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The Hadamengou gold deposit, located on the northern margin of the North China Craton, represents one of the region‘s most significant gold mineralization clusters. However, exploration in its deeper and peripheral sectors is constrained by ecological protection policies and the structural complexity of the ore-forming systems. Multivariate analysis combined with multi-model integration provides an effective mathematical approach for interpretating geochemical datasets and guiding mineral exploration, yet, its application in the Hadamengou region has not been systematically investigated. To address this research gap, this study developed a pilot framework in the key Buerhantu area, on the periphery of the Hadamengou metallogenic cluster, applying and adapting a multivariate-multimodel methodology for mineral prediction. The goal is to improve exploration targeting, particularly for concealed and deep-seated mineralization, while addressing the methodological challenges of mathematical modeling in complex geological conditions. Using 1:10,000-scale lithogeochemical data, we implemented a three-step workflow. First, isometric log-ratio (ILR) and centered log-ratio (CLR) transformations were compared to optimize data preprocessing, with a reference column (YD) added to overcome ILR constraints. Second, principal component analysis (PCA) identified a metallogenic element association (Sb-As-Sn-Au-Ag-Cu-Pb-Mo-W-Bi) consistent with district-scale mineralization patterns. Third, S-A multifractal modeling of factor scores (F1–F4) effectively separated noise, background, and anomalies, producing refined geochemical maps. Compared with conventional inverse distance weighting (IDW), the S-A model enhanced anomaly delineation and exploration targeting. Five anomalous zones (AP01–AP05) were identified. Drilling at AP01 confirmed the presence of deep gold mineralization, and the remaining anomalies are recommended for surface verification. This study demonstrates the utility of S-A multifractal modeling for geochemical anomaly detection and its effectiveness in defining exploration targets and improving exploration efficiency in underexplored areas of the Hadamengou district.
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1. Introduction
The Hadamengou gold deposit, one of the largest mineralization clusters along the northern margin of the North China Craton, has been systematically explored for over three decades, with most near-surface ore bodies already delineated. Identifying concealed and deep-seated mineralization has thus become essential for advancing China’s new strategic mineral exploration initiatives. As a key tool in mineral exploration, geochemical prospecting faces growing challenges in geologically complex settings, highlighting the need for more accurate and effective methods to delineate geochemical anomalies [1,2].
In recent years, mathematical approaches have been increasingly integrated into geoscientific research. Among them, the spectrum-area (S-A) multifractal model [3,4] has proven particularly effective in detecting and characterizing weak geochemical anomalies under cover, and has been successfully applied in diverse mineral exploration contexts [5,6,7,8,9,10,11]. For instance, Mao et al. [12] applied the S-A model in the Jiaoxi area, delineating high-intensity, spatially continuous anomalies controlled by NE-trending subsidiary faults, thereby highlighting the role of secondary structures in localizing mineralization. These findings revealed intrinsic relationships between geochemical anomaly distribution and mineralization in complex and provided a robust framework for understanding regional metallogenic processes and guiding deep exploration. Similarly, Wei et al. [13] demonstrated that the S-A model outperformed conventional geochemical methods in the Zhangbaling-Guandian area by effectively filtering background noise and delineating reliable Au targets beneath cover. In addition, Cheng Qiuming [14,15] integrated multifractal geochemical modeling with three-dimensional structural modeling in the Jiaoxi district, successfully resolving anomaly–fault relationships and offering valuable guidance for deep mineral exploration.
Collectively, these studies confirm the effectiveness of the S-A multifractal model in identifying concealed ore bodies and predicting undiscovered deposits. Although the Hadamengou area is a well-studied and mature gold metallogenic cluster, the current processing and interpretation of geochemical data largely rely on simple statistical treatment followed by the application of inverse distance weighting (IDW) to generate anomaly maps. This approach presents several limitations: (1) the delineated anomalies tend to be overly broad, reducing their effectiveness in constraining exploration targets and guiding subsequent field work; (2) the accuracy of anomaly identification remains insufficient, resulting in limited predictive reliability; and (3) the method fails to adequately characterize inter-element relationships, thus providing an incomplete representation of regional geochemical signatures. These issues collectively restrict the improvement of deep and concealed mineralization prediction in the area. Identifying new concealed mineralization in the deeper and peripheral sectors of this district is therefore of strategic importance for future exploration breakthroughs.
The Buerhantu area, located in the eastern part of the Hadamengou cluster, is characterized by sparse vegetation and good bedrock exposure, conditions favorable for lithogeochemical surveys. However, structural complexity and partial surface cover pose challenges for anomaly recognition. Previous studies using conventional methods, such as inverse distance weighting (IDW) interpolation or kriging [8], produced unsatisfactory results due to their limited ability to extract weak anomalies from complex background signals, thereby reducing exploration effectiveness.
To overcome these limitations, lithogeochemical datasets from the Buerhantu area were reanalyzed using an integrated workflow combining isometric log-ratio (ILR) and centered log-ratio (CLR) transformations, principal component analysis (PCA), and S-A multifractal modeling [16,17,18,19]. The objectives were to improve anomaly detection accuracy and provide a robust geochemical basis for further exploration in the district. The workflow comprised three main steps: (1) preprocessing 1:10,000-scale lithogeochemical data with ILR and CLR transformations to strengthen inter-element relationships and evaluate methodological performance; (2) applying PCA, supported by Q-Q plots and biplots, to identify ore-related geochemical associations, evaluate spatial patterns, and assess mineralization potential; and (3) employing S-A multifractal modeling to suppress noise and background effects, thereby improving anomaly delineation.
The application of this workflow fills a methodological gap in geochemical data processing within the Hadamengou area, and represents a clear advancement over previous approaches by incorporating a comparative assessment of ILR and CLR transformations—extending beyond the conventional multifractal modeling strategies commonly applied elsewhere. The introduction of a reference component effectively mitigated the inherent limitations of ILR transformation. During data processing, principal component analysis (PCA) was used to extract dominant geochemical factors, thereby enhancing data discrimination for classification modeling. This was followed by S-A fractal modeling, which further improved the accuracy of geochemical anomaly delineation and significantly reduced background noise. Collectively, this integrated methodological framework provides a more robust and reliable basis for predicting deep and concealed mineralization within the region.
Validation using surface mineralization evidence and drilling results further confirmed the reliability and exploration value of the identified anomalies. Overall, these findings establish a solid geochemical foundation for the Buerhantu prospect area and delineate promising exploration targets, offering new opportunities for breakthrough discoveries within the Hadamengou gold district.
2. Geological Setting
2.1. Regional Geology
The Wula Mountains-Daqing Mountains gold metallogenic cluster lies on the southern limb of the Wula Mountains-Daqing Mountains composite anticline, in the central-western Yanshan uplift along the northern margin of the North China Craton. It is bounded to the north by the NEE-trending Linhe-Jining fault zone and to the south by the Baotou-Hohhot fault zone [20,21] (Figure 1). Since the Archean, the region has undergone multiple tectono-magmatic events, including craton formation, continental accretion, and repeated subduction-collision processes. These geodynamic episodes produced extensive Precambrian strata, a complex structural framework, recurrent magmatism, and widespread metallogenesis. As a result, the area hosts diverse mineral resources including gold, iron, molybdenum, rare earth elements, coal, asbestos, and siliceous rocks [22,23,24,25,26,27,28,29,30]. The giant Hadamengou gold deposit, hosted within the Archean high-grade metamorphic belt, formed through multi-stage metallogenic evolution spanning from the Archean to the Mesozoic [31,32].
The Buerhantu area, located in the western part of the metallogenic cluster, forms an integral segment of the Hadamengou deposit. Regionally, it developed in a continental back-arc setting associated with oceanic plate subduction [35]. Its tectonic evolution records major geodynamic events, including the subduction-collision-closure of the Paleo-Asian and Mongol-Okhotsk Oceans, the subduction and rollback of the Paleo-Pacific Plate, and the subsequent destruction of the North China Craton [36,37]. The northern margin of the craton was assembled through the accretion of microcontinents, oceanic basins, and related magmatic arcs [38]. From Paleozoic to Middle Triassic, the tectonic regime evolved from a passive continental margin to an active continental arc, culminating in the amalgamation of the Xing’an-Mongolia orogenic belt [39]. Hydrothermal activity during the Hercynian and Yanshanian orogenies produced two principal mineralization stages in the district [33,40,41].
