New Insights into Element Distribution Patterns in Geochemistry: A Perspective from Fractal Density

Liu, Yue; Cheng, Qiuming; Zhou, Kefa

doi:10.1007/s11053-018-9374-7

Cited by 36 publications

(5 citation statements)

References 62 publications

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“…Hence, to address the closure problem and to modulate the minimum and maximum values of geochemical data, log-ratio transformations have been carried out [55]. In this regard, the original data of six elements, including Au, As, Cu, Pb, Sb, and Zn, have been subjected to the clr-transformation [14,48,55,56]. The clr transformation is appropriate for opening compositional data in statistical analyses because of symmetric results [55] and the feasibility of interpreting resulting values [54].…”

Section: Preprocessing Of Selected Elementsmentioning

confidence: 99%

“…For this reason, spatial statistical techniques are presently applied to distinguish geochemical anomalies [9,10]. Fractal/multifractal methods [11][12][13][14] are able to regard both frequency distribution and spatial variability in geochemical data for the identification of ore-related geochemical targets, and so are more applicable within complex geological environments. Furthermore, fractal/multifractal techniques can enhance the weak geochemical patterns of buried sources.…”

Section: Introductionmentioning

confidence: 99%

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Recognizing Geochemical Anomalies Associated with Mineral Resources Using Singularity Analysis and Random Forest Models in the Torud-Chahshirin Belt, Northeast Iran

Bigdeli,

Maghsoudi,

Ghezelbash

2023

Minerals

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Identifying the local geochemical anomalies from stream sediment samples is challenging in regional-scale exploration programs. For this purpose, some robust and reliable techniques must be applied to distinguish the geochemical targets from the background values. In this research, a procedure of several tools, including singularity mapping (SM), random forests (RF), success-rate curves, and the t-Student method, were employed to analyze the geochemical anomalies within the intrusive-plutonic Torud-Chahshirin belt (TCB), northeast Iran. In this regard, the success-rate curves were initially applied to extract efficient geochemical signatures. Then, singularity analysis was used on the selected geochemical elements (Au, Cu, Pb, and Zn), which were transformed via centered log-ratio (clr) transformation. In the next step, due to the complexity of the ore-forming processes in the TCB, the structural factors (e.g., fault intersection and faults with different orientations) were determined. Based on the success-rate curves, NE-trending faults and fault density were distinguished as critical structural criteria. Afterward, the RF model as a robust machine learning algorithm was executed on the four efficient SM-based geochemical layers and two efficient structural factors. The anomaly map derived by the RF model (Accuracy = 98.85% and Error = 1.15%) illustrates a very high relationship with Cu ± Au mineral occurrences. Therefore, the RF algorithm assisted by the singularity method is more trustworthy for highlighting the weak geochemical prospectivity areas in the TCB.

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Section: Preprocessing Of Selected Elementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Recognizing Geochemical Anomalies Associated with Mineral Resources Using Singularity Analysis and Random Forest Models in the Torud-Chahshirin Belt, Northeast Iran

Bigdeli,

Maghsoudi,

Ghezelbash

2023

Minerals

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“…(b) At a regional to deposit scale, fractal analysis is widely utilized as a quantitative means to characterize the intricate distributions of ore-forming systems [8][9][10][11][12], i.e., exploring the correlation between mineralization and ore-related spatial-temporal structures through fractal exponents and searching for mineralization patterns [13][14][15][16]. The most prominent achievement in this field is the effective decomposition of geochemical populations using a variety of fractal models [17][18][19][20][21][22][23][24][25][26], including concentration-area fractal model [19][20][21], concentration-distance fractal model [22], concentration-volume fractal model [23], spectrum-area multifractal model [24] and singularity indices [25,26]. (c) At a microscopic scale, fractal dimensions derived from various fractal/multifractal analyses, such as the box-counting model, perimeter-area model and number-area model [13,[27][28][29], have been employed to quantify the irregularities in the shape and distribution pattern of mineral grains.…”

Section: Introductionmentioning

confidence: 99%

Fractal-Based Pattern Quantification of Mineral Grains: A Case Study of Yichun Rare-Metal Granite

