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By A. M. Marabini, V. Alesse, Belardi. G.

An alternative flowsheet was designed for the flotation treatment of a complex sulfide ore from the Sotiel Mine in Spain. The ore contains 0.71% Cu, 2.24% Pb and 5.63% Zn. Two specially developed synthetic collectors, methyl-mercapto-benzoxazole (MMBO) and 6n-propoxy-mercapto-benzo-thiazole (PMBT), were examined. MMBO exerts a specific action on copper and zinc minerals after treatment with copper sulfate, and PMBT exerts a specific action on Pb minerals. Flotation operating variables (pH, frother type, frother quantity and feed particle size) were examined by means of rougher flotation tests to determine the optimum conditions for the new collectors. Once the optimum conditions were determined, a series of open flotation circuits were run on feeds of various particle sizes (obtained by different types of grinding). The objective was to obtain high-grade Cu and Zn concentrates. The results of the open-circuit tests demonstrated that a Cu concentrate grading from 18% to 23% Cu and a Zn concentrate grading from 40% to 48% Zn can be produced.

Jan 1, 1996

By S. Svoronos, B. Moudgil, R. Stana, A. El-Midany

Due to their similar surface properties, it is not always easy to separate carbonate minerals from other salt type minerals by froth flotation. A particular example is the difficulty of separating dolomite impunities from phosphate minerals. Such challenging fundamental and practical problems have inspired several research efforts in various laboratories around the globe to find methods for economically removing the dolomite. However, a universal and cost effective process is not in commercial use. In this paper, a new process for separation of carbonate minerals (dolomite or calate) from other associated minerals is presented. Differential solubility of carbonates in slightly acidic solution is utilized to generate micro GO, bubbles at the carbonate mineral/ water interface. Particle (e.g., dolomite)/ bubble aggregates float to the surface leaving phosphate concentrate with low MgO content. Interestingly, up to 6.0 mm particles can be floated by such micro bubble/particle aggregates. Different sutface-active agents were tested to stabilize the bubbles. Results of these tests are presented and the mechanisms involved are discussed.

Jan 1, 2005

By Peter J. Huck, Yoginder P. Chugh, M. Jennings

INTRODUCTION Large areas of the United States coal reserves have been undermined by room-and-pillar mining over the past century. These abandoned mines generally cause subsidence of the ground surface many decades after mining. Reports from England (1) where there is a longer history of room-and-pillar mining indicate that mines abandoned two centuries ago may still be causing subsidence, and causing surface destruction to urban areas or farm lands that have been developed in the interim. The devastation wrought by subsidence, both in terms of property loss and societal disruption is enormous. The authors discuss here the methods by which subsidence in abandoned mines may be controlled. Two distinctly different subsidence control technologies have been developed in the U.S. for abandoned coal mines. These are referred to as (1) Point Sup- port methods, and (2) Areal Backfilling. As the names imply, point support methods are used to protect individual structures, or even individual foundation elements of structures, whereas areas backfilling techniques may be applied to protect entire neighborhoods or urban districts hundreds of acres in extent. Both point support methods and areal backfilling have specific sub-categories of techniques that may be applied under different conditions as appropriate. POINT SUPPORT METHODS Point support methods are characteristically employed by civil engineers chartered with the design of a new structure or the protection of an existing structure. The subsidence control measures are only a part of a larger project, the safety of which must be assured to a degree of near certainty. The costs of point support methods involve a large number of bore-holes and the use of expensive materials in relatively small quantities. There exist several dozen point support methods, which operate either to support the underground cavities, controlling subsidence, or to isolate the structure from the effects of subsidence if it should occur. The latter methods usually involve deep foundations through the mine opening supporting the structure on the underlying strata. Our concern will be with the former method to support underground cavities to prevent subsidence. Gravel Columns and Associated Methods Gravel columns may be placed in the mine opening using the methods shown in [Figure 1]. Boreholes are drilled through the mine strata, and gravel poured down the borehole to form a pile on the mine floor. When the tip of the pile contacts the mine roof, it is rodded down to spread the pile, and permit additional gravel to be placed. The objective is to place as much gravel as possible in the mine opening, and to achieve firm contact with the mine roof. The gravel pile acts to reduce subsidence by three mechanisms. The filling of a significant fraction of the open mine volume reduces the amount of potential subsidence simply by killing open volume within the mine. In effect, the extraction ratio has been reduced by introducing the volume of gravel. The toe of the gravel pile abuts against nearby pillars, providing lateral support and protection against pillar deterioration. In effect, the height of the pillars has been slightly reduced by burying their lower portions. Finally, some direct support is provided to the roof strata, reducing the roof span and enhancing stability. The gravel column method may be used in a variety of applications, and with materials other than gravel. For example, gravel columns may be placed in a close line around the perimeter of the building to form a continuous gravel wall. The interior of the site may then be completely filled with sand, slurry or other material. Alternatively, a lean concrete may be used in place of gravel, so that the piles achieve significant structural capacity. The grout column, shown in [Figure 2], begins with the installation of a conventional gravel column which is placed around a grout pipe that extends through the borehole into the mine opening. When the gravel column is in place, portland cement grout is injected in stages. At each stage, sufficient grout is injected to fill the interstices in the gravel to build a column perhaps two meters in diameter and a meter tall. The group pipe is then raised one meter, and after the previously injected grout has set, the next stage of grout is injected. The process builds a column of grouted gravel to the

