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Fractals and chaos in geology and geophysics
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Earth-Science Reviews36 (1994) 131-148
Book Reviews Fractals
Donald L. Turcotte, 1992. Fractals and Chaos in Geology and Geophysics. Cambridge University Press. 221 pp. (Paperback), Price: £17.95. ISBN 0-521-44767-4. The mathematical concepts underlying fractals and chaos date to the work of Cantor and Poincar6, almost a century ago. But, until very recently, fractal sets and chaotic dynamical systems were considered curiosities of interest only to mathematicians. Mandelbrot's book The Fractal Geometry of Nature has done much to draw the attention of scientists from all disciplines to fractals. A paper by Lorenz, demonstrating the existence of chaos in Rayleigh Benard convection, convinced scientists that many systems in nature are indeed chaotic. Applications to many field of sciences have mushroomed during the past ten years. Don Turcotte was among the first geoscientists to see the potential of these concepts and to advocate their introduction in the Earth sciences. With his students, Don Turcotte has made many research contributions and demonstrated the usefulness of very simple physical models that contain all the complexity of earth sciences systems. Based on the author's research, the book Fractals and Chaos in Geology and Geophysics is an excellent introduction for the solid Earth geoscientists. The first half of the book is devoted to fractals. The author has chosen to introduce fractals through scale invariance because of the many examples in the Earth sciences. The concept of self-similarity, power law distributions, self-affinity follow naturally. Useful relationships between the spectral and fractal properties of distributions are derived. Many geological examples are presented of scale invariant phenomena (fragmentation, distribution of faults, earthquakes, topogra-
phy, drainage systems, natural ressource distribution, etc.). Fractal geometry is useful to model many distributions in Earth sciences because they are produced by chaotic dynamical processes. The second half of the book introduces chaotic dynamics and applies it to some geophysical systems. Some systems of equations, such as the equations describing thermal convection in a fluid, exhibit exponential sensitivity to initial conditions. Although the systems are deterministic, their evolution is computationally impossible to predict. Many geophysical problems (magnetic reversals, mantle convection, earthquakes, etc.) seem to exhibit chaotic behavior. The author introduces and analyzes simple models that exhibit the same complexity as the earthquake or the geodynamo. Useful information on these systems can be extracted from application of chaotic dynamics. Systems with many degrees of freedom are not chaotic but they exhibit critical behavior near phase transitions. The properties of large systems near the critical point can be treated through the renormalization group theory. The author introduces the renormalization group to build a model of the earthquake process. Finally, he presents the concept of self-organized critically. This book is an excellent introduction to fractals and chaos for geoscientists. The references to the solid Earth literature are very complete, but the list of more general references seems quite limited. One could also find a lack of historical perspective, as the pionneer work of Poincar6, Hausdorf, and the Russian mechanicians is ignored. However the merits of the book outweigh by far its weaknesses. Fractals and Chaos in Geology and Geophysics demonstrates that these concepts are useful and do not require a formidable mathematical apparatus. This book, like many publications of the author, shows that there is much insight to be gained from simple physicals
0012-8252/94/$26.00 © 1994 Elsevier Science B.V. All rights reserved
132
Book Reviews ~Earth-Science Reviews 36 (1994) 131-148
models. These simple models remain very remote from the real Earth. The value of the book is to challenge the reader to find the link between these models and the Earth. It will be a key reference for all geophysicists involved in research on fractals and chaos. All geoscientists who are simply curious about fractals, chaos and their applications in the Earth sciences, will find in this book the best introduction. Jean-Claude Mareschal, Montreal, Que. SSDI 0012-8252(93)E0038-J
Palynology Inge-Lise Marie Stuijts, 1993. Late Pleistocene and Holocene Vegetation of West Java, Indonesia. A.A. Balkema, Rotterdam. Hardcover, XII + 173 pp., ISBN 90-5410-148-2. This latest contribution in the valuable series "Modern Quaternary Research in Southeast Asia" is a monograph derived largely from the dissertation of Inge-Lise Marie Stuijts from the University of Groningen. It focuses on the results of pollen analysis of volcanic crater sediments from the Gede Pangrango National Park and Telaga Patengan plateau regions of tropical, humid, West Java, and was undertaken in order to reconstruct the history of climate and to document the impact of people on the vegetation. Nine pollen diagrams from 8 sites are presented, covering lower montane altitudes from about 1000 to 1600 m, and age ranges from the last 3000 to 17,000 years. Interpretation is assisted by a general knowledge of the present day ecology of represented plants and by limited modern pollen studies. Although some of the information has been published previously, it is extremely useful to have these data together in one volume. The monograph is clearly written and logically structured with introductory chapters on the aims of the project including a history of late Quaternary palynological studies within the Indonesian region, the physical environment and modern vegetation. These are followed by chapters on
