Abstract
Geochemical anomalies are the basis of mineral deposit prediction. Through the study of the characteristics of geochemical anomalies, we found that their distribution was consistent with a generalized Pareto distribution (GPD). In the present study, we designed a model for geochemical anomaly extraction via a GPD. In the designed GPD model, we used the kurtosis method to estimate the threshold value of the GPD. Furthermore, a principal component analysis (PCA) was used to extract comprehensive information of different geochemical elements in which minerals are enriched. On this basis, a new algorithm named the GPDA model was designed for deep mineral prediction by using the GPD and PCA, and the methods of the GPDA for selecting parameters were studied. The study data for Ba, Pb, As, Cu, Au, Mo, Co, and Zn originated from 26 exploration lines of the Jiguanzui Cu-Au mining area in Hubei, China. The proposed GPDA model was applied to deep mineral prediction in the study area. We estimated the parameters of the GPDA model, and the thresholds of Ba, Pb, As, Cu, Au, Mo, Co, and Zn were 457.8612, 56.1823, 28.8454, 910.1272, 89.4283, 34.5267, 84.9445, and 121.4863, respectively. The comprehensive information threshold value was 0.4551. The comprehensive abnormal distribution area of geochemical element contents was obtained from thresholds. The results showed that the method used to identify abnormal areas was consistent with the range of ore bodies identified by actual engineering exploration, demonstrating that the GPDA model was effective. Finally, we predicted that there was a new blind ore body located at a depth of about 1100 m below ground between drill holes KZK10 and KZK11. The results have important theoretical and practical significance for deep ore prospecting.
1. Introduction
Mineral resources are important natural resources for human society. In recent years, humans have produced a high demand for mineral resources with the rapid development of modern society, and since surface and shallow mines are nearly exhausted [1], mineral resources are obtained from the deep earth [2]. We thus need to select reasonable methods for mineral deposit prediction. As minerals are formed by enrichment of different geochemical elements [3], an effective method of mineral resource prediction would be used to study the distribution law and association relationships of primary halo geochemistry in strata, as this could reveal the traces of migration, precipitation, and enrichment of elements in strata [4]. In recent years, researchers have studied methods of mineral prediction based on primary halo geochemistry such as singularity theory [5], deep learning algorithms [6], PCA [7], and fractal methods [8]. However, the diagenesis, mineralization, and regional geological background that form anomalies of geochemical elements are complex and diverse, and thus, it is difficult to find a reasonable method for the extraction of geochemical anomalies that fits all geological environments [9]. We thus need to develop new methods for mineral prediction.
The anomalies of geochemical element contents are often located at the tail of the observed distribution, which characteristically follows a GPD [10]. The GPD considers the distribution of the maximum values of observation data [11]. The mathematical foundation of geochemical anomaly analysis was described as an extreme value distribution by Chen et al. [12], a famous Academician of CAS, and thus, we can use a GPD to extract anomaly information on geochemical element contents [10]. However, if the threshold estimation of the GPD is too large, then it will lead to a decrease in the anomaly area of the geochemical element, and hence, the anomaly area will not cover the actual ore body. Conversely, if the threshold value is too small, it will lead to an increase in the anomaly area of the geochemical element; the anomaly area will far exceed the scope of the ore body, and this is not conducive to mineral prediction [10]. Unfortunately, there is no exact method for threshold estimation. Graphical methods and computational methods are widely used to estimate thresholds. The mean excess function (MEF) is a graphical method as it estimates the threshold according to the linearity of fitting observational data [13, 14], but the MEF lacks theoretical support; i.e., the threshold is determined only according to the linearity of a scatter plot [10]. Calculation methods also have some drawbacks in threshold estimation; for example, the exponential regression model [15] and the sequential method [16] are only suitable for medium-sized sample data, while the subsample bootstrap method [17] is suitable for large amounts of sample data.
A kurtosis method was proposed in order to meet the applicable range of different types of sample data [18]. The principle of the kurtosis algorithm is to continuously remove the maximum value of the sample data until the kurtosis value of the remaining sample data is less than 3. Then, the remaining maximum observed value is used as the threshold value of sample data. Thus, we estimate the thresholds for geochemical element contents by modeling with the kurtosis method.