The study area lies within the Khondalite Belt between the Yinshan and Ordos blocks [42]. Exposed strata are dominated by the Neoarchean Wulashan Group, the Paleoproterozoic Sertengshan Group, and the Mesoproterozoic Bayan Obo Group. Ore-hosting units mainly include the first and second members of the first formation (Ar2wl1−1, Ar2wl1−2) and the first member of the second formation (Ar2wl2−1) of the Wulashan Group. Structurally, the area occupies the southern limb of the Wulashan composite anticline and is primarily controlled by the Urad Front Banner-Hohhot and Linhe-Jining fault zones. Secondary EW-, NE-, and NNE-trending faults act as major ore-controlling structures (Figure 2). Alkaline magmatism spans from the Hercynian to Yanshanian periods, represented by the Dahua’bei and Shadegai alkaline granite Hercynian plutons to the west and north, respectively, and along with numerous dikes of diabase, diorite porphyrite, granite pegmatite, and granite, most striking along EW, NE, and NNE orientations [43,44]. These intrusions are interpreted as heat and fluid sources, driving hydrothermal circulation and gold deposition within favorable structures.
In 2024, the Hohhot Institute of Geological Survey submitted newly identified gold resources totaling 41 t from the No. 100, No. 99, and No. 98 lodes, increasing the filed and approved resources of the Hadamengou mining area to 150.38 t Au. Within the Hadamengou segment of the Wulashan gold belt, auriferous lodes are distributed from west to east, including vein groups 313–314, 113 (incl. 14/8), 59, 51–55, 100, 99, 98, 268, 25, 28, 20, 24, 13, 32, 1, 2, 2-1, 3, and 207. In addition to the filed resources, 45.4 t of resources have been identified through preliminary exploration, and 76 t of potential resources are inferred from ongoing exploration efforts. Altogether, the Hadamengou district demonstrates a substantial resource potential approaching 272 t Au, highlighting the mining area as one of the key gold-bearing centers in the western North China Craton and indicating considerable capacity for further resource expansion (Table 1). Mineralization is hosted in Archean Wulashan Group rocks and is associated with a south-verging thrust nappe structure. Ore bodies are predominantly oriented EW, NE, and NNE, typically occurring within gneissic units of the Wulashan Group (Figure 3). Structurally, mineralization is controlled by dense networks of secondary faults, with EW-trending faults serving as the principal ore-hosting conduits, while NE- and NNE-trending faults mainly act as ore-breaching structures [45,46].
The Hadamengou-Buerhantu mineral cluster is characterized by widespread potassic-silicic alteration and well-developed quartz vein systems that host the majority of Au mineralization. The principal ore-bearing lithologies include potassic-silicified altered rocks and quartz veins, where K-feldspar, quartz, and plagioclase constitute the dominant mineral assemblages. Metallic minerals are mainly fine-grained native gold, associated with pyrite, chalcopyrite, hematite, electrum, galena, molybdenite, specularite, and limonite, accompanied locally by minor pyrrhotite, calaverite, petzite, covellite, and malachite. Gangue and alteration mineral assemblages include plagioclase, amphibole, quartz, epidote, chlorite, biotite, muscovite, sericite, calcite, and barite, with rutile, apatite, titanite, and zircon as accessory phases (Figure 4) [48].
Two distinct mineralization stages can be recognized: (i) an early stage dominated by K-silicified alteration and (ii) a later stage characterized by overprinting silicified quartz veins that significantly enhance gold enrichment [49,50,51]. Based on alteration assemblages and mineral chemistry, the Hadamengou gold system is interpreted as a medium- to low-temperature, alkaline magmatic-related hydrothermal deposit. This is supported by pervasive K-feldspathization, silicification, sericitization, and pyritization, all of which exhibit strong spatial relationships with Au-rich zones. Fluid inclusion and isotopic results further indicate a mixed magmatic-metamorphic fluid source and multi-pulse hydrothermal evolution, implying substantial potential for concealed mineralization at depth.
Regionally, the mineral cluster is located along the northern margin of the North China Craton, where granitoids (e.g., K-feldspar granite and syenogranite), mafic-ultramafic intrusions, and intermediate- to acidic volcanic rocks are widely distributed and temporally consistent with regional Au metallogenesis. Intrusive bodies in the district are mainly represented by the Dahubai and Degai plutons, composed predominantly of biotite granite, quartz diorite, and diorite [45], providing a favorable magmatic and structural framework for gold mineralization.
2.2. Landscape Features
The study area is located south of the Wulashan-Daqingshan watershed, along the southern margin of the central Inner Mongolia Plateau, forming a transitional zone between the mountainous terrain to the north and the Hetao Plain to the south. The northern boundary follows the southern slope of the Wulashan Range, where elevations range from 1100 to 1700 m. Drainage on the southern slope dominated by N–S-trending valleys, with subordinate near-EW orientations. Most streams are ephemeral, though several valleys maintain perennial flow, and flash floods are common during the rainy season (Figure 5).
Bedrock exposure is generally good, with Quaternary cover restricted to small, localized areas. Lithologies are easily distinguished in the field, primarily by color contrasts. Reddish rocks include quartz-K-feldspar veins, granitic pegmatites, K-silicified alteration zones, piedmont K-alteration belts, and biotite-hornblende syenitic gneiss enriched in potassic minerals. Dark-colored rocks are mainly biotite-hornblende plagioclase gneiss, diabase, and amphibolite, whitish rocks are dominated by granulite-facies units and plagioclase-amphibole gneiss.
3. Sampling and Methods
The workflow of this study consists of five main stages (Figure 6): Sample collection and acquisition of raw geochemical data, Data preprocessing, PCA and factor analysis, S-A multifractal modeling, and Geochemical mapping.
After obtaining the raw dataset, we first performed data preprocessing, a critical step that directly affects the reliability of subsequent analyses. While previous studies have primarily used CLR transformation, we applied both ILR and CLR methods. To address the dimensionality-reduction of ILR, we introduced a reference component to improve data stability and interpretability.
PCA and factor analysis were then conducted on both ILR- and CLR-transformed datasets for comparison. The results show that the ILR-transformed data more effectively captured inter-element relationships and clearly reflected mineralization-related elemental association in the study area. Therefore, the ILR-based factor analysis results were selected for further modeling. Based on these results, S-A multifractal modeling was performed. Through threshold segmentation, noise, background, and anomaly filters were established, and corresponding geochemical anomaly and background maps were generated.
Validation through comparative analysis of anomalous features indicates that the proposed workflow performed effectively in the Hadamengou area, producing significantly better geochemical interpretation and anomaly delineation results than conventional processing methods.
3.1. Rock Sampling and Chemical Analysis
The dataset used in this study was obtained from a 1:10,000-scale lithogeochemical survey. Sampling locations were recorded using a handheld GPS. Following standard protocols, samples were collected at 40 m intervals along lines spaced 100–150 m apart, yielding 1297 samples, with an average density of approximately 240 samples/km2. Each sample weighed more than 300 g (Figure 7). A professional GNSS handheld GPS device (Model G138BD, Beijing UniStrong Science & Technology Co., Ltd., Beijing, China) was used for sample collection. The instrument supports multi-constellation positioning (BeiDou, GPS, and GLONASS) and includes an integrated navigation module and antenna. Coordinate calibration was performed at known control points and drillhole locations previously measured using RTK instruments, ensuring positional accuracy within 1 m during the sampling process.
The analytical dataset included 15 elements: Cu, Zn, Pb, W, Mo, Sn, Bi, Sb, As, Au, Ag, Ni, Co, Cr, and TFe2O3 (total). Analyses followed national standards, including: (i) DZ/T0279.13-2016, Part IV: determination by fire assay-foam plastic enrichment-ICP-MS; (ii) DZ/T0279.13-2016, Part XI: Ag, B, and Sn by AC arc-emission spectrometry; (iii) DZ/T0279.13-2016, Part XIII: As, Sb, and Bi by hydride generation-atomic fluorescence spectrometry; and (iv) GB/T 14506.30-2010, Part XXX: determination of 44 elements in silicate rocks (Table 2).
3.2. Statistical Analysis and Methodology
The isometric log-ratio (ILR) and centered log-ratio (CLR) transformations are among the most advanced methods for processing compositional data in geoscience research. In this study, both ILR and CLR approaches were applied to preprocess the raw geochemical dataset.
The ILR transformation is both an isomorphism and an isometry; it constructs an orthogonal coordinate system through log-ratio balances based on orthogonal log-ratio coordinates, while preserving the original geometric structure of the data [52,53]. This method effectively eliminates the closure effect inherent in compositional data and ensures orthogonality. However, its implementation is computationally complex, as it requires a specific basis. Without an appropriate reference, one column of the original data may be lost, reducing dimensionality.
To address this limitation, a reference column (YD) with a constant value of 1.00 was added to the dataset prior to ILR transformation. After repeated testing, this approach was found to preserve all original data columns, minimize the effect of basis selection on data interpretation, and maintain the geometric structure.
The principle of ILR transformation can be summarized as follows: let x denote the geochemical dataset, where xi represents the concentration of the ith element (e.g., x1 = YD, x2 = Cu, x3 = Zn, etc.), m denotes the total number of elements, and k represents the kth column in the dataset.
