Application of Multi-Source Data Mining Technology in the Optimization of Prospecting Target Areas for Copper Deposits in the Beishan Region of Gansu Province, China

Abstract

The effectiveness of geological prospecting depends on the accuracy of the prediction of the prospecting target areas. In comparison with the conventional qualitative method (Mineral Exploration and Development), the use of big data concepts and methods for the in-depth analysis of the potential value of geological information has emerged as an effective way to improve the accuracy of prospecting target area predictions. The Beishan area in Gansu Province, China, is a prominent polymetallic metallogenic belt in northwest China. In recent years, geologists have encountered challenges in achieving effective breakthroughs in prospecting through conventional methods. In this study, we apply the big data concepts and methods to analyze the geochemical and aeromagnetic data of the Beishan area and utilize a series of self-developed software to rectify errors in the original data. A new geochemical remediation plan is proposed for the main elements of ore formation, and on this basis, a copper ore prospecting model based on multi-source data information mining is established. The prospecting model is used to predict the formation of copper ore in the Beishan area, and 100 level I and II preferred target areas with significant prospecting significance have been identified. Level I and II preferred target areas account for 2.7% of the study area. Verified by field sampling, the actual mineralization rate of the level I target area is 39.47%. This study proves the effectiveness of the proposed multi-source data mining method in improving the prediction accuracy of prospecting target areas.

1. Introduction

The current global economic development requires a stable and sustainable supply of copper (Cu) ore resources [1,2]. Copper exploration is becoming increasingly important to global economic growth [3]. The Beishan area is an important metallogenic belt in northwestern China. The challenges in discovering large-scale copper deposits through conventional geological exploration methods have led to a stagnation in prospecting activities in the region. The effectiveness of geological prospecting depends on the accurate predictions of target areas.

Big data methods use data mining to investigate the correlations between data and extract valuable information, with the objective of solving scientific and technological problems [4,5,6,7,8,9,10]. With the progress of geological prospecting, the number of deposits discovered using traditional predictive prospecting theory and methods is decreasing. In the optimization of mineral prospecting targets, geoscience big data are in sharp contrast with the conventional analog method for studying the genesis of typical mineral deposits [11,12,13,14,15,16,17,18]. The big data method involves using all existing geological data as the research object, incorporating multivariate statistical analysis and machine learning as methods, and using high-performance computers as tools [19,20]. Mathematical models are constructed for the quantitative determination of the similarity between the study area and the known mining areas in specific information dimensions [21,22,23,24,25]. Areas with high similarity are identified as predicted mineral prospecting target areas. This approach not only circumvents the complex genesis of mineral deposits but also eliminates the influence of subjective human factors on the research process and outcomes [26]. Consequently, the research on the optimization of mineral prospecting target areas is rendered more direct and effective, and the prediction results are rendered more accurate and realistic [27,28,29]. With the continuous advancement of mineral exploration and the increasing accumulation of geographic information system (GIS) data, the prospect of quantitative metallogenic prediction research in geological prospecting has become a reality [30,31,32]. In particular, exploration geochemistry provides direct and effective data for quantitative metallogenic prediction using GIS, establishing a solid research foundation for the application of big data thinking in the prediction of mineral prospecting target areas [33,34,35,36]. The presence of the Cu element in nature is rare, and it exists in particulate form with uneven distribution, especially in aquatic sediments. This results in the lack of corresponding Cu geochemical anomalies in some copper deposits (points). Additionally, during the sampling and testing process of geochemical exploration, the characterization of Cu abundance is affected by factors such as representativeness, thereby reducing the application value of data on water system sediments [37]. Consequently, it is becoming increasingly challenging to use elemental anomalies for the exploration of potential copper deposits and for conducting geological prospecting and metallogenic prediction research. To improve the prediction accuracy of Cu ore target areas in the Beishan area of Gansu Province, this study applied big data thinking, took the geochemical and aeromagnetic data of the area (49,430 km²) as the data source, and established a series of prediction models based on geophysical and geochemical information by using Statistical Product and Service Solutions software (SPSS Statistics Trial Version), a commonly used professional statistical analysis software, to process the original data. The quantitative prediction and optimization of Cu prospecting target areas in the Beishan area were carried out, representing a new application of aeromagnetic and geochemical data in metallogenic copper mine prediction.

