Application Of Fractals In Earth Sciences

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Application Of Fractals In Earth Sciences

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Author : V.P. Dimri
language : en
Publisher: CRC Press
Release Date : 2000-01-01

Application Of Fractals In Earth Sciences written by V.P. Dimri and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Science categories.

This text examines the emerging field of fractals and its applications in earth sciences. Topics covered include: concepts of fractal and multifractal chaos; the application of fractals in geophysics, geology, climate studies, and earthquake seismology.

Fractals In The Earth Sciences

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Author : C.C. Barton
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Fractals In The Earth Sciences written by C.C. Barton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Technology & Engineering categories.

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 Many of these ideas will grow and inspire further work, others will be superseded by new observations and insights, most probably with future contributions by the authors of these chapters.

Wavelets And Fractals In Earth System Sciences

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Author : E. Chandrasekhar
language : en
Publisher: Taylor & Francis
Release Date : 2013-11-20

Wavelets And Fractals In Earth System Sciences written by E. Chandrasekhar and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-20 with Science categories.

The subject of wavelet analysis and fractal analysis is fast developing and has drawn a great deal of attention in varied disciplines of science and engineering. Over the past couple of decades, wavelets, multiresolution, and multifractal analyses have been formalized into a thorough mathematical framework and have found a variety of applications w

Fractals

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Author : Behzad Ghanbarian
language : en
Publisher: CRC Press
Release Date : 2017-11-23

Fractals written by Behzad Ghanbarian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-23 with Mathematics categories.

This book provides theoretical concepts and applications of fractals and multifractals to a broad range of audiences from various scientific communities, such as petroleum, chemical, civil and environmental engineering, atmospheric research, and hydrology. In the first chapter, we introduce fractals and multifractals from physics and math viewpoints. We then discuss theory and practical applications in detail. In what follows, in chapter 2, fragmentation process is modeled using fractals. Fragmentation is the breaking of aggregates into smaller pieces or fragments, a typical phenomenon in nature. In chapter 3, the advantages and disadvantages of two- and three-phase fractal models are discussed in detail. These two kinds of approach have been widely applied in the literature to model different characteristics of natural phenomena. In chapter 4, two- and three-phase fractal techniques are used to develop capillary pressure curve models, which characterize pore-size distribution of porous media. Percolation theory provides a theoretical framework to model flow and transport in disordered networks and systems. Therefore, following chapter 4, in chapter 5 the fractal basis of percolation theory and its applications in surface and subsurface hydrology are discussed. In chapter 6, fracture networks are shown to be modeled using fractal approaches. Chapter 7 provides different applications of fractals and multifractals to petrophysics and relevant area in petroleum engineering. In chapter 8, we introduce the practical advantages of fractals and multifractals in geostatistics at large scales, which have broad applications in stochastic hydrology and hydrogeology. Multifractals have been also widely applied to model atmospheric characteristics, such as precipitation, temperature, and cloud shape. In chapter 9, these kinds of properties are addressed using multifractals. At watershed scales, river networks have been shown to follow fractal behavior. Therefore, the applications of fractals are addressed in chapter 10. Time series analysis has been under investigations for several decades in physics, hydrology, atmospheric research, civil engineering, and water resources. In chapter 11, we therefore, provide fractal, multifractal, multifractal detrended fluctuation analyses, which can be used to study temporal characterization of a phenomenon, such as flow discharge at a specific location of a river. Chapter 12 addresses signals and again time series using a novel fractal Fourier analysis. In chapter 13, we discuss constructal theory, which has a perspective opposite to fractal theories, and is based on optimizationof diffusive exchange. In the case of river drainages, for example, the constructal approach begins at the divide and generates headwater streams first, rather than starting from the fundamental drainage pattern.

Fractal Solutions For Understanding Complex Systems In Earth Sciences

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Author : V.P. Dimri
language : en
Publisher: Springer
Release Date : 2015-11-21

Fractal Solutions For Understanding Complex Systems In Earth Sciences written by V.P. Dimri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-21 with Science categories.

