure of performance to be quantified, called multifactor productivity (MFP), and allowing performance between industries to be compared on a consistent basis. At the time of writing, the last released data was for 2011-2012. For Australia, the plot of mining industry productivity and a basket of the 12 most significant industries in Australia?s economy (including mining) are shown in Fig. 1. For the United States, mining and petroleum and all manufacturing productivity are also displayed in Fig. 1. The trends are as follows: ? The MFP in the Australian mining sector rose 36 percent from 1986-1987 to 2000-2001. There was a 47-percent decline in MFP from 2000-2001 to 2011-2012 (Australian Bureau of Statistics, 2011). ? The MFP in the United States mining sector rose 17 percent from 1986-1987 to 2004-2005. There was a 7-percent decline in MFP 2004-2005 to 2010-2011, (Topp et al., 2008).

Sep 1, 2013

By J. M. Barker, V. T. McLemore

Most discussions of sustainable development (SD) in mining relate to metal mines in rural areas. Industrial minerals (IM) are closer to urban areas primarily owing to a high transport-cost component of delivered cost. This visibility to large populations overshadows IMs relatively small operation size and generally lower waste volume and toxicity. The IM industry needs to rethink its way of doing business to fit into the SD paradigm. Society and business in general will also undergo significant change to enable industrial SD along the lines of triple-bottom-line accounting with government pushing everyone. The benefit to IM mining from embracing SD is a renewal in their social license to operate and a rebirth of mining as a positively-viewed force in society. This positive view would lead to lower acquisition costs because society would not fight so hard to eliminate nearby mining. This would ease the current exploration woes of the IM industry by opening up new deposits for exploration and more readily allowing placement of mines nearer to markets. The earlier in the exploration process SD is initiated, the better.

Jan 1, 2004

By H. Lyn Bourne

This is the fourth annual tabulation that gives mineral royalty information. The table presents previous information plus about two dozen new entries. In addition to the royalty information, some entries show the cost of purchased reserves. Last year's tabulation appeared in two issues, to accommodate all of the information. This year the format has been changed slightly so the table can be printed in one issue. This year's table presents the commodities in the same sequence as last year. Sand and gravel information appears first, followed by: crushed stone for aggregate; other stone; industrial sand; other industrial minerals; energy minerals (coal, oil shale, uranium); and finally metals. As always, a caveat relates to factors that influence the reserve values. The data should serve only as a general reference. The table is not intended to present an absolute scale of reserve costs. Several factors influence the value of mineral commodities. These factors include: • location and transportation costs (especially significant for most industrial minerals); • market conditions for both the commodity and the company acquiring the right to mine it; • quality or grade of the deposit as it reflects the amount of processing and beneficiation necessary to produce the finished product; • and legislative restrictions and conditions for mining a given material at a given site. These and other factors will influence reserve costs of reserves. The table shows the range of royalties and the variations in the basis of computing the fees. In a few instances, it gives the cost of acquired reserves based on purchase price and quantitative estimates of the material in place. The table lists the commodity; the location (either by state, US geographic area, or Canadian province); the cost (R for royalty and P for purchased cost); and the year in which the lease or purchase agreement occurred. The last column offers either comments or gives a footnote number for more information. The cost column requires more explanation. The units may refer to cubic yards (/yd), cubic feet (/cuft), tons (/T) (2000 lbs) or acres (/A). 1 cu yd = 0.76m3 1 cu ft =0.28m3 1st = 0.9 t7 1 acre = 0.40 ha or m2 In several cases the royalty is a percentage of the finished products, sale price and is levied against either the amount produced or the amount sold. We thank those who contributed information for the table: J. Dunn, T. Eyde, K. Loda, L. Morgan, F. Nix, H. Sorenson, and L. Williams. Several people have said they would like this to be an annual tabulation. That can happen if new information comes to the writer. What appears in the table is only a very small fraction of the cost information relative to the various commodities and the geographic areas for which there is royalty information. If you find this column of interest and possess information write or call: H. L. Bourne, c/o Neyer, Tiseo & Hindo, Ltd., 38955 Hills Tech Dr., Farmington Hills, MI 48018, (313) 553-6300. Only with new information can this become an annual and current source of reserves costs.