Jan 1, 1982

By E. M. Hill, D. E. Walsh, J. T. Hollow, H. K. Lin

Fairbanks Gold Mining, Inc. (FGMI) began blending and processing True North ore at their Fort Knox mill on April 12, 2001.Gold extraction subsequently dropped from 88% to 71% during the last week of April 2001. 25% of the gold values remaining in the leach tailings were gravity recoverable free gold. Significant quantities of stibnite and arsenopyrite were also identified in the tailings. In laboratory bottle roll tests, the gold extraction from a composite of leach circuit feed collected during the same period was 72.6%, when leached at an average NaCN concentration of 0.16 g/kg. The extraction increased to 82.4% and 91.7% with 0.5 g/kg NaCN, and 0.5g/kg NaCN plus 0.075 g/kg Pb(NO3)2, respectively. A passivating layer surrounding liberated gold particles and resulting from sulfide mineral dissolution, likely contributes to reduced gold recovery, which can be substantially increased by the addition of lead nitrate. Lead species remain in the solid residues after leaching and were not mobilized using Meteoric Water Mobility Procedure.

Jan 1, 2003

By Michal Bukovansky

The Sahara Desert presents a serious obstacle to transportation route development in northwest Africa. Most highways and railroads are now limited to the coastal regions. A network of pioneer roads is the only connection between Algeria, Morocco, and Tunisia on the north, with Mali and Niger on the south. A feasibility study has recently been made for a paved highway between these countries. Climatic, geologic, physiographic and hydrologic conditions will significantly influence the construction of the road. In order to reduce costs, special construction methods will be required. An outline of these I conditions and methods is presented as an example of an engineering geological investigation in desert conditions.

Jan 1, 1970

By Verne Huser

The intensity of environmental conflict, the delays and legal battles that have marked the 1970's suggest the need for additional processes to resolve environmental disputes. Our present means frequently fail to address the real issues separating individuals and institutions. They are primarily adversary processes that foster polarization and reduce cooperative efforts. At the Office of Environmental Mediation, we have no quarrel with adversary processes nor with polarization, for both serve as important spurs to necessary change. We do seek cooperation among parties at a point where there can be a realistic expectation of success in facilitating a resolution of their mutual differences.

