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Fractal Fract
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Fractals in Geology and Geochemistry
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Fractals in Geology and Geochemistry

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 31 August 2024 | Viewed by 5510

Special Issue Editors

Dr. Fan Xiao

E-Mail Website
Guest Editor
School of Earth Sciences and Engineering, Sun Yat-Sen University, Guangzhou 510275, China
Interests: fractal modeling of geochemical data
Prof. Dr. Qiuming Cheng

E-Mail Website
Guest Editor
School of Earth Science and Engineering, Sun Yat-Sen University, Zhuhai 519000, China
Interests: fractal modeling of extreme geological events
Prof. Dr. Frits Agterberg

E-Mail Website
Guest Editor
Geological Survey of Canada, 601 Booth Street, Ottawa, ON K1A 0E8, Canada
Interests: fractal analysis and its application in geosciences

Special Issue Information

Dear Colleagues,

As a significant branch of nonlinear science, the fractal concept has been widely used in many scientific fields including geosciences. In the fields of geology and geochemistry, fractal and multifractal models have been successfully employed to characterize the irregularity of geological features such as mineral textures, crystal structures, and grain size; the spatial distribution of geological objects such as mineral deposits, veins, and faults and/or fractures; the singularity geochemical anomalies associated with mineralization; and many other properties of geological and geochemical processes. In recent years, these studies have made much progress and/or many updates to their applications.

The focus of this Special Issue is to continue to advance research on topics relating to the theories, models, algorithms, and applications of fractal analysis in geology and geochemistry. Topics that are invited for submission include (but are not limited to):

  • Fractal modeling of geochemical data;
  • Fractal analysis in mineral prospectivity mapping;
  • Fractal modeling of extreme geological events;
  • Fractal modeling of ore deposits;
  • Fractal modeling of faults and/or fractures;
  • Fractal modeling of geothermal resources;
  • Fractal analysis in geological data fusion;
  • Fractal modeling of geological and/or geochemical processes;
  • Fractal analysis of minerals and rocks.

Dr. Fan Xiao
Prof. Dr. Qiuming Cheng
Prof. Dr. Frits Agterberg
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (5 papers)

