Abstract
To improve the limitation associated with a single data set and obtain more comprehensive anomaly information, this paper adopts the adaptive weighting fusion and multifractal SVM method for radioactive exploration data processing. Firstly, the adaptive weighting fusion method was used to fuse various radioactive exploration data from the field, including ground gamma-ray spectrometry, thermoluminescence, and 210Po activity. Then, we compared and analyzed it against the anomalous results obtained from each method. It is observed that the adaptive fusion yielded a more comprehensive dataset, which effectively reflected the anomalous geophysical characteristics of radioactivity, thereby eliminating the need to map each method separately. Finally, the concentration-area (C-A) multifractal model was used to classify the supervised learning labels, 70% of the sampling point data were selected as the training data, and the SVM was executed to predict the favorable prospecting target area, and the prediction accuracy reached 82.7%. At the same time, a model has been established to analyze the spatial distribution characteristics of the abnormal radioactive ore body and infer the deep favorable ore-forming target area.
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Introduction
Radioactive geophysical exploration is an important branch of geophysics attracting the concerns remarkably. The methods of radioactive geophysical and geochemistry data exploration mainly include ground gamma-ray spectrometric surveys, thermoluminescence, geo-gas measurement, 210Po activity measurement, etc. Moreover, many scholars are using other geophysical methods to explore radioactive ore bodies1,2,3. Some research has also been done in the processing of radioactive exploration data4,5,6,7,8,9,10,11,12. Although a variety of existing radioactive data processing methods have certain guidance for finding radioactive minerals, these data processing methods are rather one-sided and fail to meet the current needs.
Multi-sensor data fusion techniques have received a lot of attention in recent decades due to the rapid development of technology and the continuous improvement of various information acquisition systems reflecting the same target body13. Multi-sensor data fusion processing techniques have been applied in many research fields such as economics, social sciences, medicine, agriculture, and geological disaster prediction14,15,16,17,18,19,20. Some advanced data fusion process techniques, including data fusion and machine learning, have been applied to geophysical exploration21.
The main idea of data fusion is to integrate multiple data into a new one, and the fusion result can obtain more reliable and accurate information than a single group of data22,23. Some scholars have argued that data fusion schemes can be divided into three levels: Low-level data fusion, direct fusion after simple pre-processing of the original data; Mid-level data fusion, extraction of data features and then fusion; High-level data fusion, combined with data classification prediction, etc14,15,24. Azcarate et al. elaborated on the structure of data fusion levels, arguing that low-level data fusion has the advantage of simplicity and intuition, and in some cases, low-level fusion may provide better results14. The adaptive weighting fusion algorithm is an effective and widely used approach for low-level data fusion25.
The adaptive weighting fusion algorithm has garnered significant attention as a simple and efficient data fusion method that does not require prior information and achieves a low mean square error26. An adaptive weighted fusion algorithm based on minimum mean square error has been used to improve the accuracy of a machine-ranging system27. A real-time adaptive weighted fusion algorithm28 is implemented to process mine gas concentration data containing redundant information to obtain more accurate information. Another adaptive fusion scheme29 integrates the different mine environmental monitoring information with redundant residual information and obtains more accurate monitoring information to improve the safety of coal mines. Xu and Lu proposed an approach that automatically determines weighting coefficients without manual intervention, achieving lower error rates in image classification and recognition30. A data-level fusion scheme based on adaptive weighting and support degree, and the weighting coefficients were reconstructed to reduce the error of similar sensor data, and more accurate greenhouse environmental quality data were obtained31. Given the direct impact of weight values on the accuracy of results, determining optimal weights is critically important. Hao et al. discussed the fuzzy relationship of multi-sensor data, introduced the logarithmic function to represent the relationship between signal data32and obtained the optimized adaptive weight value based on the fuzzy relationship thus making the calculation results more accurate. Meng et al. improved the random adaptive weighting fusion theory to adjust the relationship between historical data and current data to obtain fusion results closer to the true value33.
Vapnik proposed support vector machines (SVM), a method based on statistical learning theory34which has been widely applied across various fields35,36,37,38,39,40,41. SVM is a supervised machine learning algorithm, which can analyze data efficiently and has attracted extensive attention from scholars. While most supervised learning methods require large amounts of training data, SVM is uniquely suited for accurate predictions with small sample sizes. Its final decision boundary is determined by only a few support vectors. Support vector machines can effectively process nonlinear data, and use kernel function to project low-dimensional indivisible nonlinear data into high-dimensional linear divisible space. Therefore, the SVM is also widely applied in the field of earth science42,43,44,45,46,47.
