MINING GEOLOGY/Mineral Reserves 627 (i.e., boreholes, shafts, etc.) into triangular, regular squares, rectangular, polygonal, and irregular or geological blocks These methods differ slightly in ways of determination of volume and grade of mineral bodies The average thickness is calculated as an arithmetical mean in all cases with an exception of the polygonal method where thickness and grade are taken from the borehole lying at the geometrical centre of each polygon In all other kinds of blocks an average grade of the mineral body is calculated as an arithmetical mean weighted by thicknesses Polygonal blocks and geological blocks are applied if the arrangement of the exploration points is irregular Contours of geological blocks are derived from the geological situation (tectonic elements, facial changes, changes of thickness, etc.) Methods of sections can be divided as follows: Longitudinal sections (along the axis of the body) Cross-sections Sections may be vertical, horizontal, and inclined, each other being parallel and non-parallel Owing to the application of geological sections the natural shape of the body is nearly preserved Volumes of blocks can be calculated either between two sections or using area of only one section The first way is applied in the case of similar in shape and near in dimension geological sections, the second one is used if the shape of the mineral body is very irregular and/ or if due to geological reasons a connection between two sections is not assumed The average grade of blocks is calculated as an arithmetical mean weighted by the areas of geological sections of the body Areas of the sections are measured by means of instruments (planimeter, scanning, etc.) or average thickness may be used For calculation by means of isolines there are used isopachs (i.e., isolines of thicknesses), isohypses (isolines of altitude), grade, density and their combination can be used Volume of mineral bodies is given by contours of isolines and can be calculated using the Simpson formula If a combination of isopachs, of isolines of grades, and of isolines of density is used the computed volume is equal to the reserve Geostatistics, in their most generally accepted use, are concerned with the study of the distribution in space of useful values for mining engineers and geologists, such as grade, thickness of accumulation, including a most important practical application to the problems arising in mineral deposit evaluation Spatial or geostatistical methods are working with statistical processing of primary data and with description of a statistical character of the distribution of main properties of the deposit in space by means of variograms The discovered statistical characteristics that allow the prediction of the distribution of studied properties in the mineral body are used for the computing of reserves One of the most known and used geostatistical methods is so called ‘kriging’, a method developed for gold reserves computing in South Africa In the international statistical overviews of the world reserves and of the regional resources of a mineral commodity, the terms ‘resources’ and ‘reserves’ base are usually given For the metallic ores the reserve are given mostly in terms of metal content Reserves of naturally occurring non-metals and fossil fuels are expressed in the tonnage of raw mineral material Quantities, qualities, and grades may be expressed in different terms and units to suit different purposes, but usage must be clearly stated and defined Mineral reserves can be defined also as: ‘‘a quantity of mineral raw materials in the Earth‘s crust which is estimated as a result of geological exploration works or during their extraction’’ They could be calculated for a single deposit, for an ore field or district, for a basin, for a region, for states, for continents, and for the whole world World mineral reserves of each raw mineral commodity are immense and their quantity is subject of changes due to the development of geological knowledge, in conjunction with considerable mining activity For example, world resources of iron ores are estimated to exceed 800 billion metric tonnes of crude ore containing more than 230 billion tonnes of iron World reserves in iron content are estimated to be 71 000 million metric tonnes, the reserve base being 160 000 million metric tonnes Annual world output of iron ore mines varies by about billion metric tonnes per year World reserves of phosphate rocks are recorded as high as 12 billion metric tonnes, reserve base being 37 billion metric tonnes World resources of coal are estimated to be about 15 Â 1012 metric tonnes, of which about 1067 billion metric tonnes are recoverable reserves In 2001 the annual world mining output of coal was 3630 metric tonnes These few examples may give an idea as to the order of huge quantities of world mineral resources and reserves See Also Military Geology Mining Geology: Exploration Petroleum Geology: Reserves Further Reading Agterberg F P (1974) Geomathematics: mathematical back ground and geoscience applications In: Developments in Geomathematics, vol.1, p 596 Amsterdam, London, New York: Elsevier