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Volume 32 Issue 2
Apr.  2021
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Pengda Zhao, Yongqing Chen. Digital Geosciences and Quantitative Mineral Exploration. Journal of Earth Science, 2021, 32(2): 269-275. doi: 10.1007/s12583-021-1440-0
Citation: Pengda Zhao, Yongqing Chen. Digital Geosciences and Quantitative Mineral Exploration. Journal of Earth Science, 2021, 32(2): 269-275. doi: 10.1007/s12583-021-1440-0

Digital Geosciences and Quantitative Mineral Exploration

doi: 10.1007/s12583-021-1440-0
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Digital Geosciences and Quantitative Mineral Exploration

doi: 10.1007/s12583-021-1440-0

Abstract: The idea of mineral exploration, which is called "exploration philosophy" in the Western countries, is the thoughts, the methodology, technology, goals and organization that guide mineral exploration. The three basic elements of mineral exploration are "what to find", "where to find" and "how to find". The concept of mineral exploration is gradually changing with the development of these three elements that provide a powerful driving force to change mineral exploration concepts, methods and technology. Innovation of mineral exploration concepts is the result of continuing exploration and development keeping pace with the times. The combination of "mathematical geology" and "information technology" can be called "digital geology". Digital geology is the data analysis component of geological science. Geological data science is a science that uses the general methodology of data to study geology based on the characteristics of geological data and the needs of geological field work. Digital mineral exploration is the application of digital geology in mineral exploration to reduce ore-finding uncertainty.

Pengda Zhao, Yongqing Chen. Digital Geosciences and Quantitative Mineral Exploration. Journal of Earth Science, 2021, 32(2): 269-275. doi: 10.1007/s12583-021-1440-0
Citation: Pengda Zhao, Yongqing Chen. Digital Geosciences and Quantitative Mineral Exploration. Journal of Earth Science, 2021, 32(2): 269-275. doi: 10.1007/s12583-021-1440-0
  • Traditional geology is commonly characterized as a qualitative science. The combination of geology and mathematics began about 180 years ago, when British geologist Lyell first applied mathematical statistics to quantitatively subdivide the Tertiary into stages (Lyell, 1833). Mathematical geology, as an independent branch of science, originated in the late 1950s and 1960s when Krumbein (1958) was the first to use the digital computer to analyze stratigraphic columns and sedimentary facies. He became known as one of the "Pioneers of Mathematical Geology" (Agterberg, 2018; Merriam, 1981). In 1962, the Soviet Union scholar Vistelius defined "mathematical geology" to be the science to study the establishment, analysis and utilization of mathematical models to quantitatively describe geological phenomena (Vistelius, 1962). The establishment of the International Association of Mathematical Geology (IAMG) in Prague in 1968 marked the international recognition of the subject (Agterberg, 2018). The science of studying geological information should be called "Information geology", which combined with "mathematical geology "was called "digital geoscience" (Zhao, 2015). Digital geoscience is the data science of geology (Zhao, 2019).

  • Mathematical geology is an interdisciplinary combination of geology and mathematics. Its main tasks include the following (Zhao, 1982): (1) study the characteristics of geological bodies in order to establish mathematical models for these bodies; (2) study the relationship and influence of various factors in geological processes to establish mathematical models for these processes; (3) study the characteristics of geological data and geological field work methods to establish mathematical models for these methods; (4) through the establishment of various mathematical models investigate and solve various practical geological problems; (5) combining mathematical geology with spatial information technology to develop digital geoscience with the help of computer technology.

    Digital geoscience is an interdisciplinary subject resulting from the combination of mathematical geology and Information technology (Zhao, 2019). Digital Geoscience, based on geological theory and information technology, tries to establish and apply various mathematical models to intelligently process big data in geology with the help of methods of data science, from which key information is mined to obtain condensed digital knowledge. This emerging interdisciplinary discipline aims to solve theoretical and practical problems such as cognition, prediction, decision-making, and evaluation in geology (Zhao, 2019).