This paper mainly focuses on radioactive geophysical data collection in the study area such as ground gamma-ray spectrometric, thermoluminescence, and 210Po activity. The adaptive data fusion method is applied to process the adopted radioactive data and discuss the characteristics of radioactive geophysical anomalies. Finally, the multifractal method is adopted to formulate data labels and establish a model to discuss the spatial distribution characteristics.
Theory methods
Adaptive weighting fusion
The model of adaptive weighting fusion is shown in Fig. 129,32,33. There are n (n ≥ 2) radioactivity measurement instruments with relative weight \({\omega _n}\), and the optimal weight value of each instrument is obtained by the adaptive method for the measurement value of each instrument under the minimum total mean square error, and the optimal fusion result \(\hat {x}\) is finally calculated.
Adaptive weight fusion satisfied expression (1).
Since \({x_1}\), \({x_2}\),…, \({x_n}\) are independent of each other and are unbiased estimates of the true value x of the radioactive data, the total mean square error \({\sigma ^2}\) can be expressed as Eq. (2).
where \(\sigma _{i}^{2}\) is the variance of the measured values.
The adaptive weighting fusion algorithm is optimal when the total mean square error is minimized, and the corresponding radioactive instrument weight \({\omega _i}\) is optimal when the total mean square error \({\sigma ^2}\) is minimized. Thus Eq. (3) can be obtained by solving Eq. (2) according to the principle of multivariate function for extrema.
The minimum mean square error can be expressed as Eq. (4).
Hence, the estimated value can be expressed as
Variance calculation for each instrument
Generally, the device variance can be calculated from the measured values of each sensor. There are two independent instruments A and B. The measured values are \({x_a}\) and \({x_b}\), and their corresponding observation errors are \({e_a}\) and \({e_b}\), where \({e_a}\) and \({e_b}\) are zero mean stationary noise. The measured values can be written as
The variance of instrument A is given by
the cross-correlation function of \({x_a}\) and \({x_b}\) is \({R_{ab}}\). This is expressed as follows:
The auto-covariance function of \({x_a}\) is \({R_{aa}}\), which can be written as
Therefore, the variance of device A is
Let k be the number of measuring data of sensor, the estimated value of \({R_{aa}}\) be \({R_{aa}}\left( k \right)\), and the estimated value of \({R_{ab}}\) be \({R_{ab}}\left( k \right)\), so that
The \({R_{ab}}\left( k \right)\) of more than two instruments expressed as
where \({\bar {R}_{ab}}\left( k \right)\) is the mean value of the \({\bar {R}_{ab}}\left( {a \ne b,b=1,2 \cdots n} \right)\).
Based on the adaptive weight fusion method, this paper fuses the radioactive data obtained in the laboratory and analyzes the fusion effect. Firstly, two gamma radiometers, (device 1) and (device 2) were used to measure in the laboratory. The measurement interval of each instrument was 10 min, and each instrument measured 48 data. The measurement results of the instrument 1 are shown as the black curve in Fig. 2a, and the measurement results of the instrument 2 are shown as the blue curve in Fig. 2a. Based on the principle of adaptive data fusion, the two groups of data are fused to obtain the fusion result, as shown in the red curve in Fig. 2a. It can be seen from the figure that the adaptive data fusion curve not only synthesizes the characteristics of the two groups of data curves but also has a smaller amplitude fluctuation range than the two groups of data. It can be seen that using the adaptive data fusion method to assign the corresponding weight to the radioactivity measurement data of each instrument can get better and more reliable results.
The weight curves assigned by the adaptive fusion method for the measured data of two gamma radiometers are shown in Fig. 2b. After calculation, the sum of the weight values of the two instruments is 1, and the two curves gradually become flat with the increase of data, that is, the weight value gradually becomes stable with the increase of data, and the weight value of instrument 2 is higher than that of instrument 1. The results of the above simulation experiments show that the adaptive fusion method can effectively fuse radioactive data.
Support vector machine (SVM)
Support vector machine is a binary classification machine learning method46. SVM is based on two ideas: margin maximization and using a kernel function to classify nonlinear data48. The classification hyperplane function is shown as follows:
where w is the weight vector and b is the bias (threshold). The data label is 1 if f (x) > 0, and − 1 if f (x) < 0.