As minerals are formed by the combination of multiple geochemical elements, the prediction of the location of an ore body needs the comprehensive consideration of anomalies of multiple elements. Through the study, we found that PCA is a statistical method that integrates multiple variables into a few comprehensive variables [19] and is widely used in the industry, and thus, we used PCA to extract comprehensive information from different geochemical element contents. Then, we used the GPD to identify the anomalies from this comprehensive information and obtained the distribution law of the anomalies of geochemical element contents. Therefore, a new model named the GPDA model was designed for deep mineral prediction by using the GPD and PCA. The main contributions of this paper are summarized as follows:(1)The features of the GPD are consistent with the distribution of geological anomalies. We designed a GPD model to extract anomalies of geochemical element content. The threshold selection and parameter estimates of the GPD model were determined.(2)We designed a new GPDA model for deep mineral prediction by using GPD and PCA, taking full account of the characteristics of the geological anomaly and practical knowledge that minerals are enriched by various geochemical elements.(3)The proposed GPDA model was applied to deep mineral prediction in the Jiguanzui Cu-Au mining area. We found that the GPDA model could effectively identify the geochemical anomaly regions of the study area, and the delineated anomaly region coincides with the distribution of ore bodies from actual engineering exploration. We predicted that there was a new blind ore body in the study area using the model, demonstrating the effectiveness of the GPDA in deep mineral prediction.
The remainder of this paper is organized as follows: Section 2 studies the theory of the GPD and PCA, using the kurtosis method to estimate the threshold and the moment method to estimate the shape and scale parameters of the GPD. The coefficient of expression and characteristics of PCA are also discussed. Section 3 presents the GPDA model for geochemical anomaly detection and discusses the feasibility of using the GPDA model to predict minerals. Section 4 demonstrates the application of the GPDA model for deep mineral prediction in the Jiguanzui Cu-Au mining area in Hubei, China. Some conclusions are presented in Section 5.
2. Study of GPD and PCA
The analysis of data for mineral resources using the methods of the GPD and PCA required data processing. Therefore, for the GPD and PCA, the corresponding parameters of GPD and PCA are considered in Section 2.
2.1. Related Theories of GPD
For a set of sample data in which the observed values are , , , that obey a common distribution and are independent, if there is a sufficiently large observed value , the excess of sample data (, , , = 1, 2,, n) satisfies the following expression [10, 20]:
(1) is called the GPD. is a shape parameter, is a scale parameter, and is the threshold of the sample data. Here, if = 1, the GPD is referred to as the standard form. To study the properties of the GPD, selecting = 0.6, 0.3, 0, 0.2, and 0.5, we obtained an image of the standard distribution function, as shown in Figure 1. The larger the value of , the more obvious the characteristics of the tail of the GPD.
The GPD model of the sample data can be determined only after the shape parameter , scale parameter , and threshold value of the sample data are evaluated. In this paper, we used the kurtosis method [18, 21] to estimate the threshold . For a set of sample data = (, , , ), the kurtosis method is given bywhere is the mathematical expectation and is the mean value of the sample data . If > 3, the sample data do not meet the normal distribution and fit a tail distribution. Then, we select the maximum value , , , = 1, 2,,n and remove it from the sample data; this process is repeated until the kurtosis value of the remaining sample data is less than 3. At this point, the maximum observed value of the remaining sample data is taken as the threshold of the GPD, and the threshold is the intersection point of the tail distribution and the normal distribution of the sample data.
The shape parameter and the scale parameter of the GPD can be estimated by the maximum likelihood method or the moment method [10], and the effect of moment estimation is better than that of the maximum likelihood function to estimate and of the GPD, because the moment method uses sample k-order moments to replace the total moment. The estimation process of the sample data is as follows.
By calculating the derivative of (1), the probability density function of the GPD is given by
According to the principle of the moment method, we use the sample mean to replace the population mean and the sample variance to replace the population variance as follows:
Here, is the variance of the sample data . The estimated value of the shape parameter and the estimated value of the scale parameter can be obtained by substituting (3) into (4):
Here, is the mean value of the sample data and is the variance of the sample data .
2.2. Related Theories of PCA
For a set of data = (, , , , , ), = 1, 2,, m, = 1, 2,, n, the model of PCA [22] is given bywhere is the transpose of , = , = , is the ith principal component, and represents the linear relationship between the ith principal component and variables. If the coefficient is determined, the PCA of the sample data can be performed. When calculating principal components, the variance of principal components needs to reach the maximum value; that is, = obtains a maximum value; is the correlation coefficient matrix of , and . Hypothesizing that , , , (, , , , , , , 0) are the different characteristic roots of and , , , , , are the unitized eigenvectors of , let ; then, , is an orthogonal matrix.