    Digital geoscience is the further development, extension and expansion of mathematical geology. It combines quantitative theory in geology with information technology. Its purpose is to effectively reveal various geological anomaly regularities by extracting key information from various kinds of geoscience big data to identify and predict deeply buried geological structures and orebodies.

  • Earth science is considered to be a data-intensive science at present (Zhao, 2011). There is no science without data, and there are no data without science. Natural science, engineering and technology or human and social science cannot be separated from data. All data must have scientific connotation and be scientifically significant. Data processing methods can be used to study science, and scientific methods can be understood as studying data. Scientific research can be regarded as data research. From the point of view of data analysis, different problems in different disciplines have a considerable degree of similarity and this makes it necessary for data science to exist and develop.

  • Big Data Science has become a new scientific paradigm constituting the fourth scientific paradigm alongside theoretical, experimental and computer science. It makes full and correct use of the data generated by itself on the one hand, and makes full and reasonable use of the large amounts of relevant data from other disciplines on the other hand in order to solve the traditional problem of data closure and other limitations. In the big data era, it is necessary to further establish new ways of thinking about data, quantification and core data knowledge (Han, 2000). At present, the basic subjects of digital geoscience mainly include the following ten aspects: (1) quantification, digitization, modeling, visualization, interrelating and understanding of geological objects; (2) complexity, superimposition, variability, multi sources, directionality, and representativeness of geological data, and sorting techniques for mixed data; (3) statistical distribution characteristics of geological data and their genetic significance; (4) quantification of geological data; (5) spatial variability and anisotropy of geological data; (6) probability rules for geological events and probabilistic estimation of geological event results; (7) quantitative combination of various geological processes and weighted estimation of each influencing factor; (8) structural characteristics, combination characteristics and entropy functions of geological processes; (9) Markov processes and transformation probabilities of geological processes; (10) nonlinear theory and methods of handling nonlinear characteristics of geological data.

  • Geological data have the following features: mixed, sampled, scarce, multi-source, polymorph, spatio-temporal, variable, causal, relevant, directional, zonal, representative, unique, summation, etc.

    (1) Mixing. The data we now observe may be the result of the superposition of various geological processes that took place during a long geological history. For example, copper grade data obtained from a copper orebody may include primary copper in granites, and superimposed copper from an ore-forming hydrothermal liquid. Then the copper grade data of the copper ore are the result of mixing due to superimposed processes. If we want to study the origin of this copper ore, we must decompose the mixed data, examine the size and spatial distribution characteristics of the copper ore originating from the different processes; otherwise, we will not draw the correct conclusions about origin of the copper ore.

    (2) Sampling. The observation, measurement, and description for various kinds of geological bodies are based on sampling according to certain rules at different points, along lines or across surfaces within the geological bodies. It is difficult for us to obtain "full data" of an entire geological body. Even with techniques such as remote sensing and geophysical exploration, observation on the Earth is restricted to a local area only. Drill-core sampling must take place along a line in a specific direction with the drill-holes arranged according to a reasonable pattern and depths of drilling determined according to the need to obtain relevant data. Consequently, geological data are mostly limited "samplings". Since so many geological data are samplings only, it is inevitable to consider the "representativeness" of the samples. Representativeness can be divided into local, hierarchical, and overall representativeness, which need to be considered separately according to different research objectives (Zhao et al., 1983). Data related to deep sampling are scarce at present with the deepest drill-core data obtained from the Kola superdeep borehole of the former Soviet Kola Peninsula CT-3, with total depth of 12 262 m. Such data for deep Earth observation are extremely scarce and valuable. Thus, although geosciences are data-intensive, such extremely precious scarce data cannot be ignored and should receive special consideration. It can also be seen that geological data is sometimes not readily available. Geological data must be collected in accordance with the principles of high efficiency and low cost.

