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Fractals and Multifractals in the Geosciences
- 1st Edition - May 17, 2024
- Author: Behnam Sadeghi
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 9 0 8 9 7 - 9
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 9 0 8 9 8 - 6
Fractals and Multifractals in the Geosciences details the application of a wide range of multifractal methods, including many novel ones developed by the author, along with the… Read more
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Request a sales quoteFractals and Multifractals in the Geosciences details the application of a wide range of multifractal methods, including many novel ones developed by the author, along with the assessment of uncertainty in sample classification and stability of spatial patterns. This book also provides criteria for selection of the most effective combination of data pre-processing and multifractal modeling to extract desired features or signals in the data. The book specifically aims to introduce, apply, and test novel multifractal models that account directly for changes in relationships between variables, as well as the effects of distance between samples and the source of anomalous metal contents in geoscience samples. Linked to this will be assessment of the effects of different pre-processing of data prior to application of the models and quantification/model uncertainty in geochemical anomaly maps, associated with sample classification and spatial interpolation. Gaussian simulations such as Sequential Gaussian Simulation and Monte Carlo Simulation will be applied to the new multifractal models developed and a suite of existing models, including (simulated) concentration-area, spectrum-area, singularity and other models.
Fractals and Multifractals in the Geosciences will be invaluable for mathematical geoscientists, geostatisticians, exploration, applied, urban and environmental geochemists, computational geoscientists, data scientists, and GIS professionals who need to better understand fractal geometry, along with its theory and applications in geochemical anomaly classification to generate maps that are helpful for decision-making for follow-up sampling and explorations.
- Provides a comprehensive overview of the use of fractal and multifractal modeling methods, with a detailed assessment of uncertainty quantification in samples and classified models
- Specifically includes novel multifractal models, as well as uncertainty quantification and decision-making methods for use in geosciences and especially geochemistry
- Includes case studies showing the application of the fractal and multifractal methods detailed in the book
Mathematical geoscientists, geostatisticians, exploration geochemists, urban and environmental geochemists, applied geochemists, computational geoscientists, data analysts, and GIS professionals, mining engineers, petroleum engineers, exploration geophysicists, mining and petroleum industry decision-makers and stakeholders
1. The theory of fractal geometry
1.1 Introduction to fractal geometry in nature and its difference with Euclidean geometry
1.2 Multi-fractal spectrums
1.2.1 Mono and Multi-Fractals
1.2.2 Continuous multi-fractals
1.2.3 Discrete multi-fractals
1.3 Multi-fractal distribution patterns in geochemical mineralisation
1.4 Fractal dimension and Hurst exponent
1.5 Power low frequency
1.6 Self-similarity and self-affinity
2. Introduction: characterising and mapping anomalies
2.1 Introduction
2.1.1 Population models
2.1.2 Spatial models
2.1.3 Traditional fractal and multi-fractal modelling in geochemical studies (with examples)
2.1.3.1 Number-size (N-S) fractal model
2.1.3.2 Concentration-area (C-A) fractal model
2.1.3.3 Perimeter-Area (P-A) fractal model
2.1.3.4 Concentration-distance (C-D) fractal model
2.1.3.5 spectrum-area (S-A) fractal model
2.1.3.6 Singularity model
2.1.3.7 Box-counting model
2.1.3.8 Concentration-volume (C-V) fractal model
2.1.3.9 Spectrum-volume (S-V) fractal model
2.1.3.10 Stochastic simulation methods applicable to fractal models