Let . We can obtain = = . Then,
Therefore,
When , we obtain = = , and theexpression for the first principal component is = As = = , the variance information of is the largest.
For the same reason, if , = 1, 2,, n. = is the ith principal component.
To select fewer principal components to meet the analyzed practical problem requirement, the value of the cumulative variance explained by eigenvalues needs to be greater than 80%. In actual data processing, in order to eliminate the dimensional influence of variables, the sample data need to be standardized before PCA [23]. At present, there are many standardization methods for data processing, but there is no general rule to select the best method. The most commonly used standardization methods are the min-max method (normalization method), Z-score method (normalization method), and proportion method. Therefore, we selected the min-max method for data standardization. The min-max method is given bywhere is the mean value of the jth variable and is the standard deviation of the jth variable .
3. Design of the GPDA Model for Deep Mineral Prediction
In Section 2, we presented an analysis of the GPD and PCA and the selection of the parameters of GPD and PCA was explained. In this section, we design the GPDA model for deep mineral prediction by using the GPD and PCA.
For the sample data of geochemical element contents = (, , , , , ), = 1, 2, , m, = 1, 2, , n, the threshold of the sample data can be obtained by using the kurtosis method, and the moment estimation method can be used to estimate the shape parameter and the scale parameter. Thus, the GPD of geochemical elements can be obtained. Then, we use PCA to extract comprehensive information from different geochemical elements and the GPD to identify the anomalies from this comprehensive information. Thus, we obtain the distribution law of anomalies of geochemical elements. Finally, we can predict the locations of new deep blind ore bodies through the distribution law of a single anomaly and metallogenic geological conditions. The process of using the GPDA model for deep mineral prediction is as follows: Step I: the test of the tail distribution of data . The kurtosis value of is calculated to determine whether meets a tail distribution. If the kurtosis value is greater than 3, then the geochemical element has a geochemical anomaly. Step II: determining the threshold. When > 3, we select the maximum value , , , = 1, 2,, n and remove it from the geochemical element content and repeat this process until the kurtosis value of the remaining sample data is less than 3. At this time, the maximum observed value of the remaining sample data is taken as the threshold of the GPD. Step III: estimating the parameters of the GPD. The shape parameter and the scale parameter of the GPD of the sample data are estimated by using the moment estimation method. Step IV: determining the distribution law of an anomaly of a single geochemical element. When the threshold , shape parameter , and scale parameter of the GPD are determined, we include them in the GPD to obtain the distribution of anomalies of geochemical element contents. Step V: diagnostic test of the GPD. A P-P plot [10, 24] is used to check whether the theoretical distribution of the GPD and the actual distribution of the sample data are consistent. If distributions are inconsistent, the GPD of the geochemical element anomaly content will not pass diagnostic tests. We return to step III and determine the new threshold , shape parameter , and scale parameter . Step VI: data standardization processing. The standardized data are obtained by using Eq. (7) to standardize ; this removes the dimensional influence of in order to meet the conditions of PCA. Step VII: calculating eigenvalues and eigenvectors. The correlation matrix of the standardized data is calculated. Then, eigenvalues and unitized orthogonal eigenvectors are obtained from . Here, , = 1, 2, , n. Step VIII: calculating the cumulative contribution rate. The cumulative contribution rate of eigenvalues is obtained by , = 1, 2, , n. If , we choose the first principal components given by where , and is the element of the jth eigenvector . Step IX: principal component scores. By substituting the standardized data into equation (8), we obtain the scores of the first principal components. Through the principal component score of each geochemical element content, we can obtain the comprehensive scores of elements. The comprehensive score of the principal component is given by where , = 1, 2, , k. Step X: obtaining the distributions of geochemical element anomalies. When the comprehensive information on geochemical element contents is obtained, we use the kurtosis method to estimate the threshold and the moment method to estimate the shape parameter and scale parameter of the GPD. Then, the GPD of the anomalies of geochemical elements is determined. Combined with the spatial coordinate position corresponding to the comprehensive information, the spatial distribution of the anomaly can be obtained by using MapGIS 6.7 [10]. Step XI: according to the distribution laws of single element anomalies, comprehensive element anomalies, and ore-forming geological conditions, we can predict the specific locations of deep minerals.