2. Geology and Data

2.1. Geological Setting

The Beishan area in Gansu Province is a prominent metallogenic belt situated at the convergence of the three ancient continental systems of Kazakhstan, Siberia, and the Tarim Basin [38,39,40,41,42]. The geological structure of the area is complex and has experienced multiple periods of tectonic movement and magmatic activity [43,44,45,46,47]. The Beishan area is predominantly composed of Precambrian metamorphic rocks, Mesozoic volcanic rocks, and intrusive rocks [48]. The widespread occurrence of these rocks in the area demonstrates the potential of copper deposits, especially for porphyry and skarn deposits [49]. The Beishan area is a promising prospecting target for its abundance of mineral resources (Figure 1).

The prominent copper deposits in the Beishan area include the Gongpoquan copper deposit, the Heishan copper deposit, the Baishantang copper deposit, and the Yaodonggou copper deposit [50,51,52,53]. The Gongpoquan copper deposit is characterized by porphyry-type mineralization, exhibiting high-grade copper ores that also contain precious metals such as gold and silver [54,55,56,57]. The Heishan and Yaodonggou copper deposits are distinguished by skarn-type mineralization, characterized by relatively low-grade copper ores within larger ore bodies [58,59,60]. The Baishantang copper mine is a notable example of a volcanic rock-type copper deposit, exhibiting a copper grade and ore body size that falls between those of Gongpoquan and Heishan copper mines [61]. Further research on these deposits will provide a deeper understanding of the metallogeny and prospecting potential of copper deposits in the Beishan area. As of the end of 2023, a total of 67 Cu deposits (points) had been discovered in the Beishan area of Gansu Province.

2.2. Data Sources

The datasets for this study are detailed as follows:

• Regional geological data: Geological and mineral resources map of Gansu Province (1:1,000,000), tectonic phase map of Gansu Province (1:1,000,000), and a total of 32 sets of regional geological maps and descriptions at a scale of 1:200,000 covering the entire Beishan area.
• Mineral geological data: A total of 32 sets of 1:200,000 mineral geological maps and descriptions covering the entire Beishan area of Gansu Province, 10 sheets of 1:50,000 regional geological data, 15 sheets of 1:50,000 mineral prospecting survey data, approximately 30 detailed geological and mineral resources investigation documents, the mineral database of Gansu Province, and the mineral data from the geological records of Gansu Province.
• Geochemical exploration data: A 1:200,000 regional geochemical database for the Beishan area of Gansu Province, containing sample locations and test results for 39 elements including Au, Cu, U, Th, Ag, Mo, Sn, W, As, Sb, Bi, and Hg, for a total of 29,783 data points.
• Aeromagnetic data: There are 2,512,247 aerial magnetic measurement points in the Beishan area of Gansu Province at scales of 1:50,000 and 1:100,000.

3. Methodology

3.1. Research Ideas

The basic concept behind this effort is to transform the traditional theoretical geological models into geological data-driven artificial intelligence (AI) models [62,63,64]. Relying on the 1:200,000-scale hydrogeological sediment survey, aeromagnetic data, and information on Cu deposits (points) in the study area, a geochemical survey database, an aeromagnetic database, and a known Cu deposit (point) information database for the Beishan area were established, respectively. A conditional association model was established through multivariate statistical analysis and machine learning methods to study the correlation between the regional geophysical and geochemical information and the discovered Cu deposits (points) in the study area. The predicted deposits (points) were associated with the geophysical and geochemical research units, which refer to study units containing discovered mineral deposits (points). It is essential to establish an optimal model database for known ore-bearing units. Using SPSS Statistics Trial Version, which is the software provided by IBM China Headquarters located in Shanghai, China, the known ore-bearing units can be linked with the geophysical and geochemical database. Through model iteration, a series of quantitative optimal models for prospecting targets in the Cu ore region were constructed. These models are employed to predict samples in the entire region, and the predicted units were optimized through the discriminant function. Finally, field inspections were carried out in the optimal target areas with high rankings to evaluate the effectiveness of the model and the actual effect of target area optimization (Figure 2).