Liu,

Sun,

et al. 2024

Fractal Fract

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The quantification of the irregular morphology and distribution pattern of mineral grains is an essential but challenging task in ore-related mineralogical research, allowing for tracing the footprints of pattern-forming geological processes that are crucial to understanding mineralization and/or diagenetic systems. In this study, a large model, namely, the Segmenting Anything Model (SAM), was employed to automatically segment and annotate quartz, lepidolite and albite grains derived from Yichun rare-metal granite (YCRMG), based on which a series of fractal and multifractal methods, including box-counting calculation, perimeter–area analysis and multifractal spectra, were implemented. The results indicate that the mineral grains from YCRMG show great scaling invariance within the range of 1.04~52,300 μm. The automatic annotation of mineral grains from photomicrographs yields accurate fractal dimensions with an error of only 0.6% and thus can be utilized for efficient fractal-based grain quantification. The resultant fractal dimensions display a distinct distribution pattern in the diagram of box-counting fractal dimension (Db) versus perimeter–area fractal dimension (DPA), in which lepidolites are sandwiched between greater-valued quartz and lower-valued albites. Snowball-textured albites, i.e., concentrically arranged albite laths in quartz and K-feldspar, exhibit characteristic Db values ranging from 1.6 to 1.7, which coincide with the fractal indices derived from the fractal growth model. The zonal albites exhibit a strictly increasing trend regarding the values of fractal and multifractal exponents from core to rim, forming a featured “fractal-index banding” in the radar diagram. This pattern suggests that the snowball texture gradually evolved from rim to core, thus leading to greater fractal indices of outer zones, which represent higher complexity and maturity of the evolving system, which supports a metasomatic origin of the snowball texture. Our study demonstrates that fractal analyses with the aid of a large model are effective and efficient in characterizing and understanding complex patterns of mineral grains.

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“…Kusák [34] discussed how to describe the drainage patterns of the Blue Nile Basin in Ethiopia using the fractal method. The geochemical distribution patterns and migration characteristics of the major and trace elements can be demonstrated well by the multifractal method and multifractal parameters [35]. Based on the model of multifractals, scholars have used many methods to calculate the distribution singularity exponent of geochemical elements to separate the geochemical anomalies from the background.…”

Section: Introductionmentioning

confidence: 99%

Multifractal Characteristics of Uranium Grade Distribution and Spatial Regularities in a Sandstone-Type Uranium Deposit in Xinjiang, China

Cai,

Tan,

Zhu

et al. 2023

Fractal Fract

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Based on an analysis of the spatial distribution of uranium grade in 338 boreholes of a uranium deposit in Xinjiang, the enrichment and spatial variation of uranium ore in two stopes of the deposit are discussed using multifractal theory. The distribution characteristics of the uranium ore of the two stopes are studied by multifractal parameters: the scaling exponent of mass τ(q), the scaling exponent α(q) of each sub-set and its corresponding fractal dimension f(α), the fractal dimension D0 and information dimension D1. The differences of uranium distribution in the two stopes can be quantified well by using multifractal spectrum and multifractal parameters such as Δα, Δf and R. After a comprehensive multifractal distribution analysis, 10 m × 10 m is defined as a fence unit, and the window sizes ε=3,6,9⋯,45 are set; the singularity exponents α of the two stopes are calculated by using this element concentration–area method. The results show that the multifractal theory and model can organically combine spatial structure information, scale change information and anisotropy information to obtain low-grade and weak mineral resources information and can effectively distinguish complex and superimposed anomalies. This will provide a basis for the local concentration and spatial variation rules of uranium distribution and the design of the parameters of the leaching uranium mining well site.

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New Insights into Element Distribution Patterns in Geochemistry: A Perspective from Fractal Density

Cited by 36 publications

References 62 publications

Recognizing Geochemical Anomalies Associated with Mineral Resources Using Singularity Analysis and Random Forest Models in the Torud-Chahshirin Belt, Northeast Iran

Recognizing Geochemical Anomalies Associated with Mineral Resources Using Singularity Analysis and Random Forest Models in the Torud-Chahshirin Belt, Northeast Iran

Fractal-Based Pattern Quantification of Mineral Grains: A Case Study of Yichun Rare-Metal Granite

Multifractal Characteristics of Uranium Grade Distribution and Spatial Regularities in a Sandstone-Type Uranium Deposit in Xinjiang, China

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