Jan 1, 1979

By J. G. Groppo, B. K. Parekh

Column flotation testing was conducted on the flotation feed slurry obtained from a preparation plant located in the Southern Illinois coal basin. The column flotation tests were conducted using three different bubble generating devices: a static sparger, a gas saver and a foam jet. Each of these devices was tested with three different types of frother and various column operating variables to provide maximum combustible recovery, minimum product ash and maximum pyrite rejection. The results show that column flotation provided improved flotation performance, in terms of combustible recovery as well as ash and pyrite rejection, for each of the bubble generating devices. However, the effectiveness of each bubble generating device was dependent on the type of frother used. Alcohol frothers were most effective for use with the static sparger, somewhat less effective for the foam jet and ineffective for the gas saver. Glycol frothers were effective for all three bubble generating systems, providing high combustible recovery (>90%); low clean-coal ash (4-6% ash) and high pyrite rejection (70-80%).

Jan 1, 1994

By Terence G. McCusker, Bruno Dietl

The only previous attempt to use a tunnel boring machine in the rock formations encountered in New York City was unsuccessful. However, technology has been developed since then which made a new attempt a practical proposition. Nine thousand feet each of 8'6" and 11'0" diameter tunnels were driven in Manhattan schist using Jarva TBM's together with 1100 ft. of the smaller diameter driven conventionally in Inwood marble and earth. (1) The selection of tunneling method was largely based on the need to avoid community reaction and hazardous tunneling conditions where the larger diameter tunnel passed beneath residential structures in poor condition in seamy and blocky rock. Experimentation with cutters and cutter mountings indicate that good cutter life and ease of change are available. It was found practical to use unusually large muck cars for an efficient muck disposal system. Conventional tunneling was successfully executed beneath a subway station whose invert was less than seven feet above the crown of the tunnel. Attempts at chemical consolidation and dewatering were unsuccessful in the earth section which was completed under compressed air.

Jan 1, 1974

By R. Hogg, L. G. Austin, R. C. Klimpel

Slurry densities and holdup were measured for open circuit grinding tests in a laboratory overflow ball mill of 0.3 m diam by 0.6 m long, by emptying and drying after stoppage of the mill. Contrary to some other results in the literature, there was negligible variation of slurry level in the mill as a function of flow rate over a range of increase of flow rate of about 5 to I. However there was a gradual increase of solid holdup at higher flow rates because the slurry density in the mill increased. Equations are given for holdup and slurry density in the mill as a function of over flow diam, ball load, and feed slurry density. The average level of slurry necessary to give over flow was found to be much higher than that necessary to fill the mill to the overflow level at rest. The total level of balls and slurry was only increased slightly by ball loads higher than the overflow level. The overflow diam appeared to be the major controlling factor in determining the mill holdup.

Jan 1, 1990

By K. H. Nimerick

Froth flotation of coal is growing in importance and complexity. Some of the reasons for these changes follow. 1) A need exists for energy resource conservation. 2) Preparation plants are processing widely varying coal -- deep seam, strip and stockpiled either separately or as blends. 3) More fines are being generated because more mines are using automatic mining equipment. 4) It is more practical and economical to remove ash and sulfur at the preparation plant than during utilization.

Jan 1, 1982

By L. Bloom

"Man-Made Parameters" refers to the importance of selecting appropriate analytical procedures to acquire useful chemical data. The correct procedures are particularly critical at the sample preparation stage where decisions concerning pulverizing equipment, sample size, contamination and dissolution will impact on the final results independent of the instrumental method of analysis. Several experiments were designed to quantify the impact of these approaches.