Here, g(x) denotes the geometric mean, xj represents the group of elemental variables excluding xk, and YD is the reference column with a constant value of 1. The calculation formula is expressed as follows:
Given a composition x = (x1, x2,…, xD), xi > 0, SDi = 1, xi = 1, the explicit ILR formula is given by:
where each coordinate zj compares one part xj+1 with the geometric mean of the first j parts, the cj scale factor making coordinate orthogonal, while the log ratio ensures scale invariance (only relative proportions matter). Note that if SDi=1xi11 (case of major + trace elements), the compositional vector should be first normalized as S = SDi=1xi, yi = xi/S. Because the last entry of v is 0, v being the log of the augmented parts v = (ln x1,…, ln xD, 0), applying a contrast matrix H of size D’(D + 1) such as a Helmet matrix, z = Hv, is equivalent to applying an ILR basis to (x1, x2,…, xD), the 1 only serving as a dummy reference part.Although the ILR transformation is mathematically dependent on the ordering of the components, this effect was explicitly tested and controlled in this study. A dummy reference column (YD) with a constant value of 1.00 was inserted and fixed at the first position of the dataset before ILR transformation, ensuring a consistent orthonormal basis. Multiple element ordering tests were performed, and the extracted factors remained stable with minimal change in eigenvalues and factor loading patterns (<2%). Therefore, the influence of column ordering on the ILR orthogonal basis is negligible for the dataset used in this research.
The centered log-ratio (CLR) transformation divides each component by the geometric mean of all components, followed by logarithmic transformation. This centers the data around zero, facilitating subsequent statistical analysis. The method is computationally simple and easy to interpret; however, it depends on the chosen reference composition, which may introduce bias and does not preserve orthogonality in the transformed space. The principle of CLR transformation is as follows:
Let y denote the geochemical dataset, and yi represent the elemental concentration of the variable (e.g., y1 = Cu, y2 = Zn, etc.). Here, n is the total number of elements, and i corresponds to the column index of the original dataset.
Here, g(y) denotes the geometric mean, which is calculated as:
Before applying the ILR and CLR transformations, the geochemical data were treated as compositional data and normalized to satisfy the closure requirement. A constant reference column (YD = 1.00) was added and kept as the first component, ensuring that all variables were positive and expressed in a proportional relationship. Therefore, both ILR and CLR transformations were performed on closed compositions consistent with the simplex space, which eliminates the closure effect and allows valid use of PCA and factor analysis in Euclidean space after transformation.
3.3. Analytical Methods for Elemental Determination
Factor analysis is a widely used multivariate statistical technique in the geosciences. It reduces the dimensionality of large geochemical datasets while preserving their structure, enabling the identification of inter-element correlations. In this method, numerous variables are condensed into a smaller set of latent factors, whose significance is interpreted through the factor loading matrix [54,55,56].
In this study, factor analysis was applied to lithogeochemical datasets transformed using both isometric log-ratio (ILR) and centered log-ratio (CLR) methods to identify element associations related to Au mineralization in the Hadamengou district. A total of 15 geochemical elements from the ILR- and CLR-transformed datasets were analyzed. Assuming the dataset comprises n samples and p elements, the raw data matrix, L = [Lαβ], with α and β being the indices of row and column, respectively, the general formulation of factor analysis is expressed as the product of a factor loading matrix Λ and a factor score matrix F, as follows:
where Λ, the factor loading matrix derived from principal component analysis (PCA), can be expressed as follows:To enhance factor interpretability [57,58,59,60], the loading matrix Λ was rotated using the varimax method, yielding the rotated loading matrix Λ*. The number of factors retained was determined through the calculation of the factor score matrix, which also identifies groups of elements with strong internal correlations. The factor score matrix F is expressed as follows:
where L denotes the original data matrix, μ represents the mean of each elemental variable, Λ is the factor loading matrix, F is the factor score matrix, and ε is the error matrix, with the error terms are assumed to be independent and identically distributed normal random variables.3.4. S-A Multifractal Modeling Approach
The multifractal model has been widely applied in geological prediction, proving its effectiveness in delineating geological, geochemical, and geophysical anomalies [56]. The S-A model performs multifractal analysis in the Fourier frequency domain, capturing the anisotropic invariance of geofields. Due to the fractional power-law relationship in the frequency domain, S-A modeling transforms geological data via Fourier transformation, computes the power spectral density (PSD), and uses its spatial distribution to extract fractal characteristics [61,62]. This approach efficiently isolates geochemical signatures, distinguishing noise, background, and anomalies, while establishing quantitative relationships between spectral energy and area [63,64]. The general form of the S-A multifractal model is expressed as follows:
where A(S > ε) represents the area of the PSD exceeding a specified threshold, α is the proportionality constant, and β denotes the slope of the piecewise-fitted curve, which separates noise, background, and anomaly populations. After filtering, the processed spectral data are used to construct geochemical maps [65].The S-A multifractal model is conceptually related to factorial kriging (FK), which decomposes spatial variability into multiple scales using multi-variograms and explicitly accounts for spatial anisotropy—an aspect only partly addressed in the current S-A formulation. Proximity analysis, another multiscale method similar to FK, has also been successfully applied in geochemical and seismic data processing.
However, the S-A model offers several advantages: (i) efficient noise-background-anomaly separation in the Fourier domain through spectral power-law segmentation; (ii) fewer structural assumptions, avoiding subjective variogram modeling; and (iii) high computational efficiency for large regional datasets. Referencing FK and proximity analysis therefore provides broader methodological context while emphasizing the strengths of the S-A model for rapid, objective, and quantitative anomaly delineation [66,67,68,69].
4. Results
4.1. Data Quality Assessment Based on Uncertainty and Spatial Autocorrelation Results
To evaluate whether the geochemical sampling density and data quality are sufficient for identifying mineralization anomalies and supporting spatial prediction, statistical uncertainty and spatial structure analyses were performed for the main ore-related elements (Cu, Zn, Pb, W, Mo, Ag, Sn, Bi, Sb, As, Au, etc.) using all 1295 samples. The classical 95% confidence intervals of elemental means largely overlapped those obtained from 1000-iteration bootstrap resampling, and the differences between bootstrap means and original means were negligible. This indicates stable mean estimates and sampling errors, reflecting effective control of statistical uncertainty. Global Moran’s I values were generally positive (≈0.03–0.11), indicating a weak to moderate positive spatial autocorrelation (Table 3). Experimental variograms further showed well-defined spatial structures for most elements, with correlation ranges of ~2.1–3.3 km, substantially larger than the actual sampling spacing. Taken together, the statistical stability and spatial-structure characteristics confirm that the sampling layout is appropriate and the dataset is of sufficient quality to support factor-based geochemical modeling and S-A multifractal anomaly delineation. These results provide a strong foundation for reliable spatial prediction and targeting of concealed mineralization in the study area.
4.2. Factor Analysis
Factor analysis of the geochemical dataset from the Buerhantu area of the Hadamengou district was conducted using the ILR-transformed variables. Based on the total variance explained (Table 4), four principal factors were extracted, each contributing more than 10% of the variance, following the criteria of eigenvalues >1 and a cumulative variance contribution of 61%.
Factor analysis based on CLR-transformed variables was performed. According to the total variance explained (Table 5), four principal factors were extracted, each contributing more than 8% of the variance, following the criteria of eigenvalues >1 and a cumulative variance contribution of 63%.
Factor analysis based on simple ln-transformed variables was performed. According to the total variance explained (Table 6), four principal factors were extracted, each contributing more than 6% of the variance, following the criteria of eigenvalues >1 and a cumulative variance contribution of 57%.
In the study area, Au is the primary ore-related element of interest. To assess the effectiveness of different data transformation methods in mitigating the geochemical closure effect, both ILR- and CLR-transformed datasets were subjected to factor analysis. For the Buerhantu geochemical dataset, four principal factors were extracted in each case (Table 7, Table 8 and Table 9). Across the ILR-, CLR-, and ln-transformed datasets, the factor associations remained generally consistent, although the coherence among ore-related elements differed by methods. The ILR transformation yielded: F1 (Co-Ni-Cr; basement background), F2 (As-Sb-Sn-Bi; magmatic-hydrothermal), F3 (Au-Ag-Cu; main ore-forming), and F4 (Zn-Pb; distal alteration). The CLR transformation produced a similar structure but with slight differences: F1 (Co-Ni-Cr), F2 (W-Bi-Mo), F3 (Au-dominated), and F4 (TFe2O3-linked background variations). The ln-transformed data showed broadly comparable factor patterns, with clear metallogenic significance. F1 (Co-Ni-Cr-Zn-Cu) reflects mafic-ultramafic contributions and early base-metal enrichment; F2 (Bi-W-Mo-Ag) indicates fractionated granitic magmatism and volatile-rich hydrothermal fluids; F3 (Sb-As) represents low-temperature hydrothermal pathfinders; and F4 (Au) highlights localized gold enrichment linked to structurally-controlled mineralization.
