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Fractals and Multifractals in the Geosciences /

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 assessment of uncertainty in sample classification and stability of spatial patterns.

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Bibliographische Detailangaben
1. Verfasser: Sadeghi, Behnam (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: San Diego : Elsevier, 2024.
Schlagworte:
Earth sciences > Mathematics.
Fractals.
Sciences de la terre > Mathématiques.
Fractales.
fractals.
SCIENCE / Earth Sciences / Geology.
MATHEMATICS / General.
Earth sciences > Mathematics
Fractals
Online-Zugang:ScienceDirect
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Inhaltsangabe:
  • Front Cover
  • Fractals and Multifractals in the Geosciences
  • Copyright Page
  • Dedication
  • Contents
  • Foreword
  • Preface
  • Target audience
  • Acknowledgments
  • 1 The theory of fractal geometry
  • 1.1 Introduction to fractal geometry in nature and its difference from Euclidean geometry
  • 1.2 Multifractal spectrums
  • 1.2.1 Mono-fractals and multifractals
  • 1.2.2 Continuous multifractals
  • 1.2.3 Discrete multifractals
  • 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
  • 2 Introduction: characterizing and mapping geochemical anomalies
  • 2.1 A short review of some of the traditional statistical models
  • 2.1.1 Exploratory data analysis
  • 2.1.2 Weights of evidence model
  • 2.2 Population models
  • 2.3 Spatial models
  • 2.4 Multifractal techniques
  • 2.4.1 Momentum technique
  • 2.4.2 Coefficient of variation
  • 2.5 Fractal techniques
  • 2.5.1 Power spectrum frequency model
  • 2.5.2 Length-step model
  • 2.5.3 Variography
  • 2.5.4 Box-counting model
  • 2.5.5 Perimeter-area model
  • 2.5.6 Radius productivity-area model
  • 2.5.7 Number-area model
  • 2.6 Technical process
  • 2.7 Traditional fractal and multifractal modeling in geochemical studies (with examples)
  • 2.7.1 Number-size fractal model
  • 2.7.2 Concentration-area fractal model
  • 2.7.3 Concentration-perimeter fractal model
  • 2.7.4 Concentration-distance fractal model
  • 2.7.5 Power spectrum-area fractal model
  • 2.7.6 Singularity model
  • 2.7.7 Concentration-volume fractal model
  • 2.7.8 Spectrum-volume fractal model
  • 2.8 Multifractal inverse distance weighted interpolation and fractal filtering in environmental studies
  • 2.9 Several other examples
  • References
  • 3 Geochemical datasets
  • 3.1 Till geochemical atlas of Sweden
  • 3.1.1 Sweden's geology and mineralization
  • 3.1.2 Quaternary glacial deposits and topography
  • 3.1.3 Till geochemistry atlas
  • 3.2 The soil geochemical atlas of Cyprus
  • 3.2.1 Geology of Cyprus
  • 3.2.2 Soil geochemistry
  • 3.2.3 Urban geochemical map of Lemesos
  • 3.3 General data processing
  • 3.3.1 Factor analysis
  • 3.4 Zaghia iron ore deposit, anomaly 2C
  • 3.4.1 Geological setting
  • 3.4.2 General data processing
  • 3.4.2.1 Borehole 13
  • 3.4.2.2 Borehole 15
  • 3.4.2.3 Borehole 21
  • 3.4.3 Comparison of the initial model and revised model
  • 3.4.4 N-S classified model
  • 3.4.5 C-V classified model
  • 3.4.6 Comparison of fractal models and geological model of the deposit
  • References
  • 4 Novel multifractal classification models
  • 4.1 Concentration-distance from centroids fractal model
  • 4.1.1 C-DC calculations
  • 4.2 Concentration-concentration fractal model.

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