In a word, the designed GPDA model of deep mineral prediction fully considers the characteristics of the tail distribution of geochemical element anomalies and ore bodies composed of many geochemical elements. As the distribution of a geochemical element anomaly is consistent with the GPD when data are greater than a certain threshold, it is feasible to extract geochemical anomalies using the GPD. Moreover, the kurtosis method can be used to estimate the threshold of the sample data applicable to all the sample data with a tail distribution. Another advantage is that the threshold estimated by the kurtosis method is a fixed value; this avoids the problem of not knowing which interval to choose when there are two increasing intervals by using MEF to estimate the threshold. This paper also uses a diagnostic test to determine whether the theoretical distribution of the GPD is consistent with the tail distribution of actual data. If distributions are inconsistent, the revised threshold and parameters of the GPD for geochemical element contents are estimated. There is another advantage in that the comprehensive information of elements is extracted through PCA, and the GPD is used to obtain the distribution of elements, which avoids the shortcomings of deep mineral prediction from single element information. This study selected an actual mining area for the GPDA model application test, and the results demonstrated that the designed GPDA model is reasonable.
4. Application of the GPDA Model in Deep Mineral Prediction
4.1. Data Preparation and Basic Analysis
To verify the effectiveness of GPDA, the model was applied to predict deep minerals in the Jiguanzui Cu-Au mining area in Hubei, China. The study area is located at 114°54′42″–114°55′45″E and 30°04′45″–30°05′50″N. The mining area is a quaternary-concealed deposit with rich mineral resources, including copper ore, copper gold ore, and gold sulfur ore. The minerals of the study area form a variety of geochemical anomalies with Ba, Pb, As, Cu, Au, Mo, Co, and Zn and their combinations. The characteristics of geochemical elements are similar to combination characteristics of element contents of magmatic rocks and are quite different from the characteristics of element contents of carbonate rocks, an indication that the ores of the study area come from magmatic rocks. The axial zoning of ore-forming elements forming minerals is very clear. Ba, Pb, and As are front halo elements, Cu, Au, and Mo are near halo elements, and Co and Zn are tail halo elements of ore bodies. As of December 24, 2021, ore bodies I, II, III, and VII are four main ore bodies that have been explored in the study area, generally being distributed in the direction of 30° northeast, arranged in an echelon, inclined to the northwest, and in some places dipping to the south (Figure 2).
Ore body VII is the main ore body in the study area, and there is still great prospecting potential at present. Therefore, the study data with Ba, Pb, As, Cu, Au, Mo, Co, and Zn originate from 26 exploration lines in the ore body VII area. We selected 36717 sample data of different depths for each element; the basic statistical analysis of element contents is shown in Table 1. The skewness of geochemical elements is greater than 0, and thus, they are not normally distributed. The kurtosis values of element contents are greater than 3; it is also shown that they are not normally distributed; i.e., they are distributed as a back tail distribution. Thus, the designed GPDA model in this paper can be used for data processing. In the stratum, the vertical anomaly intensity relationship between various geochemical element contents with the change in depth is shown in Figure 3. In Figure 3, it can be seen that the vertical anomaly intensity of geochemical elements does not increase or decrease linearly at different depth positions, but there are different forms of changes, which indicates that there is a multistage hydrothermal superposition phenomenon in the deposit. Based on the abovementioned reasons, we can conclude that there is an ore body hidden deep in the earth.
4.2. Determining Thresholds and Parameters of GPD
Since geochemical element contents obeyed the rear tail distribution, we used the kurtosis method to obtain the thresholds of Ba, Pb, As, Cu, Au, Mo, Co, and Zn, which were 457.8612, 56.1823, 28.8454, 910.1272, 89.4283, 34.5267, 84.9445, and 121.4863, respectively, and used the moment estimation method to estimate the shape parameter and the scale parameter of GPDs for geochemical element contents. The estimation results of thresholds and parameters are shown in Table 2.