3.2. Raw Data Processing

The geochemical data that were selected were recorded by different units in different years, leading to large systematic errors between different map sheets for the same element [65,66]. The aeromagnetic data are composed of data at different scales in different areas. Therefore, it is necessary to perform noise reduction on the original data to ensure the quality of the original data and thus the accuracy and validity of the results.

3.2.1. Raw Data Denoising and Its Effect

Given that the 1:200,000-scale hydrogeological sediment geochemical data of varying map frames were completed by different units in different years, there is a substantial systematic error for the same element between different map frames. To improve the accuracy of the preferred prospecting target area, it is imperative to perform denoising procedures, such as determining the abnormal lower limit and frame-by-frame adjustment of the raw data.

Abnormal lower limit determination: The determination of the lower limit of the anomaly is a crucial aspect of this process. To enhance the effectiveness of the noise reduction processing of the original data, we independently developed the “Linear Approximation” Method and the Algorithm Model Software for lower limit anomaly determination (invention patent number: ZL201910863798.5, software registration number: 2020SR0713005, 13 July 2020). This innovative software employs the principles and methodologies of “machine vision” to accurately calculate 21 relevant parameters, such as the lower limit of positive anomalies and the upper limit of negative anomalies for each element on each map in the study area, significantly improving the accuracy and efficiency of determining significant parameters.

The software’s effectiveness in determining the lower limit of anomalies is evident in Figure 3, which presents a schematic representation of geochemical anomalies processed using internally developed software. The presence of small, low-amplitude anomalies, indicated by red circles in Figure 3a,b, demonstrates that the software accurately calculates the lower limits of anomalies for all elements in all maps. Furthermore, the regional sub-frame adjustment processing has yielded optimal results. This finding resolves the long-standing issue of “loss of low-amplitude anomalies” that has hindered geochemical data processing. Furthermore, it serves to substantiate the precision and dependability of the software.

Frame-by-frame leveling: To improve the effect of noise reduction in the original data, an algorithm based on artificial intelligence, machine vision, and fractal theory was designed and developed, and the “Geochemical Data Frame-by-Frame Adjustment Software” was created. This software enabled the simultaneous leveling of the 39 elements measured in the 29 1:200,000-scale water system sediments in the study area to the regional background reference. The “Geophysical Data Partitioning and Adjustment Software,” which was independently developed, was utilized to perform partitioning and adjustment processing on aeromagnetic data from various periods, survey areas, and scales across the region. This software also facilitated the leveling of the aeromagnetic data onto a single map.

The impact of the sub-frame adjustment software is illustrated in Figure 4a,b, which depicts the outcomes of employing traditional sub-frame adjustment software (derived from the China Resource Potential Assessment Project) and the self-developed sub-frame adjustment software, respectively, in the Anxi area of Gansu Province. In comparison to conventional software, the novel software possesses the capability to simultaneously level multiple maps and elements, exhibiting numerous advantages, including efficiency, accuracy, and effectiveness.

3.2.2. Information Extraction

Mineral information extraction: Based on the aforementioned geological data of the mineral, 67 copper deposits (points) have been discovered in the area. The present study extracts 20-dimensional information on the location, stratum, structure, magmatic rock, ore body characteristics, ore-bearing structure (rock), resource (reserve) quantity, and data source of these deposits and ore (mineralization) points, respectively. The objective is to realize the mathematical statistical analysis of all the basic geological data using a computer.

Geochemical information extraction: Through the processing of the geochemical data of the 1:200,000 scale sediment survey in the Beishan area, 24,782 sample units were formed after 2 × 2 km² gridding processing. The geochemical data include the upper background limit, lower background limit, background value, median (mean) value, background difference rate, standard deviation, variation coefficient, skewness, kurtosis, upper limit difference rate, and lower limit. The 33 parameters that were analyzed included the difference rate, goodness of fit, number of iterations, number of samples, overall-maximum value, minimum value, arithmetic mean, standard deviation, coefficient of variation, number of samples, enrichment anomaly maximum value, minimum value, arithmetic mean, standard deviation, coefficient of variation, number of samples, loss anomaly maximum value, minimum value, arithmetic mean, standard deviation, coefficient of variation, number of samples, etc.

