In the long historical process of understanding and studying the earth, the traditional geological research method is mainly descriptive induction, which meets the needs of the social productivity level at that time and the development of ancient geology. /kloc-from the end of 0/9 to the beginning of the 20th century, driven by the industrial revolution, the rapidly rising and developing modern industries greatly increased their demand for mineral resources. As an industry, mining industry has begun to be independent from social economy. The development of social production requires paleogeology to change from simply studying and understanding geological objects to discovering and exploring mineral resources to meet the growing demand of industrial development for mineral raw materials. Therefore, traditional geology needs to arm itself with advanced theories and technical methods of modern natural science. This has greatly promoted the combination of geology and modern natural sciences, such as physics, chemistry, biology and mathematics. Under this background, new geological marginal disciplines, such as paleontology, stratigraphy, geochemistry, geophysics, geomechanics, plate tectonics, marine geology and mathematical geology, have emerged one after another, forming modern geology, which is a leap in the history of geological development. In the second half of the 20th century, the world economy and modern science and technology developed rapidly. These two high-speed developments have promoted the sharp increase of output and human consumption, and the demand for mineral resources is increasing day by day. This requires geology to have a higher theoretical level and expand the space for finding mineral resources (such as deep crust and marine fields). So it stimulated the development of earth science to a greater extent. In the past 30 years, the emergence and development of four highly comprehensive, cutting-edge and interdisciplinary emerging disciplines, namely, cosmic geology (especially astronomical geology), plate tectonic geology, global geology and deep earth geology, have pushed the whole earth science research to a new height. During this period, the role of mathematics became more and more prominent. Under the background of social development and progress, on the one hand, the rapid economic development has a huge demand for mineral resources. According to relevant statistics, more than 90% of energy and 80% of industrial raw materials needed for China's economic development come from mineral resources. On the other hand, people realize that the mineral resources available for economic development are limited, not infinite. Today, it is more and more difficult to find the developed mineral resources in the world, and the developed mineral resources should be developed and utilized reasonably. Large-scale industrial production and high-tech products need stable reserves of mineral resources, and the stable reserves of mineral resources are closely related to ore grade, so geologists pay extensive attention to the important role of reserves calculation in the exploration and development of mineral resources. The calculation of mineral resources reserves is increasingly prominent in all stages of the whole exploration, exploration, mine design and mining process.

However, for a long time, geologists have been using the traditional calculation method of mineral resources reserves and calculating reserves according to the traditional geological theory. The traditional reserves calculation methods are profile method and block method. On this basis, according to the difference of calculation amount and calculation unit, various methods have evolved: arithmetic average method, block method, excavation block method, nearest area method (polygon method), contour line method, triangle method, parallel section method, non-parallel section method and so on.

The general mathematical form of calculating ore reserves by traditional reserves calculation method;

Application of basic theories and methods of geostatistics (spatial information statistics)

Where: P is the metal reserve; Q is the ore reserve; For the average score; V is the volume of ore block; D is the weight of the ore.

The calculation of V, D and C in the formula is the average of engineering observation data, which is basically an arithmetic average, and it is only adjusted and changed according to the size of the block in the calculation. Taking the commonly used block method as an example, whether it is geological block method or mining block method, the ore body is divided into several blocks, and the ore body area, average thickness, average grade and ore weight of each block are calculated respectively, and then the volume and mineral reserves of each block are obtained. The sum of the reserves of each block is the reserves of the whole ore body. The ore grade is calculated by weighted average method, that is, line weighting, surface weighting, block weighting, etc. This kind of weighting only considers the different proportions of sample values in line (sample length), surface and block, and it is still an arithmetic average thinking mode. Therefore, it can be said that the block method is the concrete application of the arithmetic average method under certain conditions. The sectional method (also called sectional method) is actually the same. The above statement clearly shows that the traditional reserve calculation method is based on the traditional geological theory and adopts the arithmetic average reserve calculation method, without considering the natural characteristics of ore body geology at all. The ore grade, which plays an extremely important role in the calculation of mineral resources reserves, is the key factor: First, the spatial position of engineering samples, that is, the influence range of a sample grade, can only be simply regarded as the grade of a block by the average combination of one or several engineering (drilling) data (ore grade). Secondly, the spatial variation characteristics of sample grade are not considered. The ore grade of the deposit is influenced by various geological factors (such as strata, rock structure, metallogenic conditions and metallogenic mechanism, etc.). ), its variability is different in different directions of ore body strike and dip. This difference in direction determines that the sample grades in different spatial positions have different functions in the calculation of reserves in the blocks to be estimated, and should be given different weights (influence values). Thirdly, the spatial correlation of sample grade is not considered. In the process of mineralization, controlled by the factors of metallogenic conditions, the enrichment and dispersion of various elements are regular, and there is a certain correlation between spatial samples. The sample grade is not independent, but shows a certain spatial correlation, which is directly related to the spatial mineralization intensity of the deposit. Without considering the spatial correlation between sample grades, it is impossible to reflect the spatial variation of mineralization intensity of the deposit. Fourthly, it can't reflect the random characteristics of sample grades. This feature is most obvious in gold mines. All geological and mining workers engaged in geological research and gold exploration and development will have the experience and understanding that the spatial distribution of gold ore grade is sometimes extremely uneven, and the sample grade at a certain point may be high, while the gold content of adjacent sample points may be very low, or even fail to reach the industrial grade. This accidental random phenomenon is another feature that is contrary to the variability of deposit laws. This kind of problem is often encountered in gold exploration and mine development, and abnormal super-high grade often appears. The only thing that the traditional reserve calculation method can do is to summarize some specific methods on the basis of studying gold mine cases and practical experience. For example, the following methods are usually used for empirical treatment of ultra-high grade samples, namely

1) Reject ultra-high grade samples and do not participate in grade calculation;

2) replacing the super-high grade with the upper limit value of the normal sample;

3) replacing the ultra-high grade sample with the average grade of the ultra-high grade;

4) replacing the ultra-high grade with the average value of samples containing the ultra-high grade;

5) Eliminate the ultra-high grade and the lowest grade, and find the sample average to replace the ultra-high grade;

6) using the average value of two adjacent super-high grade samples or three consecutive samples including super-high grade to replace the super-high grade;

7) Use the lower limit determined by several methods commonly used in daily life (variation score method, frequency curve method, statistical analysis method and influence coefficient method) to replace the ultra-high grade samples.