    (3) Causality. Geological data, according to their statistical distribution, stationarity and variability are strictly controlled by their genesis. Taking iron ore as an example, the iron ore grade from iron deposits with different geneses can vary greatly. There are significant differences between the iron grade of sedimentary metamorphic banded magnetite ore and the iron grade of contact metasomatic skarn iron ore. Some ore grade data display normal distribution, others follow lognormal distribution, etc. These differences are related to their genetic characteristics. Therefore, it cannot be considered in any case that big data analysis has been changed from causality analysis to correlation analysis (Zhang et al., 2018; Schonberger and Cukier, 2013). In the application of big data analysis, causality and correlation are both very important and should be performed differently according to different requirements and purposes. Geoogical data have spatiotemporal properties. Geological data are likely to be spatio-temporally varied, and each data item represents a certain feature of a geological entity in space and time. The spatio-temporal nature of geological data resulted in many special features such as directionality, zonation, sequence, dependence, and variability. For example, in directionality, geological data sometimes have their own variation regularity in a certain direction, such as the grain size of sediments in the vertical direction of a sedimentary sequence that shows grain size reduction from the margin toward the center of a sedimentary basin. Some geological bodies display horizontal or vertical zonation in ore-forming elements (Chen et al., 2010, 2008; Chen and Zhao, 1998); e.g., a copper ore body may display regular zonation from primary sulfide ore at depth, to secondary enrichment by weathering or leaching, onto a hardened cap at the surface. The spatio-temporal variation of geological data produces an ordered data set reflecting regular variation of a geological body in both time and space.

    (4) Polymorphism. Geological data can be subdivided into qualitative and quantitative data, or continuous and discrete data according to different rules. The polymorphism of geological data is related to its multi-source nature and how they are observed. For example, qualitative data are obtained from observation and description of a geological body, whereas quantitative data are obtained from measurements performed on it. Discrete data are obtained by successive point measurements on a geological body, and continuous data are obtained from sampling continuously like in aeromagnetic surveys or by remote sensing from satellite surveys. Different research methods must be used for different types of data to obtain key information and the corresponding digital knowledge.

    (5) Pluralism. The genesis of geological bodies is controlled by many geological factors. The characteristics of geological bodies can be observed in many ways (Zhao et al., 2001). In short, a survey on a geological body can be considered as a point measurement in multidimensional space. Thus, it is necessary for us to apply spatial dimensional information to accurately define a certain geological body. Consequently, geological data displays pluralism and diversity. For example, the ore-forming system of a deposit contains five basic elements: "source, transport, storage, change, and preservation" (Zhai et al., 2014). In order to find undiscovered ore deposits, it is necessary to collect and obtain data honoring these five aspects contributing to the pluralism of geological data. However, even if an ore deposit is characterized from the point of view of pluralism, because the occurrence of ore-forming events remains uncertain, predicting the occurrence of ore deposits needs to be quantitatively evaluated in probabilistic terms.

  • In the process of digital geological research, different types of data need different forms of expression. It is necessary to pre-process and transform the data to facilitate comprehensive analysis. The main objectives of data pre-processing are the following: (a) unify the data level of geological variables and reduce dimensional effects; (b) make geological variables obey normal frequency distributions as much as possible; (c) transform the nonlinear relationships between the variables and their functions into linear relationships; (d) reduce the number of variables, i.e. use a new set of fewer combination variables with mutual independence to replace the original geological variables. In the process of data pre-processing, different transformations are tried to achieve different goals. Currently, common data pre-processing and data transformation include the following five basic types: (a) standardization of raw data causes the data to be of the same order of magnitude; (b) logarithmic transformation of the original data with positively skewed frequency distribution brings the data closer to normality; (c) data with nonlinear relationship between a dependent variable and independent variables can be approximately changed into data with linear relationships between them; (d) R-type principal component analysis of raw data can reduce the number of original variables and create new variables that are independent of each other. Data pre-processing and data transformation are important for extracting key ore-related information from a huge quantity of data; (e) transformation of the data with mixed distributions should be sorted firstly into single populations before proceeding to use them for further analysis.