3.2.3. Geochemistry of Related Elements and Remediated Cu Value

Using the lower limit anomaly determination software we developed, the Cu element data are divided into five categories: high, medium, and low positive anomalies, background, and negative anomalies. Subsequent analysis revealed that only 21.7% of the Cu deposits (points) were concentrated in the high, medium, and low positive Cu element anomaly areas, with the remaining deposits distributed in the background or even negative anomaly areas (Figure 5). This finding shows that it is challenging to effectively optimize Cu prospecting target areas in the study area based solely on Cu element anomalies, demonstrating the limitations of relying exclusively on Cu geochemical information. Metallogenesis is a series of enrichment processes of related elements, and elements related to Cu metallogenesis, such as Ag, As, Sb, Hg, Au, and Bi, are mostly evenly distributed in the water system sediments in ionic states. These elements must have a certain relationship with Cu. Based on this idea, a stepwise regression fitting model Cuh of other elements with Cu was established using SPSS software (

Table 1. Stepwise regression fitting model of elemental Cu for 1:200,000 water system sediment measurements.

Variant	Constant	Co	Zn	Ag	Sr	Mn	Bi	V	Ti	Be	Zr
factor	20.13	0.45	0.12	0.04	0.005	0.005	2.91	0.21	−0.004	−1.19	−0.01
variant	Al2O3	Fe2O3	SiO2	CaO	Ba	Ni	Cd	Hg	MgO	Mo	Cr
factor	0.28	0.54	−0.23	−0.27	0.002	0.01	−0.01	0.02	−0.61	0.63	0.01
variant	Au	Pb	Sn	P	K2O	B	La	U	Th	As	Na2O
factor	0.09	−0.04	0.30	0.002	0.48	0.02	0.02	−0.20	0.04	0.10	−0.51

). A stepwise regression simulation model was established for Cu and related elements, and the fitted theoretical value Cuh of Cu was calculated to improve the potential value of geochemical prospecting information in the quantitative and optimal research of regional prospecting target areas. The theoretical Cu fitting value, Cuh, of all units in the region was obtained by calculating all the samples in the study area. Geochemical maps of the fitted values, Cuh, and the measured Cu were drawn separately. Among the 67 deposits (points) in the whole region, only one did not fall within the geochemical anomaly area of the Cu element or the fitted Cuh value anomaly area, i.e., 98.51% of the Cu deposits (points) in the region fall within the Cu or fitted Cuh anomaly area. Therefore, the fitted Cuh value adequately accounted for the impact of the extremely uneven distribution of the Cu element in the aquatic sediment on the quantitative and optimal accuracy of the regional prospecting target area.

The function of the Cuh fitting is as follows:

Cuh = 20.13 + Co × 0.45 + Zn × 0.12 + Ag × 0.04 + Sr × 0.005 + Mn × 0.005 + Bi × 2.91 + V × 0.21 − Ti × 0.004 − Be × 1.19 − Zr × 0.01 + As × 0.10 + Al₂O₃ × 0.28 + Fe₂O₃ × 0.54 − SiO₂ × 0.23 − CaO × 0.27 + Ba × 0.002 + Ni × 0.01 − Cd × 0.01 + Hg × 0.02 − MgO × 0.61 + Mo × 0.63 + Cr × 0.01 − Na₂O × 0.51 + Au × 0.09 − Pb × 0.04 + Sn × 0.30 + P × 0.002 + K₂O × 0.48 + B × 0.02 + La × 0.02 − U × 0.20 + Th × 0.04

(1)

3.2.4. Specification of Unit Division

The study area encompasses 24,782 sample units, selected after the geochemical exploration grid, with the mean value of each element within the grid serving as the representative variable for that element in the grid’s modeling. The grid units containing 67 known Cu deposits (points) are designated as known ore-bearing units, resulting in a total of 67 known ore-bearing units. The ratio of known ore-bearing units to the total number of research units within the study area is used to calculate the background ore content rate of Cu, which is determined to be 0.27%, expressed as “known-ore-content rate”.

3.2.5. Combination of Aeromagnetic and Geochemical Data

In order to facilitate the simultaneous quantitative processing of geophysical and geochemical exploration data within the study area, the maximum (ΔTd) and minimum (ΔTx) values of the adjusted aeromagnetic data were selected as the new aeromagnetic parameters. These were positioned at the center of the coordinate points of the chemical exploration data and had a length of 2 km on each side. This approach considers both positive and negative anomalies of aeromagnetic data, as well as the characteristics of the aeromagnetic gradient belt. After the sorting process, a “basic database of Cu mineralization exploration information (24,782 × 42)” (abbreviated as CuMin Database) was constructed for the designated study area, covering 24,782 samples and 42 variables (39 measured values of geochemical elements, plus Cuh, ΔTd, and ΔTx).