Jan 1, 1993

By T. W. Peterson

There are two approaches to developing a minicomputer based application for an industrial grinding circuit. Usually, the control program is coded and compilation-debugged on a large-scale scientific computing system or the minicomputer itself if the machine is available. Final debugging and testing must wait for installation and checkout of the entire minicomputer system. Two immediate disadvantages of this approach are the need to obtain, install and check out the hardware before the final debugging stages of program development can begin, and interference with normal mill operation during such final testing. This work reports on an alternative to the usual procedure. Here both compilation and execution bugs are eliminated from the application program before hardware installation by testing the control program against a reasonable dynamic simulation of the entire process. Thus, software development can be completed before the target mini is installed. Such off-line development requires a reasonably accurate mathematical model for the entire process system as well as a suitable simulation package for communication between the simulated environment and the minicomputer application program. Specific data describing the design configurations and dimensions of the mills, cyclones, sumps, pump characteristics and analog controller configuration were supplied by ANAMAX for a grinding division consisting of a rod mill followed by two ball mills in parallel. This information was used to set up a plausible model structure. Steady state ANAMAX data on particle size analysis at various points in the circuit and corresponding values of flow rates, pump speeds, sump heights and slurry densities were used for model parameterization. The preferred operating control strategy - "best grind at operator-set rod mill feed rate" - was set by ANAMAX. An inferential particle size analysis technique using the cyclone cluster as an on-line particle size sensor was used in a novel control strategy_ to achieve the stated objective. Two disturbances common in the ANAMAX circuits - rod mill scoop pluggage and shut down/start up of one of the ball mills - were studied in detail. This report out- lines the steps in system development and testing and the results obtained.

Jan 1, 1974

By Yoshinori Shimada, Oleg Kotiaev, Hiroaki Sakamoto, Toshihiro Asakura, Naotoshi Yasuda, Norikazu Misaki, Masahiro Shinoda

"To ensure that trains run safely, the performance of railway civil engineering structures is checked by periodic inspections. General inspection method has merits and demerits, but none of them offers the combination of high accuracy and quick inspection. In an effort to resolve this problem, West Japan Railway Company, the Institute for Laser Technology and the Railway Technical Research Institute jointly developed a remote laser sensing system as an alternative to the impact acoustics method for detecting defective concrete elements in tunnel linings. The proposed remote laser sensing system has two lasers, one to apply an impact to the concrete surface and the other to measure the vibration of the concrete generated by the impact laser. The impact laser is a high-energy pulse laser that induces vibration in the concrete. The detection laser has a signal beam and a reference beam. The signal beam reflects on the concrete surface and goes into the dynamic hologram crystal. The reference beam diffracts in the dynamic hologram and enters the detection sensor with the signal beam. The vibration of the concrete surface can be measured to detect the movement of an interference pattern. A prototype of the remote laser sensing system was developed as shown in Figure1. A vibration and acoustic insulators are equipped to remove a noise generated from a maintenance car or electric generator in this system. The proposed laser remote sensing system and the detection algorithm were verified with the help of field test conducted in a tunnel on the Shinkansen. An impact test using hammering was applied to obtain the accurate response acceleration on the surface of the concrete before application of the proposed method. In this test, the result obtained from the proposed method has good agreement with that obtained from the impact test by hammering. Consequently, it is verified that the proposed method can be used as an alternative to the standard impact acoustics method."

Jan 1, 2016

By T. P. Weldum, W. Conger

"These studies address the relationship between mill media sizing and its grinding efficiency. Starting with the results from a review of the literature, the issues of initial media sizing for a new ball milling circuit, and then optimal media sizing for an existing milling operation, were studied. The Functional Performance parameters “Mill Grinding Efficiency” and cumulative “Mill Grinding Rates” from both plant and test-scale equipment were used, and provide valuable new insight into this topic. A plant media sizing diagnostic tool is presented, as are newly developed testing equipment and evaluation methods, and recent case studies. REVIEW OF MEDIA SIZING LITERATURE For a plant metallurgist to answer the question “How can I maximize plant profit by manipulating this grinding circuit variable?” she must know what effect the variable has on grinding circuit efficiency. Despite the significant cost of grinding media and its potential effect on production capacity, the ‘best’ media sizing remains ill-defined for any given ball mill circuit in the industry today. The underlying reasons for this will be discussed. But the importance of this issue drove Metcom and its industrial partners to take on the challenge of how to engineer the ball charge for an existing grinding circuit. In the absence of any proven method, the first step was a review of the literature. Sponsored by Cleveland-Cliffs, Inc., a broad review of the literature was undertaken, producing “The Effect of Media Sizing on Ball Milling Efficiency” (McIvor, 1997). Among hundreds of publications that were reviewed that discuss the topics of media sizing or wear, forty-five were studied in detail. These were grouped into: plant experiences; laboratory and pilot plant investigations; media wear studies; population balance modeling studies; and general papers on ball milling which included the topic of media sizing. The reader is encouraged to refer to that review. The findings remain unchanged, although some relevant papers have been written since (e.g. Staples et al, 1997; Banasi et al, 1999; Orford et al, 2006; LaMarsh, 2015). The main findings of the review were as follows."