  • Geological, geophysical, geochemical and remote sensing geological anomalies of ore deposits and their surrounding areas constitute a basis for understanding the ore-forming conditions and evaluating mineral resource potential (Chen and Liu, 2001; Zhao et al., 2001, 2000, 1999, 1996; Zhao and Chen, 1999, 1998; Zhao and Meng, 1993; Zhao and Chi, 1991). Digital mineral exploration is realized by establishing digital mineral exploration patterns (Zhao, 2002; Chen and Liu, 2001). Digital mineral exploration firstly involves the extraction of single-disciplinary ore-finding information such as geology, geochemistry, geophysics and remote sensing data based on the establishment of a conceptual mineral exploration model with comprehensive information (Zhao and Chen, 2011; Wang et al., 2010, 1996, 1992). Then, the multi-disciplinary ore-finding anomaly information is integrated and used to establish a digital mineral exploration model. Finally, the ore-finding targets are quantitatively delineated and the resource potential evaluated by means of a digital mineral exploration pattern (Chen and Liu, 2001). This digital mineral exploration pattern is a quantitative expression of the ore-controlling factors and ore-finding evidence (Chen and Zhao, 2009).

    The main applications of digital geology include digital characterization of geological bodies, their genetic analysis, evaluation and prediction of ore bodies (Zhao and Chen, 1999, 1998). Quantitative geoscience is the application of data science in geoscience, and digital mineral exploration is an important part of quantitative geoscience. It constitutes the application of data science in mineral exploration.

    The superiority and necessity of digital mineral exploration include the following: (a) quantitative characterization of a geological body includes its structural, spatial, statistical, geometric, evolutionary characteristics; (Zhao, 1982); (b) quantification and digitization form the basis and are the prerequisite for fully extraction of the ore-finding information; (c) data analysis is necessary for the extraction of various kinds of ore-finding information, identification of deep geological structures and ore bodies, and quantitative evaluation of both ore-finding targets and establishing uncertainty of mineral exploration (Zhao, 2007); and (d) quantitative description of the history of pertinent geological events (Zhao, 1992).

  • The Gejiu super-large Sn-Cu polymetallic deposits are located at the western margin of the South China Block near the meeting point of the Yangtze, Indo-China, and Cathaysian blocks (Fig. 1a). Outcropping strata in the Gejiu area belong mainly to the Triassic Sedimentary Formation which consists of carbonates in the lower part, and clastic and carbonate rocks with the intercalated basic lavas in the upper part. The most significant fault in the Gejiu tin polymetallic ore field is the NS trending Gejiu fault, which separates the Gejiu field into eastern and western districts (Fig. 1b). Other, secondary faults are NE-trending, NW-trending and EW-trending. Intrusions in the Gejiu district include: (1) porphyritic granite and equigranular granite; (2) alkaline rocks; and (3) gabbro-monzonite. These intrusions are well exposed in the western part, but buried deeply in the eastern part (Fig. 1b). It has been shown that these intrusions are buried deeply in the eastern part, including the Malage-Songshujiao, Laochang-Kafang plutons are predominant S-granites which had experienced high degrees of fractionation. The intrusions exposed in the western part, including Jiasha gabbro-monzonite, Baiyunshan-Changlinggang alkali granites, as well as Longchahe porphyritic granites are predominantly I-granites. Sn-Cu polymetallic deposits are associated with the S-granites in the eastern Gejiu region, and U-Th-Nb-Ta-REE mineralization is related to the I-granites in the western Gejiu region (Chen et al., 2020).

    Figure 1.  (a) Geological outline map of southeastern Asia, showing major tectonic units and location of where the Gejiu tin-copper polymetallic ore field is situated and (b) simplified geological map showing the spatial distribution of intrusions and the various types of ore deposits in the Gejiu Sn-Cu polymetallic ore field and surrounding areas. CB. Cathaysia Block; YB. Yangtze Block; SB. Sibumasu Block; TP. Tibet Plate; ICB. Indo-China Block; IP. India Plate (revised after Chen et al., 2017).

