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By J. Fu

"Since it was first identified in 1817, selenium has received considerable interest. Native selenium and a few selenium minerals were discovered several decades later. With the increasing number of selenium minerals, the occurrence of selenium minerals became the focus of much research. A great number of selenium deposits were reported all over the world, although few independent selenium deposits were discovered. Selenium is obtained mainly as a byproduct of other metals, and is produced primarily from the anode mud of copper refineries. This paper presents a comprehensive review of selenium minerals, as well as the treatment of copper refinery anode slimes for the recovery of selenium. Our focus is on the selenium minerals, including their discovery and occurrence, and the distribution of selenium resources. In addition, the main methods of recovering selenium from copper anode slimes are summarized. IntroductionSelenium (Se) was first observed in 1817 in a laboratory (Greenwood et al., 1984). The discovery of selenium was made by the Swedish chemist J.J. Berzelius and J.G. Gahn, who isolated selenium from a red residue in sulphuric acid from pyrite mined at Fahlun, Sweden. Selenium was named from the Greek word selene (moon), since it resembled tellurium, which had been discovered a few years earlier and named from the Latin word tellus (Earth).After the first observation of selenium in the laboratory, selenium received considerable interest. In 1954, E.P. Kaiser pointed out that Se is enriched in sulphide ores and often associated with Bi, Co, Sn etc. (Kaiser 1954). In 1959, Hawley and Nichol investigated selenium in Canadian sulphide minerals, and presented the content of selenium in sulphide from several deposits of different types. They also proposed that Se is enriched in lowtemperature hydrothermal pyrite (Hawley and Nichol, 1959). The thermodynamic conditions for forming native selenium and selenium minerals in sedimentary rocks were discussed, as well as geochemical behaviour of selenium near the oxidation zones of sulphides in the 1970s (Howard III, 1977; Zhu et al., 2003). Zhu et al. examined the morphology, features, and genesis of native selenium from Yutangba, Enshi City, Hubei Province, China in 2004, and pointed out, from the different forms of native Se, that selenium can be activated,transformed, remobilized, and enriched at sites such as in the unsaturated subsurface zone or in the saturated zone (Zhu et al., 2005). The transport and deposition of selenium in felsic volcanic-hosted massive sulphide deposits of the Yukon Territory, Canada was studied and reported by Layton- Matthews et al. (2005)."

Jan 1, 2016

By Ernst-Ulrich Reuther, Alexander Donmen

Mine ventilation in the German coal mining industry is concerned mainly with problems of thermal environment arising from greater depths and with increasing emission of methane gas. The development of computer techniques over the past ten years for solving these and ancillary problems is reviewed. The emphasis from a planning and control point of view falls mainly on ventilation network calculations, temperature predictions and advance estimates of methane emission.

Jan 1, 2014

By M. A. Mahboob, T. Celik, B. Genc, I. Atif, S. Ali

"Mapping of hydrothermally altered areas, which are usually associated with mineralization, is essential in mineral exploration. In this research, open source reflectance spectroscopy data from the multispectral moderate-resolution Landsat 8 satellite was used to map altered rocks in the Gauteng and Mpumalanga provinces of South Africa. The unique spectral reflectance and absorption characteristics of remotely sensed Landsat data in the visible, near-infrared (NIR), shortwave-infrared (SWIR) and thermal infrared (TIR) regions of the electromagnetic spectrum were used in different digital image processing techniques. The band ratios (red/blue, SWIR 2/NIR, SWIR 1/NIR), spectral band combinations (Kaufmann ratio, Sabins ratio) and principal component analysis (Crosta technique) were applied to efficiently and successfully map hydrothermal alteration minerals. The results showed that the combination of spectral bands and the principal component analysis method is effective in delineating mineral alteration through remotely sensed satellite data. The validation of results by using the published mineral maps of the Council for Geoscience South Africa showed a good relationship with the identified zones of mineralization. The methodology developed in this study is cost-effective and time-saving, and can be applied to inaccessible and/or new areas with limited ground-based knowledge to obtain reliable and up-to-date mineral information.IntroductionMany developing nations depend on exploration and exploitation of mineral resources to sustain their economic growth. Usually, the traditional mineral exploration techniques require enormous finances, prolonged time, and tremendous manpower, particularly in areas that are not easily reachable (Maduaka, 2014). Furthermore, mineral exploration required state-of-the-art techniques and expertise along with geological, geochemical, and geophysical datasets, which may not be easily available or may be lacking where access is problematic (Kaiser et al., 2002; Bemis et al., 2014). Modern remote sensing technology has proved to be one of the highly efficient and robust techniques used for mineral exploration. The use of remote sensing satellite images for geological mapping and mineral exploration usually involves studying the physicochemical properties of rocks and weathering soils, such as mineralogy, landforms, geochemical signatures, and the spatiall distribution of lineaments (Bhattacharya et al., 2012)."

