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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
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Foreword
- Preface
- Target audience
- Acknowledgments
- Chapter 1. The theory of fractal geometry
- Abstract
- 1.1 Introduction to fractal geometry in nature and its difference from Euclidean geometry
- 1.2 Multifractal spectrums
- 1.3 Fractal dimension and Hurst exponent (H)
- 1.4 Self-similarity and self-affinity
- 1.5 Power law frequency
- 1.6 Fractal and multifractal modeling in geochemical studies
- References
- Chapter 2. Introduction: characterizing and mapping geochemical anomalies
- Abstract
- 2.1 A short review of some of the traditional statistical models
- 2.2 Population models
- 2.3 Spatial models
- 2.4 Multifractal techniques
- 2.5 Fractal techniques
- 2.6 Technical process
- 2.7 Traditional fractal and multifractal modeling in geochemical studies (with examples)
- 2.8 Multifractal inverse distance weighted interpolation and fractal filtering in environmental studies
- 2.9 Several other examples
- References
- Chapter 3. Geochemical datasets
- Abstract
- 3.1 Till geochemical atlas of Sweden
- 3.2 The soil geochemical atlas of Cyprus
- 3.3 General data processing
- 3.4 Zaghia iron ore deposit, anomaly 2C
- References
- Chapter 4. Novel multifractal classification models
- Abstract
- 4.1 Concentration-distance from centroids fractal model
- 4.2 Concentration-concentration fractal model
- 4.3 Application of C-C and C-DC modeling: enhancing the detection of Cu deposits in Cyprus
- 4.4 Application of C-C modeling: separating anthropogenic from geogenic patterns in soils of Lemesos
- 4.5 Stochastic simulation methods applicable to fractal models
- 4.6 Simulated multifractal models
- 4.7 Category-based fractal modeling
- References
- Chapter 5. Effectiveness and uncertainty in geochemical anomaly classification models
- Abstract
- 5.1 Uncertainties in geochemical modeling
- 5.2 Problem statement
- 5.3 Aims and approach
- 5.4 Introduction
- 5.5 Comparison of model efficiencies
- 5.6 MCSIM applied to the characterized populations to quantify the thresholds’ uncertainties
- 5.7 The Cyprus soil atlas
- References
- Chapter 6. Spatial uncertainty in categorizing geochemical data
- Abstract
- 6.1 Introduction
- 6.2 Spatial uncertainty evaluation theory
- 6.3 Discussion
- References
- Chapter 7. General discussion, conclusions, and recommendations for the future
- Abstract
- 7.1 Discussion
- 7.2 Conclusions
- 7.3 Future work
- References
- Appendix
- Supplementary figures
- Index
- No. of pages: 302
- Language: English
- Edition: 1
- Published: May 17, 2024
- Imprint: Elsevier
- Paperback ISBN: 9780323908979
- eBook ISBN: 9780323908986
BS
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