Importantly, Au consistently appeared as the dominant element in the third factor across all three transformations, confirming its role as the primary mineralization indicator in the Buerhantu area. However, the ILR transformation revealed a stronger coupled association among Au-Ag-Cu, whereas CLR and ln transformations showed weaker correlations between Au, Cu and Ag. This indicates that ILR more effectively mitigates the closure effect and enhances recognition of true geochemical relationships, making it the most suitable method for delineating Au-related mineralization signatures.
Factor analysis of the geochemical dataset identified four principal factors: F1 (Co-Ni-Cr), F2 (Sn-Sb-As), F3 (Au-Ag-Cu), and F4 (Bi-W) (Figure 8, Figure 9, Figure 10 and Figure 11). The Co-Ni-Cr association reflects mantle-derived contributions and is closely related to mafic-ultramafic intrusions, consistent with the crust-mantle mixing model proposed for gold mineralization in the Hadamengou district. The Sn-Sb-As assemblage indicates the influence of highly fractionated granites and intermediate-acidic intrusions, and is indicative of low-temperature hydrothermal enrichment processes, aligning with the medium- to low-temperature gold mineralization style of the area [52].
The Au-Ag-Cu factor highlights the strong metallogenic association between gold and Cu-Ag sulfides, representing a key signature of Au-rich hydrothermal alteration. The Bi-W association reflects enrichment in intermediate to high-temperature magmatic or metamorphic hydrothermal fluids derived from cooling S-type granitoids or tectonically remobilized sources. Bi commonly correlates spatially coupled with Au in orogenic and intrusion-related gold systems due to their similar behavior in low-density hydrothermal fluids. Thus, pronounced Bi-W anomalies (F4) likely delineate structurally controlled mineralized corridors or intrusion-related disseminated ore zones, with variations in the Bi/W ratio potentially indicating proximity to hydrothermal conduits such as fault or intrusive contacts.
These covariance structures are more effectively preserved using isometric log-ratio (ILR) transformation than centered log-ratio (CLR) transformation. ILR provides clearer loadings for Au-related components, improving the discrimination of geochemical anomalies and enhancing the accuracy of mineral exploration targeting in this district.
Regionally, the characteristic geochemical association is Au-As-Sb-Hg, while within the ore district it is defined by Au-As-Bi-Hg. Rock geochemical profiles show an Au-Ag-Mo association, and the proximal halo is dominated by Au-Ag-Mo-Cu, consistent with the F3 factor association. The intermediate halo is characterized by As-Sb-Bi-Hg, corresponding to factors F2 and F4, whereas the distal halo comprises Zn-Co-Ni-W, aligning with factors F1 and F4. The Au-Ag-Cu assemblage (F3) reflects hydrothermal mineralization dominated by sulfides such as pyrite and chalcopyrite, which is structurally controlled by E-W-trending faults and intrusion-wallrock contacts; sulfides act as metal carriers during fluid cooling and precipitation, and the typical Au-Ag association in orogenic gold systems may also indicate potential Ag-Au mineralization [32,47,49]. Thus, the third principal factor (Au-Ag-Cu), dominated by Au, provides a strong basis for predicting mineralization in the Hadamengou-Buerhantu area and represents the most effective elemental association for delineating prospective targets (Figure 12).
4.3. Anomaly Identification Using S-A Multifractal Modeling
In this study, inverse distance weighting (IDW) interpolation was used to construct geochemical distribution maps for the four principal factors (F1–F4). These maps were then analyzed using S-A multifractal methods to further examine the geochemical patterns.
For each principal factor (F1–F4), S-A multifractal modeling was performed to generate log-log plots of spectral energy versus area (Figure 13). The S-A model identified threshold values partitioning the spectra into distinct domains. Based on thresholds, t reported in Table 10, three filters, representing noise, background, and anomaly components, were established and then used to generate geochemical anomaly and background maps. The spectral power density-area model originates from power-law analyses in geology and geochemistry, and therefore commonly employs base-10 logarithmic transformation.
The F1 elemental association (Co, Ni, and Cr) reflects a genetic link to mafic-ultramafic intrusions and mantle-derived processes, showing strong spatial correspondence with that of local titanomagnetite deposits. Using the S-A multifractal model, the spectral-area (S-A) relationship for F1 was fitted by least squares regression, yielding a three-segment partition: Log(S) < 3.096, 3.096 < Log(S) < 6.411, and Log(S) > 6.411, corresponding to noise, anomaly, and background domains, respectively.
The slopes of these segments, along with their coefficients of determination (R2) are reported in Table 10. These results indicate excellent fits for the noise and anomaly domains, while the background segment (R2 > 0.3) is acceptable but would benefit from additional data for refinement.
Geochemical maps were then generated, including the original geochemical distribution (Figure 14a), background-filtered map (Figure 14b), noise- and background-filtered anomaly map (Figure 14c), and the background map (Figure 14d). These maps revealed a general NE-trending pattern, with low background values in the northwest and higher levels in the southeast. The original map displayed extensive high-value anomalies in the southwest; however, after filtering noise and background effects, anomalous in the northwest were significantly enhanced, while spurious anomalies in the southwest—primarily caused by elevated background—were effectively removed. In contrast, anomalies associated with titanomagnetite mines in the south-central area became more distinct after filtering.
Regionally, gold is mainly hosted in pyrite and chalcopyrite. Thus, delineating F1 anomalies provides an effective means of distinguishing mineralization-related anomalies from those influenced by Fe mineralization, thereby reducing interference and improving the reliability of Au anomaly interpretation.
The F2 elemental association (Sn, Sb, and As) showed distinct geological significance. Tin is closely related to the widespread granitic pegmatites and the Dahua’bei and Shadegai plutons, whereas Sb and As form major components of the proximal geochemical halos around the Hadamengou gold orebodies, serving as reliable indicators of deep-seated gold mineralization.
Application of the S-A multifractal model to F2 data yielded a three-segment partition: Log(S) < 3.075, 3.075 < Log(S) < 5.899, and Log(S) > 5.899, corresponding to noise, anomaly, and background domains, respectively. The slopes and coefficients of determination (R2) are reported in Table 10 and Table 11. These results indicate that the noise and anomaly segments are well constrained, whereas the background segment is weakly fitted and may require additional data for refinement.
Filtered geochemical maps (Figure 15) highlight the spatial characteristics of the F2 association. The background distribution gradually decreased in intensity from the SSW toward the ENE. In the unfiltered geochemical map, high-value anomalies were widespread in the western part of the study area, largely reflecting background effects. After background correction, anomalies became more concentrated in the NW, SW, and locally in the eastern sector. These filtered anomalies showed a strong spatial correspondence with Au anomalies delineated by F3 (Figure 16), supporting the inference that Sb-As halos may indicate concealed gold mineralization at depth. Notably, the F2 factor highlights the genetic coupling between granitic magmatism and gold mineralization in the Hadamengou district.
The F3 elemental association (Au, Ag, and Cu) represents the principal ore-bearing assemblage in the study area. In the Hadamengou district, Au, Ag, and Mo form the dominant mineralization suite. Given its metallogenic importance, F3 was analyzed in detail using the S-A multifractal model. The results showed a three-segment partition (Table 10 and Table 11): Log(S) < 4.485, 4.485 < Log(S) < 6.247, and Log(S) > 6.247, corresponding to the noise, anomaly, and background domains, respectively.
The background distribution displayed a NW–SE-trending decrease in intensity, forming an en echelon pattern. In the unfiltered dataset (Figure 16), scattered anomalies within the belt were largely masked by elevated background values. Background correction effectively enhanced anomaly recognition in the NW sector, highlighting Au mineralization sites while eliminating spurious anomalies caused by the NW–SE high-background zone. In the SW anomaly belt, a mineralized site identified during 1:10,000-scale mapping was later confirmed by drilling. Although sample spacing along the S–N traverse was uneven due to topographic constraints, filtering of noise and background effectively reduced sampling bias.
The corrected anomaly maps clearly delineated two significant mineralized sites in the NW and SW sectors (designated P01 and P02 from south to north). In addition, a pronounced anomaly in the SE sector may indicate a concealed orebody, potentially representing the southern extension of the NW mineralization zone and thus defining a promising target area for further exploration.
The F4 elemental association (Bi and W) represents the principal halo assemblage in the distal zones of ore bodies. Its spatial distribution was compared with those of F2 and F3 to further constrain the extent of Au-related anomalies. Application of the S-A multifractal model yielded a three-segment division corresponding to noise, anomaly, and background, respectively (Table 10 and Table 11).
Bi-W background anomalies were particularly pronounced in the northern part of the study area, showing an east–west-trending enhancement. In the uncorrected geochemical maps, anomalies were mainly concentrated in the MN-NE sector. After background removal, these anomalies were significantly reduced in size, while two additional low-intensity anomalies emerged in the MS-SW region (Figure 17; Table 11).