Mar 1, 2019

By K. Hodgson, Cook. N. G. W.

Most structures are designed so that the possibility of failure is eliminated. However, some degree of failure in the rock around deep mine excavations is inevitable if mining operations are continued. The presence of failed rock constitutes a hazard the magnitude of which can be predicted by computer models from calculations of the energy change per unit area mined in stopes, or the field stress around service excavations. Empirical relationships between these calculable quantities and the incidence of rock failures and delays associated with them have been established. Experiments on the computer using different layouts enable the mining engineer to select the least hazardous of otherwise acceptable alternatives, and to predict the incidence of damage ahead of actual mining, so that appropriate measures to maintain an adequate degree of safety and productivity can be planned in advance.

Jan 1, 2014

By S. A. Allison

The Conference began with registration, followed by a well-attended cocktail party on the evening of Sunday 25th, where, in a convivial atmosphere, Dr Louw Alberts, President of Mintek, welcomed the delegates and wished them an enjoyable and informative week. The Conference was formally opened by the Minister Mineral and Energy Affairs, the Honourable Mr D. W. Steyn, at 9hOO on Monday. Sketching the history of Mintek and its predecessors, Minister Steyn described the objective and achievements of Mintek, as well as the background to mineral-processing research in South Africa and the policy of the South African government towards the development of the mineral industry.

Jan 1, 1984

By D. Sethuram, P. G. Koppad, S. Iyengar, R. Shobha

TiB2 and CeO2 particle-reinforced Al6061 hybrid composites were manufactured using stir casting and hot rolling techniques. The base alloy and composites were hot-rolled at 500ºC and a 50% reduction was achieved through 12 passes. The effect of varying TiB2 and CeO2 particle additions on the microstructure and mechanical properties of the Al6061 matrix was studied. Scanning electron microscopy showed uniform dispersion of both the reinforcements, with good interfacial bonding. Microhardness and tensile properties like yield and tensile strength were found to be higher for hybrid composite with 2.5% TiB2 and 2.5% CeO2 compared to Al6061 alloy and other hybrid composites. The increased tensile strength is attributed to good dispersion and interfacial bonding between the particles and Al6061 matrix. Fracture analysis using a scanning electron microscope revealed ductile fracture for the Al6061 alloy and mixed characteristics of ductile-brittle fracture for hybrid composites

Oct 1, 2021

By C. Hartford, T. Holmes

Bulk-solids handling systems are often the most over-looked component and thereby weakest links in a processing plant’s value chain. Since their performance can dictate that of the entire operation, they actually deserve special attention. When designing a liquid handling plant, density and viscosity are well known and commonly used as design parameters. Bulk solids however, differ. While the design process is similar, the relevant parameters in handling bulk solids are instead friction, cohesive strength, compressibility, and permeability. These then vary depending on the mineralogy, particle size distribution and shape, moisture content, storage time-at-rest, temperature, and consolidation pressure. With so many variables, it becomes important to characterize each individual bulk solid across the full range of representative process conditions within the handling system, plant wide – or if you are not very lucky, suffer the consequences of poor material flow. Measuring flow properties and applying them correctly in bulk solid handling system design reduces project risk, saves significant capital, and drastically increases throughput, especially when done in the early stages of a project. Keywords: Flow Properties, Bulk Solids, Process Conditions, System Design

Jan 1, 2020

By J. P. Gouvea, W. Geel

Resin bolting in South Africa has been developed and refined in underground coal mines (i.e., soft rock) since the late 1940s. The extension of resin bolting to hard rock mines started in 2003 and has required significant adaptations, challenging the status quo from both a supplier and applicator perspective. As far as resin bolting is concerned, the most affected aspect in coal mining and hard rock mining environments, is the rock drills or machinery used for installation. Hard rock mines mostly use hand-held airlegs with limited thrust, low torque, and rotation speed, relative to coal mine mechanised bolters. Resin bolt development for hard rock mines was, and still is today, predominantly focussed on compensating for the ‘shortfalls’ of using hand-held airlegs. At face value, hydro-powered rock drills, which are more powerful than traditional handheld equipment, provided hard rock mines with a means to attain more consistent and reliable resin bolt installations. This paper assesses the quality and performance of hydro-powered resin bolting at an intermediate to deep level platinum mine in South Africa and its potential contribution to rock-related instabilities when applied erroneously. The findings of this paper necessitate a revision of current quality control and quality assurance measures related to resin bolting for underground support.