2.1.3.10.1 Lower-upper simulation (LUSIM)
2.1.3.10.2 Direct sequential simulation (DSSIM)
2.1.3.10.3 Sequential indicator simulation (SISIM)
2.1.3.10.4 Sequential Gaussian simulation (SGSIM)
2.1.3.10.5 Turning bands simulation (TBSIM)
2.1.3.11 Simulated-fractal models
2.1.3.11.1 Simulated size-number (SS-N) fractal model
2.1.3.11.2 Global Simulated size-number (GSS-N) fractal model
2.1.3.11.3 Co-simulated Size Number (CoSS-N) fractal model
2.2 Uncertainties in geochemical modelling
2.3 Problem statement
2.4 Aims and approach
3. Geochemical datasets
3.1 Overview
3.2 The till geochemical atlas of Sweden
3.2.1 Geology and mineralisation of Sweden
3.2.2 Quaternary glacial deposits and topography
3.2.3 Till geochemistry atlas
3.3 The soil geochemical atlas of Cyprus
3.3.1 Geology of Cyprus
3.3.2 Soil geochemistry
3.3.3 Urban geochemical map of Lemesos
3.4 General data processing
3.4.1 Log-ratio transformation
4. Novel fractal classification models
4.1 Introduction
4.2 Concentration-distance from centroids (C-DC) fractal model 304.2.1 C-DC calculations
4.3 Application of C-C and C-DC modelling: Enhancing the detection of Cu deposits in Cyprus
4.4.1 Data processing
4.4.2 Results and discussion
4.5 Application of C-C modelling: Separating anthropogenic from geogenic patterns in soils of Lemesos
4.5.1 Data processing
4.5.2 Results and discussion
4.6 Simulated fractal models
4.7 Category-based fractal modelling
4.7.1 Category-based fractal modelling based on the related bedrocks representative samples
4.7.2 Category-based fractal modelling based on the related bedrocks whole simulated samples
5. Effectiveness and uncertainty in geochemical anomaly classification models
5.1 Introduction
5.2 Comparison of model efficiencies
5. Monte Carlo simulation (MCSIM) applied to the characterised populations to quantify the thresholds’ uncertainties
5.3.1 Results and discussion
5.4 The Cyprus Soil Atlas
5.4.1 Results and discussion
6. Spatial uncertainty in categorising geological data
6.1 Introduction
6.2 Data analysis
6.2.1 Swedish till data
6.2.2 Cyprus case study
7. General discussion and conclusions
7.1 Discussion
7.1.1 Introduction
7.1.2 Performance of the developed classification models based on their systematic and spatial uncertainties
7.2 Conclusions
7.3 Future Work
7.3.1 3D modelling in depth
7.3.2 C-C and SC-SC fractal models in urban geology
7.3.3 Decision-making
7.3.4 Simulations applicable
7.3.5 Systematic uncertainty of the other classification models
7.3.6 Other multi-variate analysis approaches
- No. of pages: 302
- Language: English
- Edition: 1
- Published: May 17, 2024
- Imprint: Elsevier
- Paperback ISBN: 9780323908979
- eBook ISBN: 9780323908986
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Behnam Sadeghi
Dr. Behnam Sadeghi, a pioneering geoscientist, is a Research Fellow at the ARRC in CSIRO, Australia, and a Fulbright Research Scholar at the Carnegie Institution for Science, EPL, Washington, D.C., United States. His expertise lies in mineral exploration, integrating mathematical geosciences, geostatistics, GIS, and data analytics, providing profound insights into critical minerals. Holding a PhD in Geosciences from the University of New South Wales, Dr. Sadeghi’s groundbreaking work includes innovative multifractal classification models and sustainable mineral exploration, recognized by his prestigious IAMG’s Founders Scholarship (2020) and Andrei Borisovich Vistelius Research Award (2023). His roles as Associate Editor and Board member for leading journals like Ore Geology Reviews highlight his influence. With global collaborations across academia, industry, and research institutes, he has earned fellowships from respected bodies, including FAAG, FAusIMM, FAIG, and the title of RPGeo by AIG.
Affiliations and expertise
CSIRO Mineral Resources, Australian Resources Research Centre (ARRC), Kensington, Australia; and Earth and Sustainability Science Research Centre, School of Biological, Earth and Environmental Sciences, University of New South Wales, AustraliaRead Fractals and Multifractals in the Geosciences on ScienceDirect