To synthesize the geochemical patterns derived from factor analysis and S-A multifractal modeling, a comparative summary of the four principal factors (F1–F4) is presented (Table 10 and Table 11). The summary integrates element associations, geological significance, fractal parameters, and anomaly distribution characteristics, providing a concise overview of their metallogenic implications.
As shown in Table 6, the four extracted factors displayed distinct geochemical associations and geological significance. F1 (Co-Ni-Cr) represents mantle-derived contributions linked to mafic-ultramafic intrusions, consistent with the spatial distribution of magnetite in the study area. F2 (Sn-Sb-As) delineates mineralization fronts related to granitic magmatism and Au-pathfinder halos, implying the presence of deep-seated ore bodies. F3 (Au-Ag-Cu) corresponds to the main ore-forming assemblage, with strong anomalies that coincide with known mineralization (P01 and P02) and further highlight concealed exploration targets toward the southeastern sector. F4 (Bi-W) defines distal hydrothermal halos, improving the delineation of Au anomalies and enhancing the discrimination of background geochemical variation.
Enrichment in Bi and W (often accompanied by Zn) is characteristic of intermediate- to relatively high-temperature hydrothermal fluids sourced from magmatic systems (e.g., cooling S-type granitoids with muscovite and garnet) or from metamorphic fluid remobilization, reflecting their similar transport behavior. Bi commonly accompanies Au in intrusion-related and orogenic gold systems due to their compatibility within low-density hydrothermal solutions. Thus, pronounced Bi-W anomalies associated with F4 may indicate structurally controlled Au-bearing veins or disseminated ores along fault corridors or intrusive contacts, where the Bi/W ratio may serve as an indicator of proximity to fluid conduits.
The Au-Ag-Cu factor (F3) reflects sulfide-dominated hydrothermal mineralization (e.g., pyrite, chalcopyrite), mainly controlled by E–W-trending structures and lithological contacts. These sulfides act as major metal carriers during hydrothermal fluid cooling and precipitation. The close Au-Ag association also suggests the possible presence of electrum, a typical feature of both orogenic and intrusion-related gold deposits.
Overall, S-A multifractal modeling effectively separates noise, background, and anomaly populations, greatly reducing the masking effects of high background values. This enhances the visibility of ore-related anomalies and provides a robust geochemical basis for target delineation. The results emphasize the dominant metallogenic role of F3, with F2 and F4 serving as auxiliary indicators constraining the extent and distribution of Au mineralization, offering valuable guidance for further exploration in the Hadamengou district.
5. Discussion
5.1. Comparison Between ILR and CLR Data Preprocessing Methods
Geochemical datasets are inherently complex and heterogeneous, making their processing and interpretation subject to uncertainty and bias. Accurate delineation of geochemical anomalies and background populations is essential for constraining anomaly distribution and improving exploration efficiency. In the study area, the southern sector is largely covered, whereas bedrock exposure elsewhere remains relatively good, providing favorable conditions for geochemical anomaly identification. However, the structurally complex framework and deep faulting present significant challenges for sample collection. Therefore, minimizing the effects of sampling-bias and environmental noise during data processing is crucial to ensure the reliability of geochemical interpretations.
Effective separation of geochemical anomalies from background signals remains a major challenge. As shown in Section 4.2 and Section 4.3, the study area has experienced multiple magmatic events. the widespread presence of lenticular iron ore bodies, granitic pegmatites, various dikes, and other geological features has produced overlapping geochemical anomalies, while cover sequences further obscure anomaly signatures. Consequently, conventional geochemical processing methods, such as inverse distance weighting (IDW) interpolation (Figure 18), tend to identify only broad anomaly zones, failing to resolve discrete mineralization-related targets. With the growing demand for precision and accuracy in modern mineral exploration, such traditional approaches are no longer adequate for identifying predictive targets suitable for engineering validation. This study, therefore, proposes an improved anomaly-background separation strategy tailored to the geochemical characteristics of the Hadamengou-Buerhantu area.
In this study, geochemical data were preprocessed using isometric log-ratio (ILR), centered log-ratio (CLR), and simple ln-transformed datasets. Compared with CLR, the ILR approach requires selecting a component, which inevitably results in the loss of one data dimension. To mitigate this limitation, repeated tests showed that introducing an additional column (YD) as the reference effectively compensates for the dimensional loss without compromising data integrity or altering the overall structure.
Subsequently, the preprocessed datasets were analyzed using principal component analysis (PCA). As shown in Section 3.1, the ILR-transformed dataset produced more robust and geologically consistent interpretations than the CLR-transformed dataset. Specifically, the ILR-based analysis identified: F1 (Co, Ni, Cr), associated with lenticular iron ore and ultra-depleted magnetite; F2 (Sn, Sb, As), indicative of a geochemical halo preceding Au mineralization; F3 (Au, Ag, Cu), representing the primary ore-forming assemblage; and F4 (W, Bi), corresponding to the distal geochemical halo of Au mineralization. Collectively, these results define a composite geochemical association (Sb-As-Sn-Au-Ag-Cu-Mo-W-Bi) consistent with the known mineralization characteristics of the study area.
The factor analysis results were further integrated with S-A multifractal modeling to construct geochemical maps. Compared with conventional methods, the S-A fractal filtering significantly refined the anomaly boundaries and effectively removed noise and background signals, thereby improving spatial resolution and anomaly clarity.
In summary, introducing the YD reference column, the ILR transformation preserves data orthogonality and mitigate the closure effect inherent to compositional datasets, without reducing dimensionality. Compared with CLR, ILR maintains stronger mathematical and geometric consistency, enhances accuracy, and minimizes interference among individual elements during factor analysis, yielding more reliable factor associations and element groupings.
5.2. Optimization of Prominent Anomalies and Recognition of Subtle Anomalies
In conventional geochemical exploration, interpolation results are strongly influenced by the spatial distribution and density of sampling points. The commonly used inverse distance weighting (IDW) method often produces artifacts such as blank zones or spurious extreme values. Improper interpolation can obscure the true character of anomalies, while edge effects further increase uncertainty in sparsely or unevenly sampled areas. Traditional methods typically display only one or two elements per map, requiring multiple map overlays for interpretation and reducing efficiency. In addition, fluctuating background values can bias geological interpretation, making it difficult to detect subtle or weak anomalies associated with concealed mineralization.
As shown in Figure 16, Au displayed three apparent high-value anomalies (Au-01, Au-02, and Au-03). Au-01 comprises three irregularly anomalies caused by extreme values, Au-02 includes three isolated single-point anomalies, and Au-03 consists of two isolated point anomalies. These patterns indicate that the anomalies are primarily driven by isolated extreme values, rather than coherent geochemical trends. As a result, the delineated anomalous zones are excessively large and unreliable, complicating anomaly verification and reducing the effectiveness of subsequent exploration.
The S-A multifractal modeling approach used in this study integrates statistical analysis. By combining ILR preprocessing, factor analysis, and principal component analysis (PCA), the method efficiently extracts key geochemical signals, clarifies inter-element relationships, and delineates meaningful geochemical associations. Based on S-A multifractal theory, the preprocessed datasets were partitioned into three domains—noise, anomaly, and background—using threshold values. These partitions were then applied as filters to generate a suite of geochemical maps, including the raw map, background-removed map, noise- and background-removed anomaly map, and background distribution map.
Comparison of the S-A multifractal results for the four principal factors (Figure 14, Figure 15, Figure 16 and Figure 17) shows that in areas of strong cover or concealed mineralization, conventional geochemical maps often display only weak point anomalies or not at all. In regions with high background values, minor anomalies may even be exaggerated into apparent strong anomalies, leading to misinterpretation. In contrast, S-A multifractal modeling effectively suppresses noise and background effects, eliminating spurious anomalies caused by single-point outliers and reducing bias from background fluctuations. This markedly improved the accuracy and precision of anomaly recognition and delineation.
5.3. Verification of Anomalies and Mineralization Prediction
The application of mathematical modeling in mineral exploration has become increasingly refined. In this study, ILR transformation combined with PCA and S-A multifractal analysis was used to predict the distribution of major mineralization within the study area. The results show that factor F1, characterized by the Co-Ni-Cr association, reflects the development of iron mineralization. The delineated anomaly in the southern part of the area showed good spatial consistency with the Chensiyao iron deposit, while a series of NW–NE-trending anomalies in the central-northern part corresponded to the widespread occurrence of podiform high-depletion magnetite and surface goethite-bearing veins (Figure 14, Table 12).