Nov 24, 2025

By B. Larsen

The Søderberg electrode was invented about 95 years ago by the company Elektrokjemisk, later known as ELKEM. It is still the most commonly used electrode system in submerged-arc furnaces for ferroalloys, platinum smelting, and slag cleaning operations. The size of the furnaces and electrodes has increased over the years and electrode diameters up to 2000 mm are today in use. Such large electrodes can be challenging to manage, and large electrodes are also more demanding when it comes to the electrode paste used in the electrodes. Although electrode sizes and equipment around the electrodes have changed, the main principles of the Søderberg electrode processes are the same. To assists in proper understanding of the electrode processes and to optimize electrode management, Elkem has developed several mathematical tools covering various aspect of the process. Both temperatures and thermal stresses can be calculated during dynamic conditions. The paper demonstrates, with examples, how the tools are used in both education and as practical input to improved electrode performance.

Jan 1, 2012

By B. McFadzean, S. Pikinini, C. T. O’ Connor

Sperrylite (PtAs₂) comprises about 21% of the platinum group minerals (PGMs) in the Platreef ore and regularly reports to the tailings due to its poor floatability. Hence, improving its recovery will be of great economic value to the South African PGM industry. The reasons for its poor floatability are not yet clear. This paper seeks to understand the interactions occurring between PtAs₂ and common thiol collectors, viz. potassium normal butyl xanthate (PNBX), sodium normal dibutyl dithiophosphate (SNBDTP) and sodium normal mono butyl dithiocarbamate (SNBDTC). By understanding its interactions with these collectors, it is hypothesised that it will be possible to suggest ligands that may help improve the floatability of sperrylite. Mineral-collector interactions were studied by determining the molar energy of interaction using isothermal titration calorimetry and electrochemical techniques. The hydrophobicity of the mineral before and after adsorption of the collectors was determined by heat of immersion and its flotation response determined by microflotation tests. Microflotation tests using synthetic sperrylite at pH 9 showed low collectorless recovery of 34.8% and after adding the equivalent of one pseudo-monolayer of the PNBX collector, the recovery of 32.5% was obtained. Moreover, the addition of up to three pseudo-monolayers coverage of PNBX did not result in any increase in flotation recovery. A small recovery improvement was noted when synthetic plant water with the ionic strength of 0.0484 mol/L was used, but this did not hold for all collectors, with SNBDTP exhibiting higher recoveries in distilled water. Keywords: Sperrylite; flotation; recovery; adsorption energy; collectors; 2SPW (synthetic plant water)

Jan 1, 2020

By T. Fraszczak, U. A. Peuker, T. Mütze, O. Ortlepp

Dolomite is a calcium carbonate sedimentary rock that can be found all over the world. In its calcined form it is employed for water treatment or as an additive in iron production. Calcined dolomite is produced at the Wünschendorfer Dolomitwerk GmbH in shaft furnaces (kilns). Because of an expansion of the mined deposit, significantly higher extraction costs were expected. Therefore, the existing upgrading processes for the kiln stone fraction had to be adapted and improved. This paper presents a process optimisation which allows for an increase of the yield of calcined dolomite by 10 % due to a redesign of the crusher circuit and by an additional 5 % due to a comprehensive characterisation of the kiln stone fraction itself. Here the interdependency between the pressure drop in the furnace during calcination and the size distribution of furnace stones was used to increase the amount of fine size fractions in the furnace feed without deterioration of the calcination process. Keywords: Dolomite, crushing circuits, kiln stone production, flowability, calcination

Jan 1, 2020

By E Matinde, M. Mnisi, I. C. Thobadi, W. Clark, J. D. Steenkamp

Pyrometallurgical smelters utilise tap-holes, through which liquid metal, matte and/or slag are tapped at regular intervals. However, tap-hole failures can have a devastating impact on smelters, which includes loss of equipment, human life and business interruptions. Contributing factors to tap-hole failures include poor and/or incorrect refractory material selection, including tap-hole clays. The functions of tap-hole clays in smelters include their ability to be extruded and drilled with ease at the end and beginning of a tap, and their ability to resist chemical wear due to molten metal and slag during tapping. Mintek is currently developing methods of evaluating properties of tap-hole clays with a specific focus on workability, and wear mechanisms of clays due to ferrochrome alloy and slag. Of particular interest to this study was the characterisation of various tap-hole clays. This paper evaluates the chemical and phase chemical properties of three different tap-hole clays. The bulk chemical composition of the tap-hole clays was determined by inductively coupled plasma optical emission spectroscopy, proximate analyses and combustion methods. The bulk phase compositions and specific phase chemical compositions were studied using quantitative X-ray diffraction, scanning electron microscope and electron probe microanalyses techniques. Keywords: Tap-hole clay, chemical analyses, phase chemical analyses, ferrochrome