4. Results and Discussion

4.1. Construction of a Quantitative Optimization Model for Prospecting Target Areas

Based on the above CuMin Database, the relevant statistical analysis modules in the SPSS software and the corresponding algorithms were integrated to construct a “Series of Models for Quantitative Optimization of Cu Ore Prospecting Target Areas in the Beishan Area of Gansu Province Based on Geophysical and Geochemical Prospecting Information” (

Table 2. Quantitative optimization series model of Cu mine regional mineral search target area based on geophysical and chemical exploration information.

Model No.	Variables and Parameters
Model I	Variable	constant	Pb	ΔTd	ΔTx	Sn	Ti
	Paramete	−1.71	0.06	0.004	−0.004	0.20	0.0003
	contribution		32.23	27.66	19.69	8.99	6.01
	Variable		MgO	SiO2	W	Mn
	Paramete		−0.001	0.07	−0.04	0.001
	contribution		2.25	1.08	1.05	1.04
Model II	Variable	constant	ΔTx	Fe2O3	Cr	CaO	Cuh
	Paramete	−2.83	−0.004	0.54	0.02	0.10	−0.07
	contribution		16.00	14.96	14.55	14.31	13.95
	Variable		MgO	Ni	Co	Al2O3	P
	Paramete		0.16	−0.03	−0.09	0.002	0.001
	contribution		6.30	6.04	5.93	5.10	2.86

Note: Model I: R0 = 1.91, F_p = 16.7; Mineral positive conviction rate 69.2%; mineral-free positive rate 97.3%; ore-bearing units total 60. Typical deposits: Gongbaquan medium-sized copper deposit, Subei County, and Baishantang medium-sized copper deposit, Jinta County. Model II: R0 = 0.93, F_p = 1.01; mineral positive conviction rate 95.7%; mineral-free positive rate 86.3%; ore-bearing units total 21. Typical deposits: Black Mountain copper–nickel deposit and Yaodonggou copper deposit, Subei County.

). This series of models consists of two models.

R1 = −1.71 + Pb × 0.06 + ΔTd × 0.004 − ΔTx × 0.004 + Sn × 0.20 + Ti × 0.0003−Mn × 0.001 + MgO × 0.07−SiO₂ × 0.04 + W × 0.03

(2)

R2 = −2.83−ΔTx × 0.004 + Fe₂O₃ × 0.54 + Cr × 0.02 + CaO × 0.10−Cuh × 0.07 + MgO × 0.16−Ni × 0.16−Co × 0.09 + P × 0.001 + Al₂O₃ × 0.002

(3)

R1: value of the specification unit identification function (model I); R2: value of the specification unit identification function (model II);

$$\mathrm{R}0=\frac{\mathrm{N}\mathrm{A} \overline{\mathrm{R}}\mathrm{A}+\mathrm{N}\mathrm{B} \overline{\mathrm{R}}\mathrm{B}}{\mathrm{N}\mathrm{A}+\mathrm{N}\mathrm{B}}$$

(4)

R0: discrimination threshold; NA, NB: number of units in A (population with minerals) and B (population to be judged), respectively [67]; and $\overline{\mathrm{R}}\mathrm{A}$ and $\overline{\mathrm{R}}\mathrm{B}$: mean value of the discrimination function values for units A and B.

If $\overline{\mathrm{R}}\mathrm{A}$ > $\overline{\mathrm{R}}\mathrm{B}$, when R1 > R0, the research unit is judged to be population A (preferably with ore), and when R1 < R0, the research unit is judged to be population B (preferably without ore). If $\overline{\mathrm{R}}\mathrm{A}$ < $\overline{\mathrm{R}}\mathrm{B}$, the result is reversed [68,69,70].