To further validate the geochemical targeting results, hyperspectral-remote sensing fusion techniques were applied to map alterations across the Hadamengou district. A regional spectral library was established using 20 ground samples and 100 drill core samples, forming a quantitative spectral evaluation system for key alteration minerals associated with mineralization. Field verification was conducted at five of the nine favorable zones previously delineated in the Dabagou segment. Across 120 validation points, chloritization, sericitization, and varying degrees of potassic alteration were consistently observed. These results confirm that sericitization and chloritization anomalies extracted from WorldView-3 data showed strong spatial consistency with existing open-pit workings and widespread altered exposures. Moreover, linear zones exhibiting overlapping sericitization-chloritization-potassic alteration aligned with outcrops of potassically altered rocks, further demonstrating the accuracy and reliability of our hyperspectral-based alteration interpretation.
Based on these improved validation results, the alteration-guided prediction model was refined, ultimately delineating 37 favorable metallogenic zones across the mining area, ecological protection zone, and surrounding regions. Notably, hyperspectral zone No. 17 showed strong spatial correspondence with anomaly targets AP01, AP02, and AP05 identified in this study, providing strong support for the effectiveness of the integrated ILR-factor analysis-S-A multifractal workflow.
The geochemical associations represented by factors F2 (Sn-Sb-As), F3 (Au-Ag-Cu), and F4 (Bi-W) collectively correspond to the ore-related element suite characteristic of the district and reflect a continuously evolved hydrothermal mineralization system. F2 delineates a proximal halo with a substantial contribution to the variance, indicating potential deep-seated mineralization. F3 defines a near-ore halo associated with shallow gold enrichment, whereas F4 marks a distal halo, representing hydrothermal fluid ascent and erosion modification. These factors provide a robust geochemical framework for anomaly prioritization.
Field validation of the major targets (AP01-AP05) further confirms their exploration significance. AP01 and AP02 lie between the Baiyougou and Hademengou faults, where surface mineralization is well developed. Grab samples from AP01 returned up to 1.96 g/t Au, and drilling (ZK0402) intersected 1.0 m at 0.62 g/t Au and 0.3 m at 0.40 g/t Au at 196~199 m depth. AP02 contains limonitized, nearly E–W-trending quartz veins yielding up to 10.1 g/t Au. AP03 aligns with a previously identified mineralized vein (No. 4), whereas AP04 is located near the Chensiyao Fe deposit within a piedmont K-alteration belt where deep, low-grade Au mineralization has been intercepted, indicating significant downward potential. AP05 comprises multiple quartz veins, the dominant ore style in the region, indicating strong potential for concealed gold mineralization at depth (Figure 19, Table 13).
Collectively, the integrated geochemical, hyperspectral, and field validation results strongly support the accuracy of the delineated targets and reveal considerable potential for further gold exploration in the Hadamengou-Buerhantu district. Overall, the combined use of ILR-based factor analysis and S-A multifractal modeling effectively enhances anomaly recognition by preserving ore-related geochemical coupling, suppressing background and noise interference, and refining target delineation. These integrated results demonstrate that the proposed workflow provides a robust and reliable basis for predictive mineral exploration and concealed ore discovery in the study area.
6. Conclusions
This study systematically compared the strengths and limitations of ILR and CLR data preprocessing methods, integrated PCA to extract geochemical associations, and applied S-A multifractal modeling for anomaly recognition. The main findings are summarized as follows: (1). Superiority of ILR over CLR and simple ln-transformation: By introducing an additional reference column (YD), the ILR transformation effectively overcomes the dimensionality constraint of compositional data and, compared with CLR, more efficiently eliminates the closure effect. This results in clearer separation between mineralization-related anomalies and background geochemical variations, thereby significantly improving exploration prediction performance. In comparison, although the natural logarithmic transformation can partially stabilize variance structures, it does not fully resolve the compositional dependency issue inherent in ratio-based geochemical datasets.
Moreover, the results show that anomaly recognition is highly sensitive to data preprocessing strategies, including the choice of transformation and quality-control procedures. ILR, in particular, demonstrates stronger robustness to variations in data standardization and sampling quality, providing more reliable anomaly extraction and exploration targeting than CLR or simple ln-transformation methods.
(2). Advantages of the S-A multifractal method: Through constructing the noise, background, and anomaly filters, the S-A model effectively suppresses non-mineralization-related interference and greatly enhances anomaly detection. Compared with the conventional IDW interpolation, which often produces broad and irregular anomalies influenced by extreme values, the S-A method offers clear advantages:
Noise reduction: It removes “false anomalies” caused by outliers and minimizes masking from high background values, revealing concealed mineralization information.
Precision in delineation: Post-S-A filtering, anomaly boundaries are sharper and more regular, reducing anomaly areas and improving targeting accuracy.
Detection of concealed signals: In areas with thick cover or hidden ore bodies, where raw geochemical maps show weak or no anomalies, the S-A method highlights subtle but significant signals, reducing misinterpretation and improving deep mineralization detection.
(3). Anomaly verification and exploration potential: Five anomaly zones (AP01-AP05) were delineated. Drilling at AP01 confirmed two Au-bearing intervals at depths of 196–199 m, validating its mineralization potential. AP02 and AP05 show strong exploration prospects and should be prioritized for follow-up. AP03 and AP04 though smaller may serve as secondary targets pending surface verification.
(4). Methodological innovation and applicability: This study establishes and validates an integrated workflow of “ILR transformation → factor analysis → S-A fractal filtering” for geochemical data processing and interpretation. The method’s strength lies in its low dependence on detailed geological background information and its strong capability to extract mineralization signals from complex datasets. However, subjective threshold selection in the S-A fractal model and computational challenges associated with large datasets remain key limitations. Future research should incorporate machine learning approaches to standardize data preprocessing, optimize computational procedures, and improve threshold determination in fractal segmentation. Machine learning-based optimization algorithms are expected to provide more objective and efficient solutions, thereby further enhancing both the computational efficiency and anomaly-detection performance of fractal modeling in mineral exploration.
Overall, the proposed approach demonstrates high robustness and transferability. It effectively identifies hydrothermal, structure-controlled gold mineralization in the Hadamengou area and can be applied to covered terrains, geologically complex regions, and concealed mineralization systems elsewhere. By mitigating post-mineralization overprinting and directly extracting geochemical associations and spatial patterns related to ore formation, this workflow transforms raw geochemical data into actionable exploration targets, enhancing both the efficiency and precision of mineral exploration. This framework provides strong technical support for rapidly delineating and validating exploration targets in China’s new phase of strategic mineral resource exploration.
Conceptualization, S.F. and D.W.; methodology, S.F. and H.M.; validation, S.F., B.Y., R.S. and L.C.; formal analysis, S.F., P.S., H.L. and X.H.; investigation, S.F., Z.X., L.C. and X.H.; resources, S.F., B.Y. and R.S.; data curation, S.F., P.S. and Z.X.; writing—original draft preparation, S.F. and H.M.; writing—review and editing, S.F., D.W. and H.M.; visualization, S.F. and H.L.; supervision, D.W. and L.C.; project administration, B.Y.; funding acquisition, B.Y. All authors have read and agreed to the published version of the manuscript.
The datasets generated during and/or analyzed during the current study are not publicly available as they are part of a separate, unpublished research project, but they are available from the corresponding author on reasonable request.
We thank Wenhui Zhou, Guilong Wang, Shaoyun Han, Pengfei Gou, Liangliang Hou, and Chengyuan Li for their assistance during this work.
Songhao Fan, Biao Yang, Rilige Su, Lei Chen, Panyun Su, Xiuhong Hou, Hanqin Lv and Zhiwei Xia are employees of Hohhot General Survey of Natural Resources Center, China Geological Survey (Innovation Base for Gold Exploration Technology in the Northern Margin of North China Craton). Da Wang is a Professor of the School of Earth Sciences and Resources, China University of Geosciences, Beijing. Huchao Ma is a Doctor of the School of Earth Sciences and Resources, China University of Geosciences, Beijing. The authors declare that they have no known competing financial interests or personal relationships that influenced the work reported in this paper.
Footnotes
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Figure 1 Schematic map of gold deposit distribution along the northern margin of the North China craton (modified from [
Figure 2 Regional tectonic map of the Hademengou area (modified from [
Figure 3 Geological map of the Hademengou gold field (modified from [
Figure 4 Burhantu mineral geology map.
Figure 5 Digital elevation model map of the Bu’erhantu area.
Figure 6 Geochemical exploration workflow in the Hadamengou area.
Figure 7 Distribution map of lithogeochemical sample locations.
Figure 8 Histogram and normal Q-Q plot of F1 from Isometric Log-Ratio (ILR) transformed geochemical data.
Figure 9 Histogram and normal Q-Q plot of F2 from Isometric Log-Ratio (ILR) transformed geochemical data.
Figure 10 Histogram and normal Q-Q plot of F3 from Isometric Log-Ratio (ILR) transformed geochemical data.
Figure 11 Histogram and normal Q-Q plot of F4 from Isometric Log-Ratio (ILR) transformed geochemical data.
Figure 12 Biplot of factor scores F1–F4 from factor analysis.