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Research

34 pages, 28362 KiB  
Article
Fractal-Based Multi-Criteria Feature Selection to Enhance Predictive Capability of AI-Driven Mineral Prospectivity Mapping
by Tao Sun, Mei Feng, Wenbin Pu, Yue Liu, Fei Chen, Hongwei Zhang, Junqi Huang, Luting Mao and Zhiqiang Wang
Fractal Fract. 2024, 8(4), 224; https://doi.org/10.3390/fractalfract8040224 - 12 Apr 2024
Viewed by 574
Abstract
AI-driven mineral prospectivity mapping (MPM) is a valid and increasingly accepted tool for delineating the targets of mineral exploration, but it suffers from noisy and unrepresentative input features. In this study, a set of fractal and multifractal methods, including box-counting calculation, concentration–area fractal [...] Read more.
AI-driven mineral prospectivity mapping (MPM) is a valid and increasingly accepted tool for delineating the targets of mineral exploration, but it suffers from noisy and unrepresentative input features. In this study, a set of fractal and multifractal methods, including box-counting calculation, concentration–area fractal modeling, and multifractal analyses, were employed to excavate the underlying nonlinear mineralization-related information from geological features. Based on these methods, multiple feature selection criteria, namely prediction–area plot, K-means clustering, information gain, chi-square, and the Pearson correlation coefficient, were jointly applied to rank the relative importance of ore-related features and their fractal representations, so as to choose the optimal input feature dataset readily used for training predictive AI models. The results indicate that fault density, the multifractal spectrum width (∆α) of the Yanshanian intrusions, information dimension (D1) of magnetic anomalies, correlation dimension (D2) of iron-oxide alteration, and the D2 of argillic alteration serve as the most effective predictor features representative of the corresponding ore-controlling elements. The comparative results of the model assessment suggest that all the AI models trained by the fractal datasets outperform their counterparts trained by raw datasets, demonstrating a significant improvement in the predictive capability of fractal-trained AI models in terms of both classification accuracy and predictive efficiency. A Shapley additive explanation was employed to trace the contributions of these features and to explain the modeling results, which imply that fractal representations provide more discriminative and definitive feature values that enhance the cognitive capability of AI models trained by these data, thereby improving their predictive performance, especially for those indirect predictor features that show subtle correlations with mineralization in the raw dataset. In addition, fractal-trained models can benefit practical mineral exploration by outputting low-risk exploration targets that achieve higher capturing efficiency and by providing new mineralization clues extracted from remote sensing data. This study demonstrates that the fractal representations of geological features filtered by multi-criteria feature selection can provide a feasible and promising means of improving the predictive capability of AI-driven MPM. Full article
(This article belongs to the Special Issue Fractals in Geology and Geochemistry)
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16 pages, 5507 KiB  
Article
Discrete Element Method Analyses of Bond Degradation Evolutions for Cemented Soils
by Jie He, Tao Li and Yi Rui
Fractal Fract. 2024, 8(2), 119; https://doi.org/10.3390/fractalfract8020119 - 17 Feb 2024
Viewed by 938
Abstract
The degradation of soil bonding, which can be described by the evolution of bond degradation variables, is essential in the constitutive modeling of cemented soils. A degradation variable with a value of 0/1.0 indicates that the applied stress is completely sustained by bonded [...] Read more.
The degradation of soil bonding, which can be described by the evolution of bond degradation variables, is essential in the constitutive modeling of cemented soils. A degradation variable with a value of 0/1.0 indicates that the applied stress is completely sustained by bonded particles/unbounded grains. The discrete element method (DEM) was used for cemented soils to analyze the bond degradation evolution and to evaluate the degradation variables at the contact scale. Numerical cemented soil samples with different bonding strengths were first prepared using an advanced contact model (CM). Constant stress ratio compression, one-dimensional compression, conventional triaxial tests (CTTs), and true triaxial tests (TTTs) were then implemented for the numerical samples. After that, the numerical results were adopted to investigate the evolution of the bond degradation variables BN and B0. In the triaxial tests, B0 evolves to be near to or larger than BN due to shearing, which indicates that shearing increases the bearing rate of bond contacts. Finally, an approximate stress-path-independent bond degradation variable Bσ was developed. The evolution of Bσ with the equivalent plastic strain can be effectively described by an exponential function and a hyperbolic function. Full article
(This article belongs to the Special Issue Fractals in Geology and Geochemistry)
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22 pages, 3961 KiB  
Article
Local Singularity Spectrum: An Innovative Graphical Approach for Analyzing Detrital Zircon Geochronology Data in Provenance Analysis
by Wenlei Wang, Yingru Pei, Qiuming Cheng and Wenjun Wang
Fractal Fract. 2024, 8(1), 64; https://doi.org/10.3390/fractalfract8010064 - 17 Jan 2024
Cited by 1 | Viewed by 1139
Abstract
Detrital zircon geochronology plays a crucial role in provenance analysis, serving as one of the fundamental strategies. The age spectrum of detrital zircons collected from the sedimentary unit of interest is often compared or correlated with that of potential source terranes. However, biases [...] Read more.
Detrital zircon geochronology plays a crucial role in provenance analysis, serving as one of the fundamental strategies. The age spectrum of detrital zircons collected from the sedimentary unit of interest is often compared or correlated with that of potential source terranes. However, biases in the age data can arise due to factors related to detrital sampling, analysis techniques, and nonlinear geological mechanisms. The current study reviewed two sets of detrital zircon datasets established in 2011 and 2021 to discuss the origins of the Tibetan Plateau. These datasets collected from different media effectively demonstrate a progressive understanding of provenance affinity among the main terranes on the Tibetan Plateau. This highlights issues regarding weak and unclear temporal connections identified through analyzing the age spectrum for provenance analysis. Within this context, a local singularity analysis approach is currently employed to address issues associated with unclear and weak provenance information by characterizing local variations in nonlinear behaviors and enhancing detection sensitivity towards subtle anomalies. This new graphical approach effectively quantifies temporal variations in detrital zircon age populations and enhances identification of weak provenance information that may not be readily apparent on conventional age spectra. Full article
(This article belongs to the Special Issue Fractals in Geology and Geochemistry)
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25 pages, 23198 KiB  
Article
Fractal-Based Pattern Quantification of Mineral Grains: A Case Study of Yichun Rare-Metal Granite
by Yue Liu, Tao Sun, Kaixing Wu, Hongwei Zhang, Jingwei Zhang, Xinwen Jiang, Quanwei Lin and Mei Feng
Fractal Fract. 2024, 8(1), 49; https://doi.org/10.3390/fractalfract8010049 - 12 Jan 2024
Cited by 3 | Viewed by 1021
Abstract
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, [...] Read more.
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. Full article
(This article belongs to the Special Issue Fractals in Geology and Geochemistry)
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19 pages, 4841 KiB  
Article
Geochemical Characteristics of Deep-Sea Sediments in Different Pacific Ocean Regions: Insights from Fractal Modeling
by Yan Zhang, Gaowen He, Fan Xiao, Yong Yang, Fenlian Wang and Yonggang Liu
Fractal Fract. 2024, 8(1), 45; https://doi.org/10.3390/fractalfract8010045 - 11 Jan 2024
Cited by 1 | Viewed by 1086
Abstract
Exploration of mineral resources in the deep sea has become an international trend. However, deep-sea mineral exploration faces challenges such as complex offshore drilling and the weak and mixed signals of ore deposits. Therefore, studying methods for identifying weak and mixed anomalies and [...] Read more.
Exploration of mineral resources in the deep sea has become an international trend. However, deep-sea mineral exploration faces challenges such as complex offshore drilling and the weak and mixed signals of ore deposits. Therefore, studying methods for identifying weak and mixed anomalies and extracting composite information in the deep sea is crucial for innovative prediction and evaluation of deep-sea mineral resources. In this study, the Central Pacific Ocean, Northwestern Pacific Ocean, and Eastern Pacific Ocean were selected as research areas. Drawing upon the fractal self-similarity exhibited by rare earth minerals in the deep-sea sediments within the Pacific Ocean, we conducted an analysis and comparison of the fractal geochemical characteristics in various regions of the Pacific Ocean’s deep-sea sediments. Thereafter, we studied the spatial distribution of rare earth elements (REEs) in deep-sea sediments in these regions to explore the mechanisms responsible for rare earth enrichment in the Pacific Ocean. The results revealed that the geochemical fractal characteristics of deep-sea sediments in the Northwestern Pacific Ocean Basin and the Central Pacific Ocean Basin were similar, whereas there were slight differences in the fractal characteristics observed in the Eastern Pacific Ocean Basin. By calculating the singularity index of CaO/P2O5, it was found that the singularity index in the Central and Northwestern Pacific Ocean basins was lower than that in the Eastern Pacific Ocean Basin, suggesting that the phosphorus content in the Eastern Pacific Ocean Basin was lower than that in the Central and Northwestern Pacific Ocean basins. In the Eastern Pacific Ocean, we found that phosphorus content in deep-sea sediments was the primary controlling factor for REE enrichment. Conversely, in the Central and Northwestern Pacific Ocean, both the phosphorus and calcium content in deep-sea sediments played significant roles in REE enrichment. Full article
(This article belongs to the Special Issue Fractals in Geology and Geochemistry)
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