Jan 1, 2020

By H. C. Van Der Merwe

In the 21st century, dynamic, accurate digital 3-D geological models are essential to the pursuit of safe, efficient and profitable mining. This is particularly true for the deep-level underground mines in South Africa. The Sirovision® solution is a collaboration project between the Australian CSIRO (Commonwealth Scientific and Industrial Research Organisation), Datamine Software Ltd. and AngloGold Ashanti Ltd (AGA). The purpose of the project is to provide a fully integrated digital rock face imaging, geological mapping and modelling system for the AGA gold mining operations. The CSIRO-developed Sirovision® Stereo Camera Rig (SCR) consists of two digital cameras, alighting system, a laser guidance system and image processing software. The imaging system works on the principles of photogrammetry, i.e. overlaying of two 2-D images with a central focus point, with mathematical algorithms extracting 3-D information from the 2-D image pair. The output from matching several image pairs is a computer-generated, full 3-D, virtual copy of the mining excavation. The image resolution and relief ares of sufficient quality to distinguish different rock types and structural contacts. Functionality within Datamine Studio3 is used to add geological intelligence to the 3-D images provided by Sirovision®. The geologist identifies and ?draws? lines representing geological features directly onto the image. By utilizing the inherent ?topography? of the 3-D image, the software is able to convert the lines into 3-D surfaces, ready for use in the 3-D geological model. Subsequent to promising underground test results from AGA?s Sunrise Dam Gold Mine (SDGM) in Australia and other mining operations worldwide, it was decided to test the Sirovision® system in the South African deep-level gold mines. The first underground tests at Moab Khotsong Mine began in January 2009. The objectives of these tests entailed the capturing of 3-D images of selected development ends, mapping of geological features onto the 3-D images and integration of the mapping data with the 3-D geological model. Some downsides have cropped up during the feasibility testing, related to practicality of the SCR for acquisition of 3-Dimagery in the deep-level underground operating environment. These constraints will have to be addressed prior to operational implementation. Facing such difficulties is not unusual when attempting to implement new technology in such a challenging working environment and testwork is still in progress at the mine in order to prove the concept of using this technology in a Witwatersrand underground gold mine. The great advantage of the Sirovision® solution is that it offers the geologist the opportunity to work remotely on a 3-D virtual copy of a mining excavation, without the heat, humidity, hazards and time constraints associated with physical mapping in an underground workplace.

Jan 1, 2009

By S. Mohanty, K. Sarangi, S. Dash, P. P. Patra

Industrial effluent from various industries contains heavy metals that are a serious threat to humans, flora and fauna in water bodies, and the environment. The heavy metals are dumped after precipitation, which has serious environmental consequences. In this paper, a 2D axi-symmetry CFD model has been developed to study the extraction of chromium ion from industrial effluent, in a hollow fibre membrane, using Alamine 336 as the carrier and kerosene as the diluent. The Navier Stokes equation was used to predict the velocity profile of the aqueous and organic phases, and species transport equation, which considers both convective and diffusive mass transfer, was used to predict the concentration profile of the chromium ion in the computational domain. The distribution coefficient was experimentally determined at a pH 4, which was found to be the optimum pH. Numerical simulations were performed considering 11.11 mol/m3 of initial feed concentration for chromium ions and extractant concentration of 0.2 M. Simulations were carried out with various aqueous and organic flow rates, and validated with experimental data. Keywords: CFD, metal extraction, hollow fibre membrane, heavy metals