Figure 13 Log-log plot of the S-A multifractal model for factor scores F1–F4 from factor analysis.
Figure 14 Geochemical anomaly map of factor F1. Delineated using the Spectrum-Area (S-A) multifractal model applied to factor score obtained from factor analysis. The map includes both lithological units and commodities anomalies.
Figure 15 Geochemical anomaly map of factor F2. Delineated using the Spectrum-Area (S-A) multifractal model applied to factor score obtained from factor analysis.
Figure 16 Geochemical anomaly map of factor F3. Delineated using the Spectrum-Area (S-A) multifractal model applied to factor score obtained from factor analysis.
Figure 17 Geochemical anomaly map of factor F4. Delineated using the Spectrum-Area (S-A) multifractal model applied to factor score obtained from factor analysis.
Figure 18 Geochemical gold and integrated anomaly maps using conventional geochemical mapping.
Figure 19 Au Anomaly Map and Drill Hole Cross-Section.
Gold resource inventory of the Hadamengou gold deposit.
| Gold Deposit | Ore Segment | Vein(s) | Gold Resources (t) | ||
|---|---|---|---|---|---|
| Filed & Approved Resources | Preliminary Exploration | Potential Resources | |||
| Hadamengou Gold Deposit | Liubagou Segment | Vein Nos. 313, 314 | 13.9 | 30 | 10 |
| Wulanburlangou Segment | Vein No. 113 (incl. No. 14/8) | 12.8 | 5 | ||
| Hulusitaigou Segment | Vein No. 59 | 2.3 | 2 | ||
| Vein Nos. 51–55 | 2 | 5 | |||
| Dabagou Segment | Vein No. 100 | 31.4 | 10 | ||
| Vein No. 99 | 6.4 | ||||
| Vein No. 98 | 3.2 | ||||
| Dabagou North Segment | Vein No. 268 | 1.08 | 5 | 5 | |
| Vein No. 25 | 1.2 | 5 | |||
| Vein No. 28 | 0.8 | 10 | |||
| Baishitougou Segment | Vein No. 20 | 0.8 | 2 | ||
| Vein No. 24 | 2.5 | 2 | |||
| Baishugou Segment | Vein No. 13 | 42.5 | 5 | ||
| Huluntu Segment | Vein No. 32 | 8.7 | 2 | 3 | |
| Hadamengou West Segment | Vein No. 1 | 22.3 | 3 | ||
| Vein No. 2 | 2.5 | 2 | |||
| Vein No. 2-1 | 2 | 3 | |||
| Vein No. 3 | 0.4 | 1 | |||
| Vein No. 207 | 2 | 3 | |||
| Total | 150.38 | 45.40 | 76 | ||
Analytical methods for elemental determination.
| Analytical Method | Number of Elements | Target Elements | Detection Limit (ppm) |
|---|---|---|---|
| Foam plastic enrichment-Inductively Coupled Plasma Mass Spectrometry (ICP-MS) | 1 | Au | Au: 0.0003 |
| Alternating Current Arc-Emission Spectroscopy | 3 | Ag, Sn, B | Ag: 0.03; Sn: 1, B:3 |
| Hydride Generation-Atomic Fluorescence Spectrometry (HG-AFS) | 2 | As, Sb | As: 1; Sb: 0.2 |
| Silicate Rock Geochemical Analysis | 10 | Cu, Zn, Pb, W, Mo, Bi, Ni, Co, Cr, Fe | Cu: 1.5; Zn: 15; Pb: 5; W: 0.5; Mo: 0.5; Bi: 0.1; Ni: 3; Co: 1; Cr: 15; Fe: 1000 |
Summary of statistical uncertainty and spatial autocorrelation parameters for major ore-related elements.
| Element | n | Mean | SD | SE | CI Low | CI High | Boot Mean | Boot CI Low | Boot CI High | Moran’s I | Range a (m) | Sill (C) | Nugget (C0) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Cu | 1295 | −1.32 | 0.75 | 0.02 | −1.36 | −1.28 | −1.32 | −1.36 | −1.28 | 0.09 | 2971 | 0.88 | 0.46 |
| Zn | 1295 | −1.32 | 0.51 | 0.01 | −1.35 | −1.29 | −1.32 | −1.34 | −1.29 | 0.09 | 2971 | 0.42 | 0.22 |
| Pb | 1295 | 0.01 | 0.87 | 0.02 | −0.04 | 0.06 | 0.01 | −0.04 | 0.05 | 0.08 | 2122 | 0.80 | 0.68 |
| W | 1295 | 3.36 | 0.77 | 0.02 | 3.32 | 3.40 | 3.36 | 3.32 | 3.40 | 0.03 | 3253 | 0.74 | 0.56 |
| Mo | 1295 | 2.26 | 0.57 | 0.02 | 2.23 | 2.29 | 2.26 | 2.23 | 2.29 | 0.06 | 3253 | 2.18 | 0.27 |
| Ag | 1295 | 3.85 | 0.44 | 0.01 | 3.82 | 3.87 | 3.85 | 3.82 | 3.87 | 0.07 | 3253 | 0.55 | 0.17 |
| Sn | 1295 | 0.60 | 0.37 | 0.01 | 0.58 | 0.62 | 0.60 | 0.58 | 0.62 | 0.09 | 2971 | 0.16 | 0.11 |
| Bi | 1295 | 3.76 | 0.68 | 0.02 | 3.72 | 3.80 | 3.76 | 3.72 | 3.79 | 0.09 | 3253 | 0.55 | 0.40 |
| Sb | 1295 | 2.11 | 0.57 | 0.02 | 2.08 | 2.14 | 2.11 | 2.08 | 2.14 | 0.11 | 2405 | 0.40 | 0.28 |
| As | 1295 | −0.12 | 0.44 | 0.01 | −0.15 | −0.10 | −0.12 | −0.15 | −0.10 | 0.08 | 2405 | 0.22 | 0.17 |
| Au | 1295 | −0.19 | 1.03 | 0.03 | −0.24 | −0.13 | −0.19 | −0.25 | −0.13 | 0.05 | 3253 | 1.61 | 0.99 |
| Co | 1295 | −2.07 | 0.81 | 0.02 | −2.12 | −2.03 | −2.07 | −2.12 | −2.03 | 0.09 | 2122 | 0.69 | 0.58 |
| Ni | 1295 | −2.77 | 0.84 | 0.02 | −2.82 | −2.73 | −2.77 | −2.82 | −2.73 | 0.09 | 1273 | 0.75 | 0.63 |
| Cr | 1295 | −3.39 | 0.94 | 0.03 | −3.44 | −3.34 | −3.39 | −3.45 | −3.34 | 0.06 | 707 | 0.92 | 0.81 |
| TFe2O3 | 1295 | −0.83 | 0.66 | 0.02 | −0.87 | −0.79 | −0.83 | −0.87 | −0.80 | 0.00 | 424 | 0.45 | 0.44 |
Notes: (1) CI = 95% confidence interval. (2) Range a (m): practical variogram range in meters. (3) Sill (C) and Nugget (C0): empirical variogram parameters. (4) Results based on ILR-transformed geochemical data.
Results of factor analysis based on ILR-transformed data.
| Principal Factor | Eigenvalue | Variance Contribution (%) | Cumulative Contribution (%) |
|---|---|---|---|
| F1 | 4.06 | 27.03 | 27.03 |
| F2 | 2.02 | 13.44 | 40.47 |
| F3 | 1.60 | 10.64 | 51.11 |
| F4 | 1.53 | 10.17 | 61.28 |
Results of factor analysis based on CLR-transformed data.
| Principal Factor | Eigenvalue | Variance Contribution (%) | Cumulative Contribution (%) |
|---|---|---|---|
| F1 | 5.11 | 34.04 | 34.04 |
| F2 | 1.62 | 10.79 | 44.83 |
| F3 | 1.49 | 9.91 | 54.74 |
| F4 | 1.25 | 8.34 | 63.08 |
Results of factor analysis based on ln-transformed data.
| Principal Factor | Eigenvalue | Variance Contribution (%) | Cumulative Contribution (%) |
|---|---|---|---|
| F1 | 4.41 | 29.40 | 29.40 |
| F2 | 1.76 | 11.72 | 41.12 |
| F3 | 1.48 | 9.88 | 51.00 |
| F4 | 0.92 | 6.13 | 57.13 |
Rotated component matrix of elemental variables (ILR-transformed).