Jan 1, 2018

By III Kimball

For many years, Arizona merely shadowed EPA's environ-mental regulation of mining operations and waste. During this period, Arizona generally assisted EPA in the implementation of federal programs and enacted environmental laws patterned closely after their federal counterparts. A growing public concern about protecting water quality, particularly groundwater quality, eventually caused the State to depart from this pattern.

Jan 1, 1989

By T. Reed Scollon

Major interrelated factors to be considered in assessing the impact of air pollution control regulations on coal are: (I) the fuel and fuel-related limitations of such regulations; (2) the rate of adoption and areal scope of the regulations; and (3) the availability of fuels and fuel-burning equipment to meet the requirements. A growing number of regulations contain provisions limiting the emissions of sulfur oxides or the sulfur content of fuels or both. With few exceptions, these limitations have not yet become fully effective in those areas which have already adopted regulations, and pertinent details of future regulations or legislation for most other areas are unknown at this time. Sufficient information is not avail- able to determine the availability of low-sulfur fuels at various demand and price levels, and large-scale commercial feasibility of sulfur-oxides removal processes and equipment is believed to be some years away. Accordingly, with the many uncertainties and unknowns, it is possible at best to make only a rough assessment of the impact of such regulations or legislation on coal.

Jan 1, 1969

By B. Ollila, L. Brown

As mining fronts converge in sill pillar extraction, the mine seismic hazard can be significantly altered and large seismic events have been known to occur. This study used common seismological tools to analyze the extraction of highly stressed sills from two deep Canadian mines with the objective of characterizing the rock mass failure process and relation to large seismic events. The approach treated a sill pillar as a mine-scale failure process, meaning the temporal and spatial analysis scales needed to exist on a similar scale to a significant part of the mine. The temporal analysis scale overlapped with the entire mining sequence, included several years of data to establish long term change in the characteristics of rock mass failure. The spatial analysis scale included the rock mass surrounding a large part of the convergent mining sequence. To accommodate the large spatial and temporal scales, the highest magnitude 2% of events in the dataset were analyzed. Similar results were shown for sill pillars in both mines. Changes in event location, time, magnitude, energy index and apparent volume were similar to expected behavior of rock failure. Indications of strain hardening and strain softening were observed in the sills. The hardening period was characterized by a high rate of small events, high energy index and low apparent volume, giving an indication of high stress and low rock yield. The softening phase was characterized by a decrease in the rate of small events concurrent with an increase in the rate of large events, low energy index and high apparent volume, indicative of release of stress and increase in deformation. Large magnitude seismicity was strongly related to the softening phase, with several Nuttli magnitude 3.0+ events occurring shortly after the transition from hardening to softening failure regimes. Sill failure was indicated by consistently low EI and low levels of seismicity and seismic hazard in the sill pillar.

Apr 26, 2022

By Earl M. Frizzell

Investigation of mined land characteristics, evaluation of irrigation systems and evaluations by the mining industry determined that irrigation is a feasible method for aiding the revegetation of coal mined lands in the western arid and semi-arid regions (Sherman, et al. 1980). The various regions studied displayed a commonality of characteristics which enables, independent of the site or region, the recommendation of solid-set irrigation. Irrigation should be supplemental by complimenting natural precipitation and should be implemented on a temporary basis. For germination, the vegetation requires application of small amounts of water in a gentle, frequent, and timely manner. For the establishment phase of growth, moisture should be applied and stored in the soil either through pre-irrigation or deep irrigation.