To find the optimal hyperplane we need to maximize the margin between the two sides of the hyperplane. However, this is a convex optimization problem, which is usually solved by introducing the Lagrange multiplier αi and transforming it into a dual problem by the Lagrange multiplier method, as shown
However, geophysical data is nonlinear. When solving complex nonlinear classification problems, the classification hyperplane is optimized by soft margin:
where C is a penalty value for misclassification error. Therefore, the dual optimization problem can be formulated as follows
where K (x, y) is the kernel function. In this study, the Gaussian radial basis function kernel is selected as the classification kernel function of support vector machine, and the expression is as follows:
Field example
Result of adaptive weighting fusion
The geological map of the research area in this work is shown in Fig. 3. The research area lies in northern Lujing, a significant granite-type uranium ore field in northern South China49,50,51. The outcrop beds in the study area are mainly Cretaceous and Cambrian. The main lithology of the Cretaceous is red sand conglomerate. The Cambrian can be divided into Chayuantou Formation and Xiangnan Formation. The main lithology of the Chayuantou Formation is quartz fine sandstone, silty Slate, and quartz medium sandstone, while that of the Xiangnan Formation is carbonaceous Slate, carbonaceous limestone, and medium-fine blastic quartz sandstone. Most of the faults in the study area are NW trending and some are NE trending. In the study area, there are known mineral outcrops in Lihuakai and Longtou.
The ground gamma-ray spectrometric survey, 210Po activity measurement, and thermoluminescence measurement were mainly carried out in the study area. Six measuring lines, each 2000 m long and spaced 300 m apart, were established in the study area. A total of 237 effective data were collected by each method. The adaptive weighting fusion method was employed to integrate the three types of measurement data and generate a radioactive anomaly distribution map for the study area.
Geological map of the study area52. ( The map is made using ArcGIS10.1 software ( version: 10.1; URL link: https://www.esri.com).
Due to the different dimensions of data measured by ground gamma-ray spectrometric, 210Po activity, and thermoluminescence, there are big differences among the measured values. To reduce the influence of data with high values, Eq. (19) is first used to normalize the data53. The original data was converted to the range of [0,1], and then the standardized data were fused to draw the anomaly map of the radioactive anomaly plane in the study area, as shown in Fig. 4.
Figure 4a shows the anomaly diagram of ground gamma-ray spectrometric of eU. There are relatively high anomaly values in the Lihuakai area, with higher values extending towards the northeast, indicating a large area of significant radioactive anomalies. In the Longtou area, lower anomaly values and smaller affected zones are observed. Figure 4b displays the 210Po activity anomaly diagram. In the Lihuakai area, a large and high-value anomaly is observed, extending northeastward beyond the study area. In contrast, the Longtou area exhibits a smaller and lower-value anomaly. Figure 4c shows the thermoluminescence anomaly map. There is a larger radioactive anomaly area between Lihuakai and Longtou with a higher anomaly value. Combined with geological data, it can be seen that the anomalies of each radioactive method correspond to the mineral information, but only a part of the mineral information. Thus, each radioactive exploration method provides distinct anomaly distribution information, failing to uniformly and comprehensively reflect the anomalies of radioactive orebodies.
Figure 4d displays the anomalies in the study area obtained by fusing ground gamma-ray spectrometry of eU, 210Po activity, and thermoluminescence data. The fusion was conducted using the adaptive weighting method. The Lihuakai area exhibits a relatively high and extensive range of anomalous information, which extends towards both the northeast and southeast directions, with the northeastern extension reaching beyond the study area. The Longtou area displays a low-intensity anomaly with a limited range. Figure 4d integrates the abnormal information of ground gamma-ray spectrometric of eU, 210Po activity, and thermoluminescence method, and fuses different abnormal information to obtain an anomaly map, which corresponds well to uranium deposits. This suggests that individual maps for each type of exploration data may not be necessary in radioactive data processing. Instead, by fusing various radioactive exploration data, a single comprehensive map of radioactive anomaly isopleths can be produced, which effectively reflects the integrated anomalous information of radioactive ore bodies in the study area.
Multifractal SVM and Spatial analysis
In practical radioactive geophysical exploration, radioactive anomalies are typically weak and spread over large spatial ranges. The presence of overlying layers makes it challenging to extract information about deep radioactive ore bodies, posing a critical problem in anomaly detection. Many scholars have carried out related work in this aspect. Cheng et al. put forward the C-A fractal method, which can reflect the relationship of several parameters of study areas with their spatial information, and can effectively divide the background and anomaly54. Zuo et al. discussed the spatial distribution characteristics of geochemical anomalies by extracting weak anomaly information in the coverage area with the fractal method55,56. Asfahani used the fractal method to process radioactivity data, which was more obvious than the indication of shape to ore body compared with the conventional method57,58,59. Therefore, the multi-fractal method is used to process the adaptive weighting fusion result in this paper. The C-A fractal model, which relates the element concentration to the area enclosed by concentration contours by a power-law relation as follows54,60
where \(A\left( \rho \right)\) represents the area with concentrations greater than or equal to the contour value \(\rho\), v is the threshold, \({\alpha _1}\) and \({\alpha _2}\) are fractal dimensions, which are greater than zero. The area of different content ranges has a power-law relationship, which can be fitted by the least squares method in the log-log plot.