After the threshold and shape parameter and scale parameter of the GPD were determined, we applied them to (1). The GPDs of Ba, Pb, As, Cu, Au, Mo, Co, and Zn are as follows:
To determine whether the thresholds of the GPD for geochemical element contents were reasonable, diagnostic tests using P-P plots were used to show the rationality of selection thresholds. The results of fitting diagnostic tests using the P-P plot are shown in Figure 4. We found that all the actual distributions of geochemical element contents beyond their thresholds were near straight-line functions of theoretical distributions, demonstrating that the designed GPD model was effective for geochemical element content processing, and the estimated thresholds and parameters were reasonable.
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4.3. Distribution Law of Single Geochemical Element Abnormalities
When the thresholds of geochemical element contents are determined, all values of data greater than their thresholds are identified as anomalies of geochemical element contents. Combined with spatial coordinate positions, the distribution area of geochemical element contents was obtained by MapGIS 6.7, as shown in Figure 5. There are currently seven mining drill holes, i.e., ZK02618, KZK23, KZK10, KZK11, KZK28, ZK02619, and ZK02620, in the exploration of ore body VII. From Figure 5, it can be seen that front halo elements Ba, Pb, and As were enriched in the upper and lower parts of the ore body, corresponding to the distribution of front halo elements. This shows that the anomaly distributions of front halo elements followed the abnormality distribution, indicating that there are blind ore bodies deep in the earth. The tail halo elements Co and Zn were enriched not only at the bottom but also in the upper part of ore body VII, indicating that the ore body has multistage metallogenic characteristics. This also shows that there are new ore bodies deep in the earth. The abnormality distributions of near halo elements Au, Cu, and Mo indicate the rich location of ore body VII, and there is a strong enrichment phenomenon below the ore body, indicating that the body has a downward extension, further indicating that there is a blind ore body deep in the earth.
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4.4. Comprehensive Information of Geochemical Element Contents
After the distribution area of a single element is determined, we can obtain the comprehensive information on geochemical element contents by using PCA. Calculations of the correlation matrix of standardized data for geochemical element contents are shown in Table 3. The correlation coefficients of Cu and Au and Cu and Mo were 0.3937 and 0.334, respectively. The correlation coefficients of Au, Mo, and Cu were high because all were near halo elements, a result that was consistent with distribution near ore body VII by using the GPD. The correlation coefficient of Ba and Co was −0.5373, the correlation coefficient of Pb and Zn was 0.3442, and the correlation coefficient of Co and Zn was 0.3442. Ba, Co, and Zn also were highly correlated, reflecting the coexistence of front halo elements Ba and Pb and tail halo elements Co and Zn, consistent with the GPD.
The eigenvalues and eigenvectors calculated from Table 3 are shown in Table 4. The characteristic values in order are as follows: = 2.0565 > = 1.56 > = 1.1338 > = 1.0144 > = 0.7955 > = 0.5273 > = 0.4936 > = 0.0524.
Through , the cumulative contribution rate of the first five eigenvalues was 82%, greater than 80%.
Therefore, the first five principal components to extract the comprehensive information met the requirement of PCA for geochemical element contents. The expression of the first five principal components is as follows:
In (13), from the first principal component expression, it can be seen that the coefficients of Co and Zn were 0.521 and 0.4371, respectively, the largest coefficients, indicating that the main contribution of the first principal component is tail halo elements Co and Zn. The coefficients of Cu and Au were −0.5713 and −0.5679, respectively, in the second principal component expression, values greater than other coefficients highlight the contribution of near halo elements Cu and Au. The third principal component expression highlights the contribution of front halo elements Ba and Pb. In particular, the fourth principal component expression reflects the contribution of the front halo element As, and the fifth principal component reflects the contribution of the near halo element Mo. Through the coefficients of PCA, we conclude that front halo elements, near ore halo elements, and tail halo elements are well integrated, a result that conforms to the distribution law of geochemical primary halo elements. As the main ore-forming element Mo is the single main contribution of the fourth principal component expression, the distribution of Mo has strong prospecting ability that corresponds to the strong anomaly area of Mo estimated, by using GDP, to be located between drill holes kzk10 and kzk11 at a depth of about 1100 m (Figure 4(f)). The results suggest that there may be a new blind ore body here. Therefore, we calculated the comprehensive scores of PCA for geochemical element contents and used the GPD to analyze whether the anomalies of all elements had strong enrichment at this location.