Jan 1, 1985

By J. H. Tu

The technical paper correctly points out that the kriging variance is not a good measure of the uncertainty of the estimated (i.e., kriged) value of individual blocks. The au thors claim that their proposed jackknife method, which is a rekriging of each block by eliminating, in turn, one sample from the original sample set and then taking the average of the rekriged estimates, not only gives good block estimates, but the resulting jackknife kriging standard deviation is a useful indicator of the "true uncertainty associated with block estimates." However, they immediately abandon the idea of using the block-by-block standard deviations, reasoning that these standard deviations are not independent and that there is no easy way to utilize them. There may be another reason for not using them. The jackknife standard deviations for individual blocks given in their example are mostly in the range of 0.004 to 0.005 oz/st (0.14 to 0.17 g/t) with only one block having a high value of 0.012 oz/st (0.41 g/ t). These individual block standard deviations are as low as the jackknife standard deviation for the mean grade of the entire shape, i.e., 0.0041 oz/st (0.14 g/t). Do they represent the "true uncertainty" of the individual block estimates? Could the authors explain this? In a global shape consisting of a large number of blocks, any given sample will affect the kriged estimate of only those few blocks within its vicinity. This is the rationale for the authors' selective rekriging, making the jackknife algorithm more efficient. On second thought, why not do away with jackknifing altogether? Just cumulate and normalize, if necessary, the kriging weights of each sample used during the ordinary block kriging process, and then compute the global variance from these kriging weights and their respective sample grades? After all, isn't the global mean grade nothing but the weighted average of the samples used in the estimation? Reply by G.S. Adisoma and M.G. Hester The jackknife is one of the many tools in a practitioner's toolbox to solve estimation problems. The strengths of the technique lies in its simplicity, i.e., it uses the concept of mean and standard deviation and the fact that it can be easily combined with other tools, in this case kriging. Because the jackknife kriging (JK) estimate is also the mean of the pseudovalues, the JK standard deviation is attractive just as the standard deviation of the mean explains the variability of the data. The difference is that the pseudovalue calculation in jackknife kriging uses the ordinary kriging (OK) weighting scheme instead of simple arithmetic averaging. The data used to illustrate the jackknife technique in the paper consist of high values that are roughly three times the low values. The resulting JK estimate of the block grades show that the highest estimate is roughly twice the grade of the lowest estimate. The contrast between the low and the high estimate is more evident in the JK estimate than in the OK estimate, even though the mean grades of the blocks for the two estimates are very similar. Nonetheless, in this paper, we are concentrating more on the need for a more realistic measure of uncertainty, or precision, for the estimate. Unlike its OK counterpart, the JK standard deviation of the blocks clearly reflects the original data variation. The highest JK standard deviation of the blocks is three times its lowest value. This follows our intuition that, when the samples used to estimate a block is more variable, the resulting estimation variance (or standard deviation) should be higher than the case where the samples are more uniformly valued. However, block-by-block standard deviation or variance is of little practical value in reserve estimation and classification, as well as in mine planning. One is usually more interested in quantifying not the variance of the individual block estimate, but the uncertainties associated with a much larger dimension, such as the minable reserve. Thus, the thrust of the paper is to find a simple way to obtain a single estimation variance or standard deviation associated with the reserve grade estimate. The discussion by J.H. Tu did not mention how one would obtain the global variance from the OK weights and the sample grades. As a technique that offers a data valuebased measure of uncertainty for its estimate, the "leave-one-out" jackknife fills this need nicely through the block kriging shortcut approach described in the paper. Note: The first column and the last two columns of Table 3 in the paper should have contained a single number each, namely, an OK estimate of 0.0317, a JK estimate of 0.0333 and a JK standard deviation of 0.0041 oz/st, respectively, for the shape, as are obvious from the text. ?