    Complicated geo-processes including evolution-differentiation of the magmas and hydrothermal systems resulted in the diversity of mineralization mentioned above (Chen et al., 2020; Zhang et al., 2008).

    On the basis of the above-mentioned analyses of ore-forming features, an ore-finding conceptual model was established for the study area, including the following: (a) SN and NW, NE and EW trending fracture systems, and their secondary linear and ring structures, which control the spatial distribution of various types of Sn-Cu polymetallic deposits; (b) the Triassic (Gejiu area) and the Cambrian-Dubian Carbonate (Bozhushan area) are the main ore-bearing strata; (c) Late Cretaceous tectonic magmatism was a necessary factor for the formation of the granitic complex and related hydrothermal ore deposits; (d) Pb-Cd-Ag-Zn-Sn-Mn-Cu-As element combination anomalies with elemental zonation are developed in some areas; and (e) U-Th-Nb and Au-Sb element anomaly associations are important markers for identifying ore anomalies (Chen et al., 2020; Huang et al., 2018; Zhang et al., 2008). This comprehensive ore-finding conceptual model forms a basis for both selecting ore-finding target variables and establishing quantitative ore-occurrence patterns (Zhao and Chen, 1999, 1998).

  • The establishment of a quantitative evaluation pattern of ore-finding targets in the conceptual model includes the following: (a) define statistical units; (b) extract ore-finding target variables based on the conceptual model; (c) assign values to ore-finding target variables; and (d) choose the mathematical model to construct a favorability function.

  • Taking a 10×10 km grid as sampling unit for defining the target variables, there are 288 sample units within the study region. Eleven target variables were selected according to the ore finding target conceptual model. These are Sn-Cu polymetallic mineralization (X1), Late Cretaceous granites (X2), faults (X3), Triassic/Devonian/Cambrian carbonates (X4); Pb-Cd-Ag-Zn-Sn-Mn-Cu-As anomalies (X5), W-Be-Bi-Cu-As-Sn anomalies (X6), U-Th-Nb anomalies (X7), Au-Sb anomalies (X8); IMF1 negative gravity anomalies (showing concealed intrusions) and circular positive gravity anomalies (showing skarn alteration zones) (X9), IMF2 negative gravity anomaly (showing concealed intrusions)(X10), IMF3 negative gravity anomalies (showing concealed intrusions) (X11).

  • The variables defined for each sample unit are quantified in binary format with the values 1 or 0, representing favorable or unfavorable for mineralization, respectively (Zhao et al., 1999; Zhao et al., 1983). The resulting 24×12 data matrix will be used for estimating the ore-forming favorability. When appearing in an unit the ore-finding target variable is assigned to the value 1, otherwise it is assigned the value 0. Element association anomaly assignment satisfies the following rules: (a) element association anomaly with three grades zonations (inner, central, and outer zone) is assigned the value 3; (b) element association anomaly with two grade zonations (middle and outer zone) is assigned the value 2; element association anomaly with one zonation (outer zone) is assigned the value 1. The mathematical model of quantitative evaluation of ore-finding targets can be established on the basis of the ore-finding target variables characterizing the geological distribution of resources in the study area.

  • The weights of the 11 variables were calculated by principal-component analysis applied to the resulting matrix using characteristic analysis (McCammon et al., 1983), the function for calculating favorability of a given sample unit is as follows,

    Equation 1 was applied to calculate favorabilities for all 228 sample units, which were grouped into nineteen groups within the interval 0.1. The resulting frequency distribution and cumulative frequency distribution are shown in Table 1 and on normal probability paper in Fig. 2, respectively.