This book deals with fractals in understanding problems encountered in earth science, and their solutions. It starts with an analysis of two classes of methods (homogeneous fractals random models, and homogeneous source distributions or “one point” distributions) widely diffused in the geophysical community, especially for studying potential fields and their related source distributions. Subsequently, the use of fractals in potential fields is described by scaling spectral methods for estimation of curie depth. The book also presents an update of the use of the fractal concepts in geological understanding of faults and their significance in geological modelling of hydrocarbon reservoirs. Geophysical well log data provide a unique description of the subsurface lithology; here, the Detrended Fluctuation Analysis technique is presented in case studies located off the west-coast of India. Another important topic is the fractal model of continuum percolation which quantitatively reproduce the flow path geometry by applying the Poiseuille’s equation. The pattern of fracture heterogeneity in reservoir scale of natural geological formations can be viewed as spatially distributed self-similar tree structures; here, the authors present simple analytical models based on the medium structural characteristics to explain the flow in natural fractures. The Fractal Differential Adjacent Segregation (F-DAS) is an unconventional approach for fractal dimension estimation using a box count method. The present analysis provides a better understanding of variability of the system (adsorbents – adsorbate interactions). Towards the end of book, the authors discuss multi-fractal scaling properties of seismograms in order to quantify the complexity associated with high-frequency seismic signals. Finally, the book presents a review on fractal methods applied to fire point processes and satellite time-continuous signals that are sensitive to fire occurrences.

Fractals And Dynamic Systems In Geoscience

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Author : Tom G. Blenkinsop
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Fractals And Dynamic Systems In Geoscience written by Tom G. Blenkinsop and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

Concepts and methods of fractal geometry penetrate various branches of human knowledge to an increasing degree. This tendency is particularly striking in the geosciences, because many processes occurring in and on the Earth result in time dependences and spatial patterns that have a fractal character. The contributions in this volume arose from the "3rd International Symposium on Fractals and Dynamic Systems in Geosciences", held at Stara Lesna, Slovakia in June, 1997. The volume contains new ideas and applications of fractal geometry in such diverse branches of geoscience as engineering geology, the physics of the lithosphere (including faulting, seismicity, and fluid flow), and climate behavior.

Fractals In Petroleum Geology And Earth Processes

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Author : C.C. Barton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Fractals In Petroleum Geology And Earth Processes written by C.C. Barton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.

In this unique volume, renowned experts discuss the applications of fractals in petroleum research-offering an excellent introduction to the subject. Contributions cover a broad spectrum of applications from petroleum exploration to production. Papers also illustrate how fractal geometry can quantify the spatial heterogeneity of different aspects of geology and how this information can be used to improve exploration and production results.

Fractals In Soil Science

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Author : Y. Pachepsky
language : en
Publisher: Elsevier
Release Date : 2000-07-19

Fractals In Soil Science written by Y. Pachepsky and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-19 with Science categories.

This book presents the state-of-the-art after fifteen years of exponentially growing applications of fractal geometry in soil science. It demonstrates the wide-ranging applicability of fractal models in soil science and indicates new opportunities to integrate processes in soils within or across scales using fractals. Contributed by some of the pioneers in the field, chapters represent a broad spectrum of applications from geochemistry to microbiology and from scales of micrometers to the landscape, and serve as an introduction to the subject. Topics include fractal aspects of soil structure, porosity and texture, scaling in preferential and hydraulic conductivity, anoxic volumes and adsorption in fractal models of soil, characterization of the pore surface irregularity, fractal properties of soil organic matter, fractal concepts in studies of soil fauna and mycelium in soils, and fractal analysis of spatial and temporal variability in soil properties and crop yields. A wide spectrum of methods for identifying and measuring fractal properties is introduced and critically discussed. Although the book focussed on solving problems in soil science, the applications and the fractal approach used share much in common with many other fields within and outside of the earth sciences. A unique bibliography on fractals in soils science is included.

Fractals And Chaos In Geology And Geophysics

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Author : Donald L. Turcotte
language : en
Publisher: Cambridge University Press
Release Date : 1997-07-13

Fractals And Chaos In Geology And Geophysics written by Donald L. Turcotte and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-13 with Mathematics categories.

The fundamental concepts of fractal geometry and chaotic dynamics, along with the related concepts of multifractals, self-similar time series, wavelets, and self-organized 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. 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.

Fractal Models In The Earth Sciences

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Author : Gabor Korvin
language : en
Publisher: Elsevier Publishing Company
Release Date : 1992

Fractal Models In The Earth Sciences written by Gabor Korvin and has been published by Elsevier Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

A fractal is a mathematical set or object whose form is extremely irregular and/or fragmented at all scales. So reads Mandelbrot's definition of the term which he coined and widely popularised in his famous monographs. This volume presents the first systematic summary of the fractal models that have been proposed to explain the irregular features and phenomena of the Earth -- from meandering rivers and rugged coastlines to the pore space of reservoir sandstones and the prediction of earthquakes. No previous knowledge of fractals is assumed. Connections and analogies with other fields of natural and technical sciences (physics, biology, fractography, etc.) are always pointed out. More than 300 illustrations are included, demonstrating how fractal geometry reveals astonishing similarities between natural phenomena at widely different scales. The readership for this book is wide and includes: geological scientists, oceanographers, and meteorologists involved in describing and analysing irregular spatial data; as well as applied mathematicians, physicists and computer scientists looking for new fields of research.