| Element | F1 | F2 | F3 | F4 |
|---|---|---|---|---|
| Cu | 0.12 | 0.08 | 0.66 | 0.24 |
| Zn | 0.54 | 0.37 | 0.07 | 0.50 |
| Pb | −0.73 | 0.36 | 0.00 | 0.27 |
| W | −0.41 | −0.12 | 0.06 | 0.66 |
| Mo | −0.37 | 0.12 | 0.11 | 0.11 |
| Ag | −0.19 | 0.24 | 0.68 | 0.00 |
| Sn | 0.04 | 0.81 | −0.03 | 0.09 |
| Bi | −0.12 | −0.07 | 0.17 | 0.75 |
| Sb | −0.53 | 0.62 | 0.17 | −0.26 |
| As | −0.45 | 0.64 | 0.13 | −0.24 |
| Au | −0.07 | −0.23 | 0.70 | 0.02 |
| Co | 0.94 | −0.11 | −0.05 | −0.07 |
| Ni | 0.87 | −0.04 | 0.09 | −0.08 |
| Cr | 0.84 | −0.04 | 0.02 | −0.02 |
| TFe2O3 | −0.15 | 0.37 | −0.33 | −0.05 |
Rotated component matrix of elemental variables (CLR-transformed).
| Element | F1 | F2 | F3 | F4 |
|---|---|---|---|---|
| Cu | 0.39 | −0.38 | 0.35 | 0.34 |
| Zn | 0.77 | −0.22 | −0.19 | 0.01 |
| Pb | −0.73 | 0.19 | −0.22 | −0.02 |
| W | −0.17 | 0.73 | 0.09 | 0.01 |
| Mo | −0.30 | 0.21 | −0.11 | 0.23 |
| Ag | −0.31 | −0.07 | 0.21 | 0.67 |
| Sn | −0.27 | −0.10 | −0.73 | 0.08 |
| Bi | −0.01 | 0.79 | 0.10 | 0.12 |
| Sb | −0.81 | −0.16 | −0.13 | 0.05 |
| As | −0.79 | −0.13 | −0.14 | −0.05 |
| Au | −0.10 | 0.09 | 0.79 | 0.10 |
| Co | 0.92 | −0.21 | −0.01 | −0.04 |
| Ni | 0.84 | −0.20 | 0.07 | −0.05 |
| Cr | 0.82 | −0.12 | −0.03 | −0.06 |
| TFe2O3 | −0.19 | −0.18 | 0.10 | −0.77 |
Rotated component matrix of elemental variables (simple ln-transformed).
| Element | F1 | F2 | F3 | F4 |
|---|---|---|---|---|
| Cu | 0.65 | 0.28 | 0.08 | 0.21 |
| Zn | 0.86 | 0.17 | −0.11 | 0.02 |
| Pb | −0.47 | 0.35 | 0.06 | −0.13 |
| W | 0.09 | 0.61 | 0.11 | 0.12 |
| Mo | 0.20 | 0.49 | 0.21 | 0.01 |
| Ag | 0.33 | 0.48 | 0.17 | 0.26 |
| Sn | 0.53 | 0.28 | 0.05 | −0.07 |
| Bi | 0.18 | 0.67 | −0.01 | 0.14 |
| Sb | −0.14 | 0.08 | 0.95 | 0.02 |
| As | −0.02 | 0.19 | 0.66 | 0.07 |
| Au | 0.14 | 0.26 | 0.08 | 0.85 |
| Co | 0.97 | 0.12 | −0.10 | 0.08 |
| Ni | 0.89 | 0.10 | −0.05 | 0.13 |
| Cr | 0.84 | 0.14 | −0.07 | 0.07 |
| TFe2O3 | 0.30 | 0.12 | 0.02 | 0.02 |
Segmented S-A multifractal fitting results: threshold points, slopes, determination coefficients (R2), and fitting errors.
| Factor | Threshold Point | Slope | Determination (R2) | Errors | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| F1 | 22.121 | 31.913 | 608.75 | 922.636 | −1.22263 | −2.08185 | −1.2757 | 1 | 0.996 | 0.44 | 7.972258 × 103 | 7.374906 × 103 | 3.638816× 102 |
| F2 | 21.662 | 364.972 | 557.226 | 701.416 | −1.71263 | −3.7425 | −0.37054 | 0.996 | 0.899 | 0.039 | 4.356555 × 103 | 2.297531 × 102 | 4.700549× 1012 |
| F3 | 21.513 | 88.737 | 516.852 | 722.064 | −1.55441 | −1.80758 | −2.92097 | 0.988 | 0.99 | 0.701 | 3.563396 × 103 | 9.595286 × 103 | 3.311625× 102 |
| F4 | 19.506 | 244.737 | 486.017 | 822.967 | −1.83547 | −1.37086 | −1.0381 | 0.996 | 0.969 | 0.709 | 5.28275 × 103 | 2.550278 × 103 | 8.622879 × 103 |
Summary of factor associations (F1–F4), their geological implications, and anomaly distribution based on S-A multifractal modeling.
| Factor | Element Association | Geological Significance | S-A Fractal Segments (Log10(S)) & Slopes | R2 Values | Anomaly Distribution Features |
|---|---|---|---|---|---|
| F1 | Co-Ni-Cr | Associated with ultramafic-mafic intrusions and mantle-derived sources; consistent with magnetite occurrences in the area | Noise: <3.096 (−1.222); Anomaly: 3.096–6.411 (−2.081); Background: >6.411 (−1.270) | 1.000, 0.996, 0.440 | NW–SE background gradient (low NW, high SE); Au anomalies enhanced after background correction, especially near magnetite-rich zones |
| F2 | Sn-Sb-As | Sn indicates granitic pegmatites and intrusions (Dahubai, Shadegai); Sb-As represent proximal halos of Au mineralization | Noise: <3.075 (−1.712); Anomaly: 3.075–5.899 (−3.742); Background: >5.899 (−0.370) | 0.996, 0.899, 0.039 | Background decreases from SSW to ENE; anomalies concentrated in NW, SW, and scattered eastern zones; partly overlap with F3 Au anomalies |
| F3 | Au-Ag-Cu | Main ore-related assemblage (Au-Ag-Mo dominant); key target of exploration | Noise: <4.485 (−1.554); Anomaly: 4.485–6.247 (−1.807); Background: >6.247 (−2.920) | 0.988, 0.990, 0.701 | High background along NW–SE belts; after filtering, Au anomalies at NW (P01, P02) and SW are emphasized; SE anomaly may indicate concealed mineralization |
| F4 | Bi-W | Distal halo assemblage; useful for refining Au anomaly boundaries | Noise: 2.970–5.500 (−1.835); Anomaly: 5.500–6.186 (−1.370); Background: >6.186 (−1.038) | 0.996, 0.969, 0.709 | Strong Bi-W background in northern area (E–W trend); anomalies shrink after background correction, with two additional low-intensity anomalies identified in MS-SW region |
Integrated geological interpretation of geochemical factors in the
| Factor | ILR | CLR | ln | Integrated Naming | Geological Meaning |
|---|---|---|---|---|---|
| F1 | Co-Ni-Cr-rich | Co-Ni-Cr-rich | Co-Ni-Cr-Zn-rich | Basement background factor | Represents the geochemical signature of the metamorphic and mafic-ultramafic basement rocks. |
| F2 | As-Sb-Sn-Bi | W-Bi-Mo | W-Bi-Mo-Ag | Magmatic-hydrothermal factor | Indicates deep magmatic sourcing and enrichment of volatile components. |
| F3 | Au-Ag-Cu | Au-dominated | Sb-As-Au | Main ore-forming factor | Directly reflects gold-bearing veins and their associated alteration zones. |
| F4 | Zn-Pb | TFe2O3 (background contrast) | Mixed (Au-Ag edge signals) | Distal alteration factor | Represents distal alteration halos and possible precipitation zones at the periphery of mineralization. |
Characteristics of geochemical anomalies and their mineralization potential.
| Anomaly | Host Rock/Structure | Main Mineralization Features | Sampling Results | Drilling Results | Mineralization Potential |
|---|---|---|---|---|---|
| AP01 | K-silicified rocks, SW-trending anomalies, between Baiyougou and Hadamengou faults | Potassic-silicic alteration; large surface exposure | Grab sample: 1.96 g/t Au | Drill hole ZK0402: 1.0 m 0.62 g/t Au; 0.3 m 0.40 g/t Au (196–199 m) | High potential; validated by drilling, favorable location and accessibility |
| AP02 | Limonitized quartz veins, near E–W trend, between Baiyougou and Hademengou faults | Strong limonitization, discrete veins | Grab sample: 10.1 g/t Au | - | Moderate-high potential; consistent with NW-trending anomaly distribution |
| AP03 | Altered rocks, E–W oriented vein (No. 4, previously defined) | Limonitized altered vein system | - | - | Moderate potential; confirmed by historical mapping, but requires further testing |
| AP04 | Piedmont K-alteration belt, adjacent to Chensiyao Fe deposit | Potassic alteration zone, structurally controlled | - | Previous drilling nearby: thick, low-grade Au mineralization | Moderate-high potential; deep concealed mineralization possible |
| AP05 | Multiple quartz veins, typical ore style in district | Quartz vein-type Au mineralization | - | - | High potential; typical mineralization type in the region, favorable for concealed deposits |
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