methodology, surface sample studies, each of the eight sites and some brief comments on representation and identification of selected pollen taxa. The subsequent discussion attempts a correlation between sites and brings out major regional vegetation and climatic changes. The patterns of change are then compared with those derived from existing studies in Sumatra. The final chapter is devoted to the description of all identified pollen taxa and is accompanied by 114 photographs of selected taxa. An appendix details the occurences of minor types not included on the pollen diagrams. The diagrams themselves are presented as large fold outs that require a great deal of desk space to examine properly. The study is very much exploratory and traditional. The amount of fossil pollen information is substantial and much of the volume is taken up with individual diagram description and detailed interpretation, much of which is very speculative. This approach, somewhat inevitably, has led to a great deal of repetition. One major limitation is the lack of stratigraphic information. Generally only one core has been taken from each site unless revisited in an attempt to collect a longer core, and no sedimentological analyses have been undertaken. Consequently it has proven difficult to make informed assessments of the relative importance of the various disturbance factors such as human activity and volcanism that characterise the records. The lack of absolute pollen data has also limited the reliability of proposed differential sediment accumulation rates. In relation to interpretation of vegetation changes, the disturbed nature of the landscape made it difficult to collect surface samples covering the range of "natural" vegetation communities that would have been represented in the area but, even so, more effort could have been put into this area. No overall analysis of the surface samples was attempted and no information was presented on methods of collection to allow any assessment of sample comparability. Despite the limitations, the study provides a good overview of the complex pattern of vegetation and environmental changes through the recorded period. In general terms Dacrycarpus montane forest was widespread from at least
SCIENCE
i
,
REVIEWS
ELSEVIER
Earth-Science Reviews36 (1994) 131-148
Book Reviews Fractals
Donald L. Turcotte, 1992. Fractals and Chaos in Geology and Geophysics. Cambridge University Press. 221 pp. (Paperback), Price: £17.95. ISBN 0-521-44767-4. The mathematical concepts underlying fractals and chaos date to the work of Cantor and Poincar6, almost a century ago. But, until very recently, fractal sets and chaotic dynamical systems were considered curiosities of interest only to mathematicians. Mandelbrot's book The Fractal Geometry of Nature has done much to draw the attention of scientists from all disciplines to fractals. A paper by Lorenz, demonstrating the existence of chaos in Rayleigh Benard convection, convinced scientists that many systems in nature are indeed chaotic. Applications to many field of sciences have mushroomed during the past ten years. Don Turcotte was among the first geoscientists to see the potential of these concepts and to advocate their introduction in the Earth sciences. With his students, Don Turcotte has made many research contributions and demonstrated the usefulness of very simple physical models that contain all the complexity of earth sciences systems. Based on the author's research, the book Fractals and Chaos in Geology and Geophysics is an excellent introduction for the solid Earth geoscientists. The first half of the book is devoted to fractals. The author has chosen to introduce fractals through scale invariance because of the many examples in the Earth sciences. The concept of self-similarity, power law distributions, self-affinity follow naturally. Useful relationships between the spectral and fractal properties of distributions are derived. Many geological examples are presented of scale invariant phenomena (fragmentation, distribution of faults, earthquakes, topogra-