4.2. Optimization of the Quantitative Models

4.2.1. Model I

The discriminant function of Model I was utilized to calculate the discriminant value (R1) of each research unit in the CuMin Database in the Beishan area. Taking R0 = 1.91 as the discriminant threshold value, the research unit is a preferred ore-bearing unit. The application of Model I has led to the identification of 660 research units as preferred units, of which 27 are known ore-bearing units, accounting for 4.09% of the total number of preferred units. This figure is 15.13 times higher than the average value of known ore-bearing units (0.27%). The preferred units were then sorted in descending order of the R1 value, and they were divided into three levels using the “golden section” method. The statistical parameters of the preferred units at each level are summarized in

Table 3. Statistics of quantitative optimization results of model I.

Class of Preferred Units	Number of Preferred Units	Ratio of Preferred Units to Total Projected Units	Number of Known Ore-Bearing Units	Ratio of Known Ore-Bearing Units to Preferred Units	Increase Multiplier for Known-Ore-Content Rate
Level I	126	0.51%	8	6.35%	23.47
Level II	204	0.82%	9	4.41%	16.32
Level III	330	1.33%	10	3.03%	11.21
Total	660	2.66%	27	4.09%	15.13

Note: Total number of projected units: 24,782; number of known ore-bearing units: 67; known-ore-content rate (ratio of known ore-bearing units to total projected units): 0.27%.

.

A total of 126 preferred units were identified in the level I of optimization, of which 8 are known ore-bearing units, accounting for 6.35% of the total. This numerial number stands at 23.47 times higher than the known-ore-content rate (0.27%). Furthermore, it was observed that 11.9% of the known ore-bearing units are distributed across a mere 0.51% of the research units. In level II, there are 204 preferred units, of which 9 are known ore-bearing units, accounting for 4.4% of the total. This is 16.32 times higher than the average proportion of the known-ore-content rate. The third level contains 330 preferred units, of which 10 are known ore-bearing units, representing a proportion of 3.03%, which is 11.21 times higher than the known-ore-content rate. Consequently, the model I constructed is remarkably effective in quantitatively optimizing the prospecting target area of Cu deposits in the Beishan area of Gansu Province.

4.2.2. Model II

The results of the Model II analysis, when employing R0 = 0.93 as the discriminant threshold value, yielded the identification of 905 research units as preferred units. Of these, 26 are known ore-bearing units, accounting for 2.9% of the total number of preferred units. This numerial number stands in stark contrast to the average value of preferred units, which is 0.27% (

Table 4. Statistics of quantitative optimization results of model II.

Class of Preferred Units	Number of Preferred Units	Ratio of Preferred Units to Total Projected Units	Number of Known Ore-Bearing Units	Ratio of Known Ore-Bearing Units to Preferred Units	Increase Multiplier for Known-Ore-Content Rate
Level I	173	0.70%	5	7.46%	10.70
Level II	280	1.13%	8	11.94%	10.58
Level III	452	1.83%	13	19.40%	10.63
Total	905	3.65%	26	38.81%	10.63

Note: Total number of projected units: 24,782; number of known ore-bearing units: 67; known-ore-content rate (ratio of known ore-bearing units to total projected units): 0.27%.

).

The preferred units with ore are sorted in descending order of R2 value and divided into three levels by the “golden section” method. The statistical parameters of the preferred units at each level are then summarized. A total of 173 level I preferred units are identified, of which 5 are known ore-bearing units. The proportion of known ore-bearing units is 2.89%, which is 10.7 times higher than the known-ore-content rate (0.27%). In total, 7.46% of known ore-bearing units are distributed in only 0.7% of the research units. A total of 280 preferred units were identified in the II level, of which 8 are known ore-bearing units. This proportion is 2.86%, which is 10.58 times higher than the known-ore-content rate. Similarly, level III comprises 452 preferred units, of which 13 are known ore-bearing units, yielding a proportion of 2.87%, which is 10.63 times higher than the known-ore-content rate. Consequently, model II is remarkably effective in quantitatively optimizing the prospecting target area for Cu deposits in the Beishan area of Gansu Province.

4.3. Validity of the Quantitative Models

The mathematical validity analysis of the model is implemented using the F-test formula.