    Intervals 0.1–0.2 0.2–0.3 0.3–0.4 0.4–0.5 0.5–0.6 0.6–0.7 0.7–0.8 0.8–0.9 0.9–1.0 1.0–1.1
    Frequency 2 10 17 60 51 37 28 23 16 9
    Probability (%) 0.69 3.47 5.90 20.83 17.71 12.85 9.72 7.99 5.56 3.13
    Cumulative probability (%) 0.69 4.17 10.07 30.90 48.61 61.46 71.18 79.17 84.72 87.85
    Intervals 1.1–1.2 1.2–1.3 1.3–1.4 1.4–1.5 1.5–1.6 1.6–1.7 1.7–1.8 1.8–1.9 1.9–2.0
    Frequency 12 6 4 3 4 3 0 2 1
    Probability (%) 4.17 2.08 1.39 1.04 1.39 1.04 0.00 0.69 0.35
    Cumulative probability (%) 92.01 94.10 95.49 96.53 97.92 98.96 98.96 99.65 100.00

    Table 1.  Frequency and cumulative frequency of sampling units in the study area

    Figure 2.  Cumulative frequency distribution of metallogenic favourable sample units in the study area.

    The normal probability plot shows two distinct populations—one with favorability less than 0.8, on the left, representing background population of ore-forming favorability of units, and the other with values greater than 0.8 on the right representing the anomalous population. The favorability value 0.8, therefore, can be used as the threshold for delineating ore-forming anomaly districts. Thus, an ore-forming anomaly district refers to an area, which consists of a cluster of units with favorability value greater than 0.8.

  • Eight ore-finding targets with F > 0. 80 were delineated and selected as the targets for further exploration (Fig. 3). Figure 3 shows that the eight ore-finding targets cover all known large Sn-Cu and Ag-Pb-Zn polymetallic deposits as well as more than 90 per cent of medium-small deposits in the study area.

    Figure 3.  Distribution of Sn-Cu and Ag-Pb-Zn polymetallic ore-finding targets in the study area.

  • The ore-finding targets can be ranked further by an index defined as the product of the mean value of favourabilities of the ore-finding targets and the target area (Chen et al., 2001),

    where Poi represents the ore-finding priority of ith target and ave (Fi) and Si the mean value of F, and the area of the ith target, respectively.

    The value Poican be normalized as below (Chen et al., 2001)

    where Pi is a normalized index standing for the priority of further exploration and POmax and POmin represent the maximum and the minimum values of POi, respectively. The ranks of the 8 targets are shown in Table 2. The Pivalue of the target Ⅴ (the Gejiu district) containing five known large Sn-Cu polymetallic deposits is 100%, and the Pi value of target Ⅶ (the Bozhushan district) containing one known large Ag-Pb-Zn-W polymetallic deposit is 5.43%. Thus, it is possible for the targets Ⅱ and Ⅲ in the Gejiu district that each of them would have resource potential of one large Sn-Cu polymetallic ore deposit, respectively, compared to the target Ⅴ. Similarly, in the Bozhushan district the target Ⅷ should contain resource potential with two large Ag-Pb-Zn-W polymetallic ore deposits compared to the target Ⅶ.

    Si (km2) 7 11 12 8 39 3 6 9
    Fi 0.965 7 1.10 1.05 0.86 1.26 0.86 0.85 0.91
    Poi 5.32 12.1 12.6 6.88 49.14 2.58 5.11 8.19
    Pi (%) 5.88 20.45 21.52 9.24 1 0 5.43 12.69
    Predicted number of large deposits 0.27 1.02 1.08 0.46 5 0 1 2

    Table 2.  Optimality and probability of prospecting in target areas

  • To sum up, geoscience is a data-intensive science. Digital geology is the data science of geoscience. The key digital geological knowledge is highly condensed information derived from the raw geological data, which can be used to derive a quantitatively exact expressions of the underlying geological process, phenomena and regularities. These scientific expressions can be used to predict occurrence, development and results of geological events in geological time. Therefore, it is necessary to establish and develop data geosciences using the characteristics of the big data era. Digital mineral exploration is a successful application of data geosciences combined with information technology in geosciences.

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