The fusion data is analyzed using a log-log scatter plot, and the least square method is applied to fit the data. The intersection of the resulting fitted lines is further analyzed for anomaly characteristics. The log-log relationship of fusion results in the study area after the C-A fractal processing is shown in Fig. 5. As shown in Fig. 5, the log-log scatter plot can be divided into five segments using the C-A fractal method. The range of anomalies is distinguished according to the intersection points of different fitted line segments, which is used as the data label. The anomalies are divided into 5 categories, and 70% of the measured points are selected as the SVM training data. As is well known, the classification performance of SVM models is greatly influenced by two key parameters (C and σ). The best C value is 31 and the best σ is 1.4 by cross-validation. The result of SVM classification in the study area is shown in Fig. 6a. According to the calculation results, the anomalies can be divided into the following parts: the fifth types are uranium deposits on the ground, the fourth types are abnormally high halos, the third types are abnormally low uranium halos, and both first and second types are considered as background fields. The accuracy of SVM classification prediction is 82.7%. However, SVM is a supervised learning method, so this paper uses the unsupervised learning method of hierarchical clustering to classify anomalies, as shown in Fig. 6b. There are obvious differences between SVM and hierarchical clustering in the classification of abnormal results. According to the processing results of the SVM in Fig. 6a, it is obvious that two abnormal areas are consistent with the mineral information. The Lihuakai area exhibits a relatively extensive range of anomalous information, which extends in both the northeast and southeast directions, with the northeastern extension reaching beyond the study area. At the same time, the anomaly range in the Longtou area is small. Clustering is the process of grouping objects with similar characteristics61,62. According to the clustering results in Fig. 6b, it is found that the second type of anomaly distribution in the study area is almost continuous, and most of these anomalies are consistent with the distribution of faults or near the fault structure. Therefore, according to the above content, SVM anomalies are consistent with mine site information, while the hierarchical clustering method is more sensitive to faults.
Radioactive elements in uranium ore have the characteristics of decay, and its decay daughter radon is a gas, that is more likely to propagate along fault and fracture zones, so the spatial latitude of radioactive anomaly distribution is large. According to the propagation characteristics of elements, the power law attenuation behavior is considered in this paper. Anomalies were defined as patterns around sources with different buried depths60,63. The simulation calculation as shown in Eq. (21), and model parameters in Table 1, result is shown in Fig. 7.
where P is the simulated value, h is the buried depth, C is constant, (x, y) is the location of the center of the anomaly source.
It can be observed that abnormal body 2 with a larger buried depth presents weak anomaly characteristics, while abnormal body 1 with a shallower buried depth presents a high anomaly. According to the model forward modeling, due to the different buried depths of ore bodies, the abnormal value of the deep ore body is lower, while the abnormal value of the shallow ore body is higher than that of the deep ore body. Figure 8 presents the measurement profile curve for anomaly bodies 1 and 2. The abnormal value of the shallow burial depth changes rapidly, and the large burial depth changes gently.
Combined with the simulation results of the theoretical ore-body element diffusion model and the abnormal results of SVM processing of radioactive data in the study area, it can be concluded that: The first and second types of anomalies are the background field, and the third type of anomaly is the abnormal high halo. The anomaly associated with the deep ore body is identified as a key area for future deep ore prospecting. The fifth type of anomaly is the uranium deposits, and the fourth type may be the high anomalous halo formed by the weathering and migration of the surface uranium ore.
Discussion
In this paper, the data of ground gamma-ray spectrometry of eU, thermoluminescence and 210Po activity were analyzed. Regarding abnormal results, each method can reflect the abnormal characteristics of uranium deposits in the study area, with relatively high anomalies primarily distributed in the northern part of the study area. However, the anomaly results were inconsistent. The abnormal range of ground gamma-ray spectrometric of eU (Fig. 4a) is extensive, with the relatively high abnormal area situated in the northeast direction of Lihuakai and extending to the outside of the study area. The range of the 210Po activity anomaly (Fig. 4b) is smaller than that of the ground gamma-ray spectrometric of eU, and the area with the highest anomaly is located in the Lihuakai region. The thermoluminescence anomaly (Fig. 4c) was found between Lihuakai and Longtou. To comprehensively analyze the abnormal characteristics of the study area, the adaptive data fusion method was employed to combine the ground gamma-ray spectrometric of eU, thermoluminescence and 210Po activity. The fusion results show that the comprehensive abnormal information in the study area can be extracted. To predict the mineral prospectivity target area, the C-A multifractal model is used to handle the adaptive fusion results, and the supervised learning label is developed to classify the anomalies into five categories. Additionally, SVM is utilized to differentiate the background field, uranium deposits and ore-forming potential areas within the study area.