Jan 8, 1986

By I. S. Parrish

One of the most common errors uncovered while performing a reserve, or resource, audit is not in the geological modeling or grade problems due to poor sampling, prepartion or assaying. The error most commonly found is in tonnage or, more specifically, in the tonnage factor - that factor applied to volume to derive tonnage. Tonnage factors In the metric system, the tonnage factor is the density, or specific gravity. Specific gravity (Sp.g.) is defined by Dana (1947): • "The specific gravity of a mineral is the ratio of its density to that of water at 4° C (39.2° F). • "Density is the mass of the unit volume or weight of the body divided by the weight of an equal volume of water." When Sp.g. is multiplied by the metric volume it yields metric tonnes. In the English system, the tonnage factor is usually expressed in cubic feet per short ton (cu ft/st). When the volume in cubic feet is divided by cu ft/st, the resulting figure is in English short tons. Table 1 gives the cu ft/st factors equivalent to specific gravities from 1.6 Sp.g. to 5.8 Sp.g. The table is based on the following equation: cu ft/st = 0.9072 divided by Sp.g. times 0.02832 The blase attitude that most geologists have toward tonnage factors is echoed in the prevailing definitions of Reserves and Ore, as provided by the US Securities and Exchange Commission (S.C Form S-18), Canadian National Policy 2A and the SME Proposal for Reporting Terminology (SME February 1991). In each case, it is stated that "quantity" (SEC, SME), or "tonnage" (Can.2A), "is computed from dimensions revealed in...." etc. Unfortunately, "dimensions" do not directly yield tonnage. Dimensions must be factored by density to derive tonnage.

Jan 1, 1993

By F. Warnaars

Historically, this area produced gold and silver from many well-known vein deposits, like Tayoltita, Topia, and San Jose de Gracia. Modern exploration identified three categories of deposits: 1) low grade porphyry golds in shallow level dacite porphyries; 2) batholith-related deposits; and 3) those formed in volcanic sequences of Late Cretaceous to Late Tertiary. At least four porphyry golds have been identified, of which Metates is best known. These are formed by and within daciteporphyries, associated hydrothermal breccias and sometimes within surrounding meta sediments. Their ages are from mid-Cretaceous to Early Tertiary. Precious metal deposits associated with batholiths occur as veins, contact haloes in meta sediments or volcanics, skarns, tectonic breccias, hydrothermal tourmaline breccias, dacite dikes or as disseminated or stockwork deposits such as La Fortuna.Several new gold discoveries were made in older EarlyTertiary Volcanic Sequences and in the younger Tertiary volcanics within prominent structures exceeding 3 to 5 km in lengths. Some of these are open-pittable but most have to be mined by underground methods.

Jan 1, 1999

By Jack A. McQuiston, Thomas A. Cross

Corrosion of equipment and machinery in the coal industry is usually the result of three main agents: acids, chlorides, and abrasion. Acids and chlorides are especially troublesome in coal preparation plants where soluble salts and sulfur in the coal produce a highly corrosive wash solution. Abrasion is common in all operations where coal is handled or conveyed. Together, the acid-chloride-abrasion combination results in some of the worst corrosive conditions found in any industry. The variety of equipment and structures in the coal industry calls for different corrosion control techniques. Table 1 lists the areas of concern for a number of items. Just as there is a wide variety of corrosion problems, there is a wide array of coating materials available. Tables 2 and 3 are selection charts to provide guidance in narrowing down the choices. Experience has shown that a limited number of coating systems work best on coal equipment and structures. These systems are described in Table 4. The good-better-best designation in the table refers to coating system longevity. Good indicates the least costly and shortest service life. In nearly all cases the lowest annualized cost can be achieved by using the coating system rated best, due to the avoidance of costly repaints and unnecessary downtime. The most expensive coating system, though, is worthless unless the coating system is properly applied. Field inspection to insure compliance with specifications is an important aspect, and is a service available from many coating suppliers. Even the best coating systems require periodic maintenance to achieve satisfactory results. Spot rusting from mechanical damage should be repaired annually to maximize the coatingsystem's results.

Jan 2, 1980

By S. S. Peng

In dealing with the mining engineering problems, the traditional approaches of laboratory experimental simulations and/or analytical solutions are not very effective. Mainly because the field problems are too complex to be solved with a few simplified assumptions. Conversely it is also true that the experimental and analytical/ numerical models currently available are far from being able to model the actual cases. Under such conditions, the most effective mean of research into mining engineering problems is to combine the mine (field) investigations with laboratory and / or analytical modelings. It is with this concept in mind this research was initiated in 1973. 'The field investigations which began in the fall of 1978 consisted of mainly visiting the mines where surface subsidence monitorings had been or were being monitored and/or surface structural changes had occurred. From such visits, subsidence data were collected. A quick analysis of those data provided preliminary understandings of the characteristics of the surface subsidence parameters in the regions (1-5). Using those date, models of various types are being developed for subsidence prediction / control. So far, a total of 44 longwall subsidence profiles in 22 longwall panels and 10 room-and-pillar profiles in 5 room and-pillar sections have been collected. This paper summarizes the combined results published previously (1-5) and present the preliminary results of the predictive models developed.