4.5. Distribution Law of Comprehensive Anomalies of Geochemical Element Contents and Mineral Prediction
When the principal component expression was determined, by substituting the standardized data of geochemical element contents into (10), we obtained the principal component scores , , , , and , as shown in Table 5. The comprehensive score of geochemical element contents was obtained by using (11). The principal component scores and comprehensive score of geochemical element contents are shown in Table 5.
The threshold value of the comprehensive score of geochemical element contents obtained by using the GPD was 0.4551. Combined with the anomaly values and the criteria that all values of the sample data are greater than the threshold and spatial coordinate positions of anomaly values, the comprehensive abnormal distribution area of geochemical element contents was obtained by using MapGIS 6.7 (Figure 6). The comprehensive anomaly distribution of geochemical element contents indicates the trend of ore body VII. The anomaly is located at about 1300 m below drill hole ZK02620 at the southeast extension end of ore body VII. The comprehensive anomaly distribution of geochemical element contents has strong abnormality enrichment, indicating the possibility of prospecting. At the ZK02620 final hole, through the exploration by the First Geological Brigade of the Hubei Geological Bureau in 2016, molybdenum ore and copper gold deposits were found at this location. The actual engineering verification is highly consistent with our predicted location, demonstrating that the designed GPDA model for deep mineral prediction presented in this paper is both practical and reasonable.
In addition, the comprehensive anomaly distribution of geochemical element contents has strong enrichment at a depth of about 1100 m between drill holes KZK10 and KZK11, where the anomaly of Mo also shows strong enrichment. This strong anomaly may be an extension of the molybdenum ore body under the drill hole ZK2620. From the profile of ore body VII (Figure 7), we can clearly see that there is rock mass between drill holes KZK10 and KZK11 at a depth of about 954 m. This corresponds to the occurrence of rock mass starting at a depth of about 1254 m below the drill hole ZK02620 and 1151 m below the drill hole ZK02619, and thus, there should be a lower contact zone of rock mass located at −1000 m in the middle and lower part of ore body VII. Therefore, we predict that there is a new ore body that is located at about 1100 m below ground level between drill holes KZK 10 and KZK 11 (Figure 7).
5. Conclusion
In this study, a GPDA model for deep mineral prediction was designed, considering the characteristics of tail distributions of anomalies for geochemical element contents and ore bodies that are composed of many geochemical elements. The GPDA model was successfully applied to deep mineral prediction in the Jiguanzui Cu-Au mining area in Hubei, China. The results of this study led to the following conclusions:(1)Using the characteristics of rear tail distributions, the GPD model was designed to extract anomalies of geochemical element contents. According to the kurtosis value of the normal distribution of the sample data being equal to 3 and the kurtosis value of the tail distribution of sample data being greater than 3, the estimated threshold of the GPD is established by the kurtosis method. Based on the characteristics of unbiased estimation via the moment method, the moment estimation method was used to estimate the shape parameter and the scale parameter of the GPD.(2)On the basis of the GPD model, PCA was introduced to establish the comprehensive anomaly zoning of geochemical element contents. Then, we designed a GPDA model for deep mineral prediction by using GPD and PCA. We used the diagnostic test of P-P plots to analyze the theoretical results of the GPD and the actual distribution of anomalies of geochemical element contents; a straight line indicates that the designed model is effective.(3)The designed GPDA model was successfully applied to the Jiguanzui Cu-Au mining area for mineral prediction. We obtained the single element abnormal distribution law and comprehensive abnormality distribution law of geochemical element contents, and the abnormality distribution law of geochemical element contents conformed to the trend of ore body VII. In the comprehensive strong anomaly area of geochemical element contents, through engineering drilling, we found that there were blind ore bodies, demonstrating that the designed GPDA model could predict mineral resources hidden deep in the earth. According to the GPDA model, the comprehensive anomaly distribution of geochemical element contents has strong comprehensive abnormal enrichment between two drill holes at a depth of about 1100 m.
Data Availability
The First Geological Brigade of the Hubei Geological Bureau provided the geological data. The data can be obtained from the corresponding author upon reasonable request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The authors are grateful to the First Geological Brigade of the Hubei Geological Bureau for providing the geological data. This study was supported by the National Natural Science Foundation of China (Grant No. 41672325), the Program of the Science and Technology Department of Sichuan Province (Grant Nos. 2021YJ0360, 2021YFG0170, and 23NSFSC1620), and the Scientific Research Project of Chengdu Technological University (Grant No. 2021ZR019).