Fractals in the Earth Sciences

Fractals have changed the way we understand and study nature. This change has been brought about mainly by the work of B. B. Mandelbrot and his book The Fractal Geometry of Nature. Now here is a book that collects articles treating fractals in the earth sciences. The themes chosen span, as is appropriate for a discourse on fractals, many orders of magnitude; including earthquakes, ocean floor topography, fractures, faults, mineral crystallinity, gold and silver deposition. There are also chapters on dynamical processes that are fractal, such as rivers, earthquakes, and a paper on self-organized criticality. Many of the chapters discuss how to estimate fractal dimensions, Hurst exponents, and other scaling exponents. This book, in a way, represents a snapshot of a field in which fractals has brought inspiration and a fresh look at familiar subjects. New ideas and attempts to quantify the world we see around us are found throughout. Many of these ideas will grow and inspire further work, others will be superseded by new observations and insights, most probably with future contributions by the authors of these chapters.

Klappentext

This well-illustrated volume reviews the many applications of fractal geometry used to study earth science patterns and processes. Designed as an introduction to this new area of study, the papers represent a broad spectrum of earth science disciplines where patterns have proven to be fractal over many orders of magnitude in time or space. This volume features an exhaustive list of published fractal dimensions measured for earth science patterns.

Inhalt

1. Fractal Distributions in Geology, Scale Invariance, and Deterministic Chaos.- 2. Some Long-Run Properties of Geophysical Records.- 3. Some Remarks on the Numerical Estimation of Fractal Dimension.- 4. Measuring the Dimension of Self-Affine Fractals: Example of Rough Surfaces.- 5. Review of the Fractal Character of Natural Fault Surfaces with Implications for Friction and the Evolution of Fault Zones.- 6. Fractals and Ocean Floor Topography: A Review and a Model.- 7. Fractal Transitions on Geological Surfaces.- 8. Fractal Analysis of Scaling and Spatial Clustering of Fractures.- 9. Fractal Fragmentation in Crustal Shear Zones.- 10. Fractal Distribution of Fault Length and Offsets: Implications of Brittle Deformation EvaluationThe Lorraine Coal Basin.- 11. Fractal Dynamics of Earthquakes.- 12. Mineral Crystallinity in Igneous Rocks: Fractal Method.- 13. Fractal Structure of Electrum Dendrites in Bonanza Epithermal Au-Ag Deposits.