The F-test is represented by the equation [36]:

$${\mathrm{F}}_{\mathrm{P}}=\frac{\mathrm{N}\mathrm{A}+\mathrm{N}\mathrm{B}-\mathrm{P}-1}{\left(\mathrm{N}\mathrm{A}+\mathrm{N}\mathrm{B}-2\right) P}\times \frac{\mathrm{N}\mathrm{A}\mathrm{N}\mathrm{B}}{\mathrm{N}\mathrm{A}+\mathrm{N}\mathrm{B}} \mathrm{D}2$$

(5)

F_P: the F-distribution value calculated by the discriminant function (model); F_0.01: the theoretical value of the F-distribution table (obtained by checking the F-test table) at the significance level of 0.01 (1% error); A and B: the two discriminant classification populations (A-discriminant ore-bearing unit population, B-discriminant non-ore-bearing unit population); NA and NB: the sample sizes of the two populations, respectively; D2 = $\overline{\mathrm{R}}\mathrm{A}$ − $\overline{\mathrm{R}}\mathrm{B}$ (Marth distance); and P: the first degree of freedom (number of variables). When F_P > F₀.₀₁, the two total samples are significantly different, and the constructed discriminant function (model) is effective in discriminating between unknown samples [71,72].

The validity of the model I was analyzed, resulting in an F_P = 16.7 value that significantly exceeded the F₀.₀₁ = 3 threshold. The model demonstrated a positive prediction rate of 69.2% for the presence of ore and 97.3% for the absence of ore. The known ore-bearing units in model I account for 4.1% of the total number of preferred ore-bearing units, which is 15.13 times higher than the known-ore-content rate. Therefore, the model is considered to have high reliability.

The validity of the optimal model II was analyzed, yielding an F_P = 1.01, which is substantially smaller than F₀.₀₁ = 3. However, the positive prediction rate for mineralization is 95.7%, while the positive prediction rate for no mineralization is 86.3%. The mineralized units that are known to be present in model II account for 10% of the total number of preferred ore-bearing units, which is 10.63 times higher than the known-ore-content rate. Consequently, it can be concluded that this model has extremely high reliability.

The model I identifies a total of 660 preferred ore-bearing units by using 10 variables, including Pb, ΔTd, ΔTx, Sn, Ti, and Mn. Representative deposits include the Gongpoquan medium-sized copper deposit in Subei County and the Baishantang medium-sized copper deposit in Jinta County. The initial three variables contribute more than 10% individually, and collectively, their contribution is 79.6%. The utilization of regional aeromagnetic information is imperative for determining prospective target areas for Cu deposits. It can be inferred from aeromagnetic geophysical characteristics that the distribution of Cu deposits (points) in the region is closely related to the aeromagnetic gradient zone. This finding is consistent with the common phenomenon that regional Cu deposits (points) mainly occur within fault zones and contact zones of different geological bodies.

The model II identifies a total of 905 preferred units through the analysis of 10 variables, including ΔTx, Fe₂O₃, Cr, CaO, and Cuh. Notable deposits include the Heishan small-scale copper–nickel deposit in Subei County and the Yaodonggou small-scale copper deposits. The initial five variables in the model each contribute more than 10%, and collectively, they account for 73.77% of the total variance. Notably, the Cuh variable contributes 13.95% to this cumulative contribution. This study hypothesizes that the parameter Cuh, a crucial element in the discriminant function, plays a pivotal role in identifying potential copper ore deposits within the study area.

The aeromagnetic information of ΔTx and ΔTd in both models has a high individual contribution to the model, which fully confirms that the aeromagnetic data, after format conversion, have excellent discrimination ability.

4.4. Quantitative Optimization of Prospecting Target Areas

The models (discriminant functions) I and II in Table 2 were utilized to process the data in the CuMin Database to calculate the discriminant values (R1, R2) of each research unit for each model. The calculation of the two discriminant values and the sum of the two discriminant values (RZ) was conducted for each preferred unit. The maximum RZ values in each concentration area were then sorted in descending order. The top 200 preferred unit concentration areas were selected as the preferred regional Cu ore prospecting target areas.

The 200 preferred target areas were then divided into three levels using the “golden section rule” (

Table 5. Statistics of quantitative optimization results for the target area of the Cu mine.