Jan 1, 1998

By J. H. Tu

The technical paper correctly points out that the kriging variance is not a good measure of the uncertainty of the estimated (i.e., kriged) value of individual blocks. The authors claim that their proposed jack-knife method, which is a rekriging of each block by eliminating, in turn, one sample from m the original sample set and then taking the average of the rekriged estimates, not only gives good block estimates, but the resulting jackknife kriging standard deviation is a useful indicator of the "true uncertainty associated with block estimates." However, they immediately abandon the idea of using the block-by-block standard deviations, reasoning that these standard deviations are not independent and that there is no easy way to utilize them. There may be another reason for not using them. The jackknife standard deviations for individual blocks given in their example are mostly in the range of 0.004 to 0.005 oz/st (0.14 to 0.17 g/t) with only one block having a high value of 0.012 oz/st (0.41 g/ t). These individual block standard deviations are as low as the jackknife standard deviation for the mean grade of the entire shape, i.e., 0.0041 oz/st (0.14 g/t). Do they represent the "true uncertainty" .of the individual block estimates? Could the authors explain this? In a global shape consisting of a large number of blocks, any given sample will affect the kriged estimate of only those few blocks within its vicinity. This is the rationale for the authors' selective rekriging, making the jackknife algorithm more efficient. On second thought, why not do away with jackknifing altogether? Just cumulate and normalize, if necessary, the kriging weights of each sample used during the ordinary block kriging process, and then compute the global variance from these kriging weights and their respective sample grades? After all, isn't the global mean grade nothing but the weighted average of the samples used in the estimation? Reply by G.S. Adisoma and M.G. Hester The jackknife is one of the many tools in a practitioner's toolbox to solve estimation problems. The strengths of the technique lies in its simplicity, i.e., it uses the concept of mean and standard deviation and the fact that it can be easily combined with other tools, in this case kriging. Because the jackknife kriging (JK) estimate is also the mean of the pseudovalues, the JK standard deviation is attractive just as the standard deviation of the mean explains the variability of the data. The difference is that the pseudovalue calculation in jackknife kriging uses the ordinary kriging (OK) weighting scheme instead of simple arithmetic averaging. The data used to illustrate the jackknife technique in the paper con¬sist of high values that are roughly three times the low values. The resulting JK estimate of the block grades show that the highest estimate is roughly twice the grade of the lowest estimate. The contrast between the low and the high estimate is more evident in the JK estimate than in the OK estimate, even though the mean grades of the blocks for the two estimates are very similar. Nonetheless, in this paper, we are concentrating more on the need for a more realistic measure of uncertainty, or precision, for the estimate. Unlike its OK counterpart, the JK standard deviation of the blocks clearly reflects the original data variation. The highest JK standard deviation of the blocks is three times its lowest value. This follows our intuition that, when the samples used to estimate a block is more variable, the resulting estimation variance (or standard deviation) should be higher than the case where the samples are more uniformly valued. However, block-by-block standard deviation or variance is of little practical value in reserve estimation and classification, as well as in mine planning. One is usually more interested in quantifying not the variance of the individual block estimate, but the uncertainties associated with a much larger dimension, such as the minable reserve. Thus, the thrust of the paper is to find a simple way to obtain a single estimation variance or standard deviation associated with the reserve grade estimate. The discussion by J.H. Tu did not mention how one would obtain the global variance from the OK weights and the sample grades. As a technique that offers a data value-based measure of uncertainty for its estimate, the "leave-one-out" jackknife fills this need nicely through the block kriging shortcut approach described in the paper. Note: The first column and the last two columns of Table 3 in the paper should have contained a single number each, namely, an OK estimate of 0.0317, a JK estimate of 0.0333 and a JK standard deviation of 0.0041 oz/st, respectively, for the shape, as are obvious from the text.

Jan 1, 1997