Due to the complexity of this problem, in 199 1 year, the former State Bureau of Mineral Reserves, which was specialized in managing mineral resources reserves, issued the document "State Reserve" (199 1) 164 to deal with ultra-high-grade gold mines in a unified way, and uniformly stipulated the principle of dealing with ultra-high-grade gold mines when compiling and approving mineral reserves reports. When the variation coefficient of ore body grade is small, the lower limit value is adopted.

It should be said that these methods summarized from experience have played a certain role in the past practical application. Before the emergence of more scientific theoretical methods, they are all feasible methods, and sometimes even get good results. However, from a scientific point of view, they reflect the limitations, imperfections and lack of advanced scientific theoretical basis of traditional reserves calculation methods.

In addition, due to the limitations of traditional reserves calculation methods, it is impossible to establish the concept of estimation accuracy because there is no standard method to measure accuracy. In other words, the error of the calculation results of mineral reserves is unmeasurable.

The existence of the above problems reflects that the traditional reserve calculation method fails to reflect the essence of spatial variability of ore deposits, to correctly describe the dual nature of geological variables, and to go beyond the traditional geological framework of describing, summarizing and treating geological variables equally. The traditional calculation method of reserves can not correctly reflect the geological law of deposit formation and can not meet the demand of economic development for mineral resources. This requires that scholars and workers engaged in geological science research and application can solve the problem of accurate quantitative evaluation of various geological bodies in time and space, and objectively and correctly estimate the mineral resources reserves that meet the needs of mining development. So mathematical geology came into being. It has been nearly 70 years since a Soviet scholar, A.G. Wester Leus, published his paper Analytical Geology in 1944, and put forward quantitative mathematical methods to study geological problems for the first time. During this period, geologists have made arduous exploration and research on the calculation method of mineral reserves. Geologists and mining engineers pinned their hopes on the classical probability and statistics theory from the beginning. Practice has proved that the classical theory of probability and statistics can not correctly describe the essential characteristics of duality of geological variables when solving the problem of geological variables in the geological field. This is beyond the limitations of classical probability and statistics theory and methods. Classical probability statistics needs variables when studying the inherent characteristics of accidental events: ① Each sampling must be carried out independently. That is, samples Xi (I = 1, 2, ... n) are required to be independent of each other; ② In principle, the variables studied can be infinitely repeated or observed in large quantities; (3) The research object must be a purely random location, which obeys the probability distribution of known random variables; ④ The spatial distribution of sample observations is not considered.

Obviously, it is not appropriate to simply apply the classical theory and method of probability and statistics to complex geological fields, nor can it correctly describe the duality of geological variables, which is essential in geological fields.

During the 30 years from 1930s to 1960s, Soviet geologists did a lot of work in this field, and put forward the correct view that geological variables are random functions, not just random variables, and the samples are spatially correlated. Unfortunately, we have never found a solution to geological variables. At the same time, geological and mining engineers in West Africa and South Africa have done a lot of research work in combination with mine production practice. Among them, two experts have done fruitful work. One is H.S.Sishel, a statistician. After studying the grade estimation of Rand gold mine, he put forward a lognormal distribution model of gold grade and wrote a paper published in 1947. Then Krieger, another South African mine geological engineer, proposed a three-parameter lognormal distribution model. After 195 1 year, these two experts and scholars put forward a method to estimate the average grade of the block to be estimated by giving each sample different weights according to the difference of spatial position and the correlation between samples. In fact, this is a simple regression model that uses the average grade of several adjacent blocks to estimate the central block, that is, kriging original regression model.

At the end of 1950s, Professor G. Mathelon, a famous French mining engineer and probability statistician, systematically studied more than 40 kinds of mineral deposits in 10 countries, including gold, iron, tin, nonferrous metals, six different types of uranium and nonmetallic minerals, talc, fluorite and so on. , obtained a wealth of first-hand information. On the basis of rich production experience, he promoted the research results of Krieger and others to theory, and put forward the term "geostatistics" for the first time by G. Mathelon in 1962, and published the monograph "Applied Geostatistics" in 1963. Since then, geostatistics has been born as a new frontier discipline.

The process of geostatistics shows that the urgent demand for mineral resources in the rapid development of world economy is the basis of geostatistics; The rapid development of modern science and technology and the introduction of advanced scientific theory and technology have greatly expanded the research field of geological science, deepened the understanding of geological objects by geological science, and created scientific and technical conditions for the emergence of geostatistics; After decades of geological work, rich, complete, systematic and accurate geological data have been obtained in mineral resources, which greatly improves the understanding of deposit geology. Rich information is the material basis of geostatistics; The variable with dual nature is the most extensive and practical variable in the geological field, which directly affects the production of mining enterprises. Therefore, in the mining industry, geological variables with dual nature are the most valued, with the longest research history and the best theoretical and technical preparation. These conditions are beyond the reach of other fields. Geostatistics is naturally born from the field of geology. At the same time, computer technology has developed rapidly, and students of geostatistics have a good life, so it has developed vigorously.