Jan 1, 2020

By G. Akdogan, C. Dorfling, L. Bumhira

Hydrometallurgical recovery of rare earth elements from phosphors obtained from end-of-life fluorescent lamps involve leaching followed by extraction of dissolved metals from solution. The similar properties of rare earth elements make selective recovery of individual elements challenging. The aim of the paper was to investigate the extraction of primarily Ce and Tb from a hydrochloric acid leach solution also containing other REEs (Y and Eu) as well as impurity metals (Ca and Al). Batch solvent extraction tests were performed with di-(2-ethylhexyl) phosphoric acid (DEHPA) at various extractant concentrations, pH conditions and organic-to-aqueous ratios. Extraction isotherms and separation factors for the range of conditions tested in the project are presented in the paper. Separation of individual REEs was not possible at the conditions investigated, but a mixed REE product can be obtained in a single extraction stage operated at a pH of 0.5 using 1 M extractant at an O/A ratio of 1; these conditions resulted in complete Y and Eu, 95 % Ce and 99 % Tb extraction with Ca and Al coextraction below 7 %. A better quality mixed REE product can be produced by operating at lower pH and extractant concentration conditions, but this would require a larger number of extraction stages. Keywords: Cerium, fluorescent lamps, phosphors, rare earth elements, solvent extraction, terbium

Jan 1, 2020

By Q. Zhang, X. C. Wang, X. Q. Ao

The flotation separation of apatite and calcium-bearing gangue minerals (dolomite and calcite) has always been a problem in phosphate ore mineral processing research. The crystal structure and surface properties of minerals have an important influence on their floatability. In this paper, the theoretical and comparative analysis of the crystal structure and surface electronic properties of apatite, dolomite and calcite were carried out using the first principle calculation based on density functional theory. As a supplement and validation, the surface wettability of three minerals under different flotation conditions were compared and analysed by contact angle test. The results theoretically revealed that the three calcium-bearing mineral surfaces have similar surface electronic properties and thus exhibit similar floatability. In the flotation process, the anion difference between apatite and carbonate gangue should be fully utilised, and the minerals can be separated only after surface modification by flotation reagent. The contact angle test shows that phosphate and carbonate can be separated by using anion flotation collector after surface modification with acid. It is expected that this research is of interest for understanding the surface structure and electronic properties of apatite and carbonate gangue minerals and providing the theoretical basis for surface interaction. Keywords: Apatite, dolomite, calcite, surface structure, electronic property, density functional theory

Jan 1, 2020

By F. Nakhaei, M. Le Roux, Q. P. Campbell, S. Botlhoko

The results of coal sink and float tests are plotted as washability curves. Analysis of these curves indicates the most effective method by which the coal can be cleaned. Sink and float experiments are samplingdependent, destructive, and use toxic chemicals. The present research introduces an alternative method based on a 3D imaging system called RhoVol, in which the density of individual particles is determined from mass and volume measurements. A quantitative error analysis was conducted on coal sample density measurements obtained by RhoVol, and the main factors influencing the errors identified and investigated. The results show that the drawback of this technique is related to its not being able to detect hidden concavities in the particle, resulting in an overestimation of particle volume. Furthermore, it is difficult to capture the impact of porosity and cracks on the volume of coal particles obtained from 3D silhouette images. This mismatch between the RhoVol data and sink and float test results has led to attempts to apply neural network (NN) and linear regression techniques to produce a fully reliable model for correction and estimation of coal density. The NN approach offers superior predictive capability over linear regression, and the estimated density distribution is in line with the sink and float analysis. The root mean square error in estimation of density using the NN model was less than 0.05 g/cm³.

Aug 2, 2022

By I. B. Fernandes, M. A. Reuter, A. Abadias Llamas

Metallurgical simulation and evaluation of the resource efficiency of whole production processes are of key importance for impact assessment, in terms of environment and resources. Exergy is a measure of resource consumption, taking into account energy, raw materials, water, and chemicals; which allows for the evaluation of different technologies to find the most resource efficient and environmentally friendly process. This paper compares the sustainability for production of rare earth magnets from primary and secondary resources through an exergetic evaluation of the production process, in addition to traditional life cycle assessment (LCA). The methodology makes use of simulation tools for tracking material flow and resources used, based on thermodynamic laws, from ore exploitation to magnet production and recycling. It highlights areas with the greatest potential for improvements in terms of resource consumption and environmental impact generation, having a thermodynamic-validated flowsheet for primary and secondary production of NdFeB magnets, present in several low-carbon technologies, such as wind turbines, electric vehicles, and cooling systems. It demonstrates the minimum exergy destruction for magnet production, through an irreversibility breakdown chart, showing where irreversible material and energy losses occur. Results show that CO2-equivalent emissions for producing NdFeB permanent magnets from primary resources could be twice as high when compared to magnets produced from recycling technologies. The theoretical maximum exergetic efficiency for primary production is 57.61%, whereas for permanent magnets produced from secondary resources, the exergetic efficiency reaches up to 82.89%. Two magnet recycling technologies were evaluated, i.e. in acidic medium and via hydrogen decrepitation, and it was observed that their exergetic efficiency and environmental impact performed better than production from primary resources. Keywords: Resource efficiency, exergy analysis, permanent magnet recycling, process simulation, system design