Based on the research, the adaptive weighting fusion27,28 and multifractal SVM have achieved excellent results. The adaptive fusion method is based on the minimum mean square error without prior information26. Although the adaptive fusion results can comprehensively reflect the anomaly distribution and highlight some anomaly areas, the weak anomalies that may be caused by buried sources are not apparent, and these ore bodies may be ignored. Distinguishing prospective from non-prospective areas constitutes a typical classification problem64which can be addressed through machine learning methods. However, it is difficult to develop labels in machine learning. Cheng et al. put forward the C-A fractal method, which can reflect the relationship of several parameters of study areas with their spatial information, and can effectively divide the background and anomaly54. Therefore, the C-A multifractal model was used to analyze the fusion data by log-log scatter plot, and the least square method was used to fit the data. The labels were developed based on the fitting results. Such labels could better distinguish the background and anomalies in the study area65. At the same time, it could enhance the weak anomaly information from deep favorable ore-forming targets60. According to the results based on adaptive weighting fusion and multifractal support vector machine (Fig. 6a), the prospecting area corresponds to the abnormally high value and fault intersection area. However, due to the influence of fractal fitting results, the anomaly range is extensive, so the fitting result should be improved as much as possible when fitting the fractal log-log scatter plot. In addition, the element diffusion model of orebodies with different buried depths was established to simulate and analyze the metallogenic prospect area. In future research, it is necessary to add information such as fault to improve the model.
Conclusions
In this paper, the adaptive weighted fusion method is used to fuse three kinds of ground gamma-ray spectrometric, 210Po activity, and thermoluminescence data, and the comparison with the abnormal results of each technique. The result shows that a set of comprehensive anomalies can be obtained by adaptive fusion, and the anomaly distribution map can comprehensively reflect the abnormal characteristics of each radioactive exploration method. It is not necessary to draw an anomaly map for each exploration data separately and a single anomaly map can comprehensively reflect the anomaly information after data fusion. The weight value gradually becomes stable with the increase of data. The adaptive weighted fusion method can effectively fuse the radioactive data.
At the same time, the multi-fractal method is used to formulate five types of labels for the abnormal characteristics of radioactive ore bodies, and the SVM method is used to predict the mineral prospectivity target area. In this paper, 70% of the data in the study area were selected as the training data of SVM, and the optimal parameters c and σ are 31 and 1.4 according to cross-validation. The final accuracy was 82.7%. A model is established to discuss the spatial distribution characteristics of radioactive anomalies. The multi-fractal method is used to analyze the latitude of the anomaly characteristics of radioactive orebodies, to predict the favorable prospecting target area in deep. Combined with the abnormal results of SVM processing of radioactive data in the study area and the simulation results of the theoretical orebody element diffusion model, it can be concluded that the third type of anomaly in Fig. 6a. May be the abnormal high halo related to deep orebodies, which is the key area for deep prospecting in the future. In summary, satisfactory results are obtained by using adaptive weighting fusion, however, only the measurement data of ground gamma-ray spectrometric, 210Po activity, and soil thermoluminescence are used for fusion processing. In radioactive geophysical exploration, these data are generally considered to reflect shallow anomalies. Therefore, data reflecting deeper anomaly information such as geo-gas will be added for fusion processing in the future.
Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request.
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Funding
This study was financially supported by the National Natural Science Foundation of China (41574102, 41774134, 42274235), Open Fund of Fundamental Science on Radioactive Geology and Exploration Technology Laboratory (No. 2022RGET17), Doctor Start-up Fund of East China University of Technology (No. DHBK2019086) and Science and technology research of Jiangxi Provincial Education Department (No. GJJ2200705).
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W.L., P.H., Y.Y., and Q.L. discussed the data and developed the concept for this study. W.L., P.H., and Y.Y. designed this study. W.L. P.H. and Y.Y. wrote the original draft. J.N. X.H. H.Y. and T.P.B revised the original draft.
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Lv, W., Huang, P., Yang, Y. et al. Radioactive geophysical processing and spatial anomalies analysis based on adaptive weighting fusion and multifractal SVM. Sci Rep 15, 22626 (2025). https://doi.org/10.1038/s41598-025-07676-1
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DOI: https://doi.org/10.1038/s41598-025-07676-1