Jan 1, 1982

By Y. C. Kim, F. Szidarovszky

G.M. Philip and D.F. Watson The article cited above reflects the difficulty that is often encountered in interpreting different aspects of kriging. Baafi et al. write : "Due to negative kriging weights, negative block grades may be obtained in some extreme situations, which makes no practical sense." Their solution to this particular problem is to constrain the kriged estimates to data values that have positive weights, i.e., reduce the subset size contributing to the estimation. As Journel (1986, p. 133) has already observed, "Negative weights are no evil." Indeed, they are an ineluctable result of the Lagrangian multipliers in the system of simultaneous equations. The fact that data distant from the estimation point may be given negative weights simply means that the influence of such distant values must be negated because their influence is contradictory to closer values (as illustrated by Baafi et al. in their Figs. 3 and 4). Of course negative kriging weights applied to distant grade values will not in themselves induce negative grade at some central interpolation point. Negative grade values, rather, seem to be a particular artifact of automatic methods of estimation involving accu¬mulations (Philip and Watson, 1985a, 1985b, 1987b). The elimination of negative weights, suggested by Baafi et al., is likely to exacerbate a quite different problem of kriging and piecewise spline interpolation discussed elsewhere (Philip and Watson, 1987a). In interpolating large data sets of scattered observations, changing local subsets or neighborhoods must be selected automatically. Because of the mathematical formulation of kriging and spline interpolation, discontinuities then occur between closely-spaced estimation points as the subset used in the estimation changes. If this subset is reduced in number and size, the discontinuities will be amplified and more common. ? References Journel, A.G., 1986, "Geostatistics: models and tools for Earth Sciences," Journal of Mathematical Geology, Vol. 18, No. 1, pp. 119-139. Philip, G.M., and Watson, D.F., 1985a, "Theoretical aspects of grade-tonnage calculations," International Journal of Mining and Geological Engineering, Vol. 3, pp. 149-154. Philip, G.M., and Watson, D.F., 1985b, "A deterministic approach to computing ore reserves. I, Grade Estimation," Earth Resources Foundation, Occas. Paper 2, The University of Sydney, 24 pp. Philip, G.M., and Watson, D.F., 1987a, "Neighborhood discontinuities in bivariate interpolation of scattered observations," Mathematical Geology, Vol. 18, No. 1, pp. 69-74. Philip, G.M., and Watson, D.F., 1987b, "Estimating interactions of topological functions," Mathematical Geology, Vol. 18, (at press). Reply by Y. C. Kim Before replying to the comments by Philip and Watson, it is desirable to establish the original perspective of our paper, which was intended primarily for the practitioners of mining who possess a working knowledge of ordinary kriging. The paper tried to convey the following practical points: (1) there are circumstances in which one observes negative weights, (2) illustration of circumstances under which one can expect negative weights, (3) should one obtain a negative estimated grade, one can resort to elimination of negative weights using the technique outlined in the paper, and (4) one could normally select only the first layer of surrounding assays to estimate the block grade. Under such a perspective, most of the comments by Philip and Watson are irrelevant and misdirected. For example, the practitioners do not find it difficult to "interpret" the results of ordinary kriging, as evidenced by the fact that they have been using the results for nearly a decade. Nor are the practitioners concerned with discontinuities in estimated block grades due to changing neighborhood of assays during kriging. What matters to the practitioners is the fact that kriging does provide the best estimate among all the estimation tools available to them as of today. ?

Jan 2, 1987

By L. E. Beverage, K. L. Johnston

This paper will address methods for minimizing liability and protecting materials from disclosure as result of self- evaluative audits and internal investigations. Specifically, the paper will cover the role of counsel in the investigative process and how best to design and conduct internal investigations to minimize the development of problematic material and disclosure of information. The paper will also address the extent of privileges that may be relied upon to protect materials and information from disclosure. These include the attorney-client privilege, the self-critical analysis privilege, and the attorney work product privilege. These privileges are qualified and understanding the limits of their coverage is essential to minimizing liability.

Jan 1, 2001