Class of Target Areas	Number of Preferred Target Areas	Ratio of Preferred Target Areas to Total Projected Target Areas	Number of Known Ore-Bearing Target Areas	Ratio of Known Ore-Bearing Target Areas to Preferred Target Areas	Increase Multiplier for Proportion of Target Areas with Minerals
Level I	38	0.08%	6	15.71%	58.19
Level II	62	0.13%	8	12.94%	47.93
Level III	100	0.20%	5	5.00%	18.52
Total	200	0.40%	19	9.50%	35.19

Note: Total number of projected target areas: 24,782; number of known ore-bearing target areas: 67; proportion of target areas with minerals (ratio of known ore-bearing target areas to total projected target areas): 0.27%.

). Level I Cu-preferred target areas include six known ore-bearing target areas with known deposits (points) within the target area. The ratio of known ore-bearing target areas to preferred target areas is 15.7%, which is 58.19 times higher than the ratio of known ore-bearing target areas to total projected target areas (proportion of target areas with minerals). Level Ⅱ has 62 preferred target areas, of which 8 have been found to contain mineralization, exhibiting a mineralization rate of 12.9%. Level III has 100 preferred target areas, of which 5 have been found to contain mineralization, exhibiting a mineralization rate of 5%. Among these, the ratio of known ore-bearing target areas to preferred target areas of the level I and II preferred target areas is higher than 10%. Therefore, we hypothesize that the quantitative optimal model for prospecting Cu mineralization areas based on geochemical information has a high accuracy in determining and optimizing Cu-preferred target areas in this region.

Level I preferred target areas cover an area of 556.64 km², while the cumulative area of 62 level II preferred target areas is 780.19 km². The total area of the preferred I and II-level target areas is 1336.83 km², accounting for only 2.7% of the total area of the study area (49,430 km²). Therefore, we believe that the quantitative optimization model for Cu ore preferred target areas, based on geophysical and geochemical exploration information, can be employed to determine and optimize Cu ore preferred target areas in the Beishan area of Gansu Province, thereby significantly reducing the area of the preferred target areas.

4.5. Field Verification of the Optimized Prospecting Target Areas

Field geological surveys were conducted in 32 previously undiscovered target areas in the level I target area, with 9 target areas having Cu grades greater than 0.2% in the collected samples (

Table 6. List of blank target area checking results.

Number of Target Area	Cu (10−2)	Number of Target Area	Cu (10−2)	Data Supplier
I-2-1	0.43–0.64	I-2-2	0.33	The Fourth Geological Survey Institute of Gansu Provincial Geology and Mining Bureau
I-2-3	0.28–0.35	I-2-4	0.96–1.04
I-2-5	0.52–0.60	I-2-6	0.42–1.21	Geological Survey of Gansu Province
I-2-7	0.44–0.73	I-2-8	0.22	The Third Geological Survey Institute of Gansu Provincial Geology and Mining Bureau
I-2-9	0.83–1.76	-	-

Note: The Third Survey Institute, the Fourth Survey Institute of Gansu Province Geology and Mining Bureau, and the Geological Survey of Gansu Province completed the field validation work, and the Comprehensive Research Office of Gansu Province Geology and Mining Bureau summarized the validation results.

), and the mineralization rate of blank target areas reached 28.13%. When combined with the six Cu target areas of the discovered deposits, the actual mineralization rate in the level I target area reaches 39.47%. The field geological surveys further verified the quantitative target area optimization method. The proposed approach in this study has a very important impact on the delineation of Cu mineral target areas in the Beishan area of Gansu Province (Figure 6).

5. Conclusions

The study presents a quantitative optimization method for determining Cu deposit prospecting target areas, which is based on the deep data mining of aeromagnetic and geochemical data and geoscience big data technology. This method was applied to Cu deposits in the Beishan area of Gansu Province and significantly improved the accuracy of the prospecting target area prediction. Compared to the traditional theory-driven method for prospecting target areas delineation, this approach eliminates the influence of subjective factors, such as human geological experience.

The article emphasizes the importance of raw data processing and the use of self-developed software to efficiently eliminate systematic errors in data from different periods and scales. A geochemical remediation plan for predicting the main elements of mineral species is also proposed.

The proposed series of prospecting models reduces the predicted preferred target areas to 2.7% of the total area of the study area, of which the actual mineralization rate of the level I predicted preferred target areas is as high as 39.47%, greatly improving the prediction accuracy of the preferred target areas.