Jan 1, 2020

1. New books 1979 Louisville Coal Conference proceedings. Epping (England), Bowker Publishing Co., 1980. 4 vols. $43.00. Proceedings of a joint meeting of the Institution of Mining and Metallurgy, the Society of Mining Engineers of AIME, and the Metallurgical Society of AIME, held in London, 27 to 30 May, 1980, by M. J. Jones (ed.). London, Institution of Mining and Metallurgy, 1981. 350 pp. £46. Economic mineral deposits, by M. L. Jensen and A. M. Bateman. 3rd ed. New York, John Wiley, 1981. 752 pp. $22.95. E & MJ intErnational directory of mining and mineral processing operations. Epping (England), Bowker Publishing Co., 1980. 1314 pp. $67.00. Physical methods in modern chemical analysis, by T. Kuwana (ed.). New York, Academic Press, 1980. Vol. 2. 432 pp. $38.25. English translations of DIN standards. Availablefrom the SABS, Private Bag 191, Pretoria 0001. Mining international year book. London, Financial Times, 1981. 730 pp. $90.00 airmail, £37.50 surface. Analytical atomic absorption spectroscopy. Selected methods, by J. V. van Loon. New York, Academic Press, 1980. 360 pp. $35.00. 2. NIM reports Report no. 1848 An electrochemical and kinetic investigation of the behaviour of gold in chloride solutions. I. The cathodic deposition of gold. (First issued 7th Jul., 1976.) Report no. 1844 An electrochemical and kinetic investigation of the behaviour of gold in chloride solutions. 11. The anodic dissolution of gold. (First issued 7th Jul., 1976.) Report no. 1846 An electrochemical and kinetic investigation of the behaviour of gold in chloride solutions. 111. The gold(II1)- gold(I) eaction on platinum and the disproportionation of gold(I). (First issued 7th Jul., 1976.) Report no. 1979 An electrochemical investigation of the behaviour of gold in chloride solutions. I V. Results obtained from Phase 2 of the investigation. (First issued 30th Jun., 1978.) Report no. 2093 The measurement of electrical variables in a submergedarc furnace. Steels for pipelines Since welding was first introduced as a method of joining pipelines, gas-pipeline engineers have taken the opportunity to increase gas pressures, and hence increase the efficiency and economy of transporting gases. Envitec '83 The International Trade Fair and Congress for Engineering in Environmental Protection - the ENVITEC '83 - will take place in Diisseldorf from 21st to 25th February, 1983.

Jan 1, 1981

[The following notations will be used: O an ore body. W a sample of size w located in O; the size of this sample. W a block or a sample, of size W, located in O; the size of this block or sample. z' a point in W. W' a block or a sample, of size W' greater than or equal to W, located in O; the size of this block or sample. z" a point in W'. y (h) point semivariogram in O. s (h) point covariogram in O. In the previous chapter, we saw that the point semivariogram y (h) usually cannot be estimated directly from the data available. Rather, the values of samples of size w are available in O, and from these a regularized semivariogram y w (h) can be estimated. The following relationship has been proved (5.8): Y w(h) = Y (w;w+h) - Y (w;w). y (w;w+h) is the average value of y (z' z") when z' takes all possible positions in a sample w and z" all possible positions in a sample w+h of the same size, h being the distance between w and w+h. y (w;w) is the value of y (w;w+h) for h = 0, i.e. the average value of y (z' z") when z' and z" take all possible positions in w. We also saw that the regularized covariogram aw(h) is related to the point covariogram a (h) as follows (5.9): w(h) Gr In the following chapters, it will be shown that calculation of the average value y of y, or -a of a, in the general case relating to samples or blocks W and W' which need not be of the same size, plays a very important part in all the practical applications of geostatistical theory. The purpose of this chapter is to introduce various methods of calculating y and a-. Furthermore, mathematical equations and graphs are provided which can be used when the point semivariogram can be represented by one of the more common equations, and when the blocks W and W' are of simple shape. By definition (Fig. 6.1): [ ] Y (W;W) = WW f dz' f y (z' z") dz" (6.1) in W z" in W']

Jan 1, 1978