The fundamental concepts of fractal geometry and chaotic dynamics, along with the related concepts of multifractals, self-similar time series, wavelets, and self-organised criticality, are introduced in this book, for a broad range of readers interested in complex natural phenomena. Now in a greatly expanded second edition, this book relates fractals and chaos to a variety of geological and geophysical applications. These include drainage networks and erosion, floods, earthquakes, mineral and petroleum resources, fragmentation, mantle convection and magnetic field generation. Many advances have been made in the field since the first edition was published. In this edition coverage of self-organised criticality is expanded and statistics and time series are included to provide a broad background for the reader. All concepts are introduced at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mathematics. Problems are included for the reader to solve.
The fundamental concepts of fractal geometry and chaotic dynamics, along with the related concepts of multifractals, self-similar time series, wavelets, and self-organised criticality, are introduced in this book, for a broad range of readers interested in complex natural phenomena. Now in a greatly expanded second edition, this book relates fractals and chaos to a variety of geological and geophysical applications. These include drainage networks and erosion, floods, earthquakes, mineral and petroleum resources, fragmentation, mantle convection and magnetic field generation. Many advances have been made in the field since the first edition was published. In this edition coverage of self-organised criticality is expanded and statistics and time series are included to provide a broad background for the reader. All concepts are introduced at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mathematics. Problems are included for the reader to solve.
Inhaltsverzeichnis
Preface; Preface to the second edition; 1. Scale invariance; 2. Definition of a fractal set; 3. Fragmentation; 4. Seismicity and tectonics; 5. Ore grade and tonnage; 6. Fractal clustering; 7. Self-affine fractals; 8. Geomorphology; 9. Dynamical systems; 10. Logistic map; 11. Slider-block models; 12. Lorenz equations; 13. Is mantle convection chaotic?; 14. Rikitake dynamo; 15. Renormalization group method; 16. Self-organized criticality; 17. Where do we stand?; References; Appendix A: glossary of terms; Appendix B: units and symbols; Answers to selected problems; Index.