phy, drainage systems, natural ressource distribution, etc.). Fractal geometry is useful to model many distributions in Earth sciences because they are produced by chaotic dynamical processes. The second half of the book introduces chaotic dynamics and applies it to some geophysical systems. Some systems of equations, such as the equations describing thermal convection in a fluid, exhibit exponential sensitivity to initial conditions. Although the systems are deterministic, their evolution is computationally impossible to predict. Many geophysical problems (magnetic reversals, mantle convection, earthquakes, etc.) seem to exhibit chaotic behavior. The author introduces and analyzes simple models that exhibit the same complexity as the earthquake or the geodynamo. Useful information on these systems can be extracted from application of chaotic dynamics. Systems with many degrees of freedom are not chaotic but they exhibit critical behavior near phase transitions. The properties of large systems near the critical point can be treated through the renormalization group theory. The author introduces the renormalization group to build a model of the earthquake process. Finally, he presents the concept of self-organized critically. This book is an excellent introduction to fractals and chaos for geoscientists. The references to the solid Earth literature are very complete, but the list of more general references seems quite limited. One could also find a lack of historical perspective, as the pionneer work of Poincar6, Hausdorf, and the Russian mechanicians is ignored. However the merits of the book outweigh by far its weaknesses. Fractals and Chaos in Geology and Geophysics demonstrates that these concepts are useful and do not require a formidable mathematical apparatus. This book, like many publications of the author, shows that there is much insight to be gained from simple physicals
0012-8252/94/$26.00 © 1994 Elsevier Science B.V. All rights reserved
132
Book Reviews ~Earth-Science Reviews 36 (1994) 131-148
models. These simple models remain very remote from the real Earth. The value of the book is to challenge the reader to find the link between these models and the Earth. It will be a key reference for all geophysicists involved in research on fractals and chaos. All geoscientists who are simply curious about fractals, chaos and their applications in the Earth sciences, will find in this book the best introduction. Jean-Claude Mareschal, Montreal, Que. SSDI 0012-8252(93)E0038-J
Palynology Inge-Lise Marie Stuijts, 1993. Late Pleistocene and Holocene Vegetation of West Java, Indonesia. A.A. Balkema, Rotterdam. Hardcover, XII + 173 pp., ISBN 90-5410-148-2. This latest contribution in the valuable series "Modern Quaternary Research in Southeast Asia" is a monograph derived largely from the dissertation of Inge-Lise Marie Stuijts from the University of Groningen. It focuses on the results of pollen analysis of volcanic crater sediments from the Gede Pangrango National Park and Telaga Patengan plateau regions of tropical, humid, West Java, and was undertaken in order to reconstruct the history of climate and to document the impact of people on the vegetation. Nine pollen diagrams from 8 sites are presented, covering lower montane altitudes from about 1000 to 1600 m, and age ranges from the last 3000 to 17,000 years. Interpretation is assisted by a general knowledge of the present day ecology of represented plants and by limited modern pollen studies. Although some of the information has been published previously, it is extremely useful to have these data together in one volume. The monograph is clearly written and logically structured with introductory chapters on the aims of the project including a history of late Quaternary palynological studies within the Indonesian region, the physical environment and modern vegetation. These are followed by chapters on
methodology, surface sample studies, each of the eight sites and some brief comments on representation and identification of selected pollen taxa. The subsequent discussion attempts a correlation between sites and brings out major regional vegetation and climatic changes. The patterns of change are then compared with those derived from existing studies in Sumatra. The final chapter is devoted to the description of all identified pollen taxa and is accompanied by 114 photographs of selected taxa. An appendix details the occurences of minor types not included on the pollen diagrams. The diagrams themselves are presented as large fold outs that require a great deal of desk space to examine properly. The study is very much exploratory and traditional. The amount of fossil pollen information is substantial and much of the volume is taken up with individual diagram description and detailed interpretation, much of which is very speculative. This approach, somewhat inevitably, has led to a great deal of repetition. One major limitation is the lack of stratigraphic information. Generally only one core has been taken from each site unless revisited in an attempt to collect a longer core, and no sedimentological analyses have been undertaken. Consequently it has proven difficult to make informed assessments of the relative importance of the various disturbance factors such as human activity and volcanism that characterise the records. The lack of absolute pollen data has also limited the reliability of proposed differential sediment accumulation rates. In relation to interpretation of vegetation changes, the disturbed nature of the landscape made it difficult to collect surface samples covering the range of "natural" vegetation communities that would have been represented in the area but, even so, more effort could have been put into this area. No overall analysis of the surface samples was attempted and no information was presented on methods of collection to allow any assessment of sample comparability. Despite the limitations, the study provides a good overview of the complex pattern of vegetation and environmental changes through the recorded period. In general terms Dacrycarpus montane forest was widespread from at least