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Spectral Analysis in Geophysics
Tectonophysics, 27 (1975) 83-92 @ Elsevier Scientific Publishing Company,
Amsterdam
-- Printed
in The Netherlands
E OK REVIEWS Spectral Analysis in Geophysics. M. Bath. Developments in Solid Earth Geophysics No. 7. Elsevier, Amsterdam, 1974, 570 pp., 101 fig., Dfl. 120.00. The spectral analysis of the title is used in its wider sense to include the theory and applications of various integral processes, based on the Fourier transform, to the analysis of time series. Spectral analysis is largely a computer-based technique, and almost all the developments and major applications have taken place during the last 15 years. Professor Bath has undertaken a difficult task in discussing techniques which are still undergoing an explosive burst of development. A measure of the magnitude of the task are the number of techniques such as maximum entropy-, high resolution-, and Walsh sequential-spectral analysis among others, which the author recognizes as important, but which have been developed too recently to have been widely applied at the time of going to press. However, a line had to be drawn somewhere, and Professor Bath has written a very convenient text book summarizing and cataloging most developments and applications of spectral techniques up until about 1972. This volume has two major contributions to make: It contains a comprehensive and easily understood theoretical background to the theory of spectral analysis in geophysics. Following the historical development, the book describes briefly the early analogue techniques, and develops the mathematical background to Fourier series and Fourier transforms, and the relation between power spectra, correlation functions, and convolution. These last developments by Blackman and Tukey in 1959, coinciding with the general availability of large computers, provided the techniques for the application of spectral methods in geophysics. These techniques were replaced in the mid-sixties by Fast Fourier Transform methods of great computational efficiency. These methods are described, and the problems of applying them to geophysical time series, of aliasing, windowing and filtering, and the reliability of the final spectra are discussed. The second major contribution is the discussion of the applications of spectral analysis to specific problems in geophysics. There are 64 pages of references to applications in seismology, meteorology, oceanography, gravity, and geomagnetism, and the discussion and cross-references in the text indicate that the author has read most, if not all, of the works he refers to. As would be expected from the author’s own research interests there are references to more applications in seismology than in the other branches of geophysics put together, but this is probably a reflection of the particular importance of spectral analysis to seismology. Professor Bath has written a book with great clarity of style, which makes available to the geophysicist some of his own prodigious reading. Reading this book will be the easiest way for a geophysicist to enter the field of
84
spectral analysis, both for the broad outline of the theory, and for the summary of applications of time-series analysis in the first decade or so of computer applications in geophysics. STUART
CRAMPIN
(Edinburgh)
The Structure of the Earth’s Crust, based on Seismic Data. S. Mueller (Editor). Elsevier, Amsterdam, 1974, 392 pp., 193 fig., Dfl. 100.00. This book is a collection of 33 papers dealing specifically with the structure of the earth’s crust in various regions of the world, including portions of the U.S.S.R., Europe, Africa, India, North and South:America, Hawaii, Australia, Japan, and both polar regions. The papers are those presented at a 1971 International Upper Mantle Committee Symposium on “Crustal Structure Based on Seismic Data”. Although predominantly seismic, as the title states, several of the papers incorporate gravity, magnetic, or other geophysical data to strengthen the interpretations. Editor Mueller, in the Foreword, succinctly emphasizes the importance of the book in which he states “the results . . . show that crustal structure cannot be considered separately from the structure of the mantle. The increasing complexity of the velocity-depth profiles makes it more and more difficult to sustain the simple motion of a lithosphere-asthenosphere model for the crust and upper mantle.” The truth of this statement is substantiated with little more than a cursory reading of the book; the diversity of measured seismic velocities and deduced structure even within a single region is so pronounced that the prevalent use of the terms “granitic” and “basaltic” to characterize a crustal section is an oversimplification at best and is misleading at worst. A significant implication of the book is that before any generalization is made concerning what might consitute a typical crust a far more complete program of crustal studies in new regions must be implemented. The selection of the particular papers is approximately representative of the levels of effort and support provided by various nations for geophysical studies. For example, the Soviet contribution is ten papers, reflecting in part the priority placed on crustal studies via the sustained and integrated Deep Seismic Sounding Program in the Soviet Union. Virtually all of the papers emphasize summary results of investigations, in the form of cross-sections or tables, and avoid discussing the details of accepted analysis techniques. However, if a discussion is desired of the various methods of analysis and interpretation, the generally excellent references included with the papers can be used to effectively pursue the subject. The amount of detail and completeness varies considerably between papers, from a single paragraph (with no references) on the central North American rift system to 34 pages with elaborate fold-outs and a rather com-
Amsterdam
-- Printed
in The Netherlands
E OK REVIEWS Spectral Analysis in Geophysics. M. Bath. Developments in Solid Earth Geophysics No. 7. Elsevier, Amsterdam, 1974, 570 pp., 101 fig., Dfl. 120.00. The spectral analysis of the title is used in its wider sense to include the theory and applications of various integral processes, based on the Fourier transform, to the analysis of time series. Spectral analysis is largely a computer-based technique, and almost all the developments and major applications have taken place during the last 15 years. Professor Bath has undertaken a difficult task in discussing techniques which are still undergoing an explosive burst of development. A measure of the magnitude of the task are the number of techniques such as maximum entropy-, high resolution-, and Walsh sequential-spectral analysis among others, which the author recognizes as important, but which have been developed too recently to have been widely applied at the time of going to press. However, a line had to be drawn somewhere, and Professor Bath has written a very convenient text book summarizing and cataloging most developments and applications of spectral techniques up until about 1972. This volume has two major contributions to make: It contains a comprehensive and easily understood theoretical background to the theory of spectral analysis in geophysics. Following the historical development, the book describes briefly the early analogue techniques, and develops the mathematical background to Fourier series and Fourier transforms, and the relation between power spectra, correlation functions, and convolution. These last developments by Blackman and Tukey in 1959, coinciding with the general availability of large computers, provided the techniques for the application of spectral methods in geophysics. These techniques were replaced in the mid-sixties by Fast Fourier Transform methods of great computational efficiency. These methods are described, and the problems of applying them to geophysical time series, of aliasing, windowing and filtering, and the reliability of the final spectra are discussed. The second major contribution is the discussion of the applications of spectral analysis to specific problems in geophysics. There are 64 pages of references to applications in seismology, meteorology, oceanography, gravity, and geomagnetism, and the discussion and cross-references in the text indicate that the author has read most, if not all, of the works he refers to. As would be expected from the author’s own research interests there are references to more applications in seismology than in the other branches of geophysics put together, but this is probably a reflection of the particular importance of spectral analysis to seismology. Professor Bath has written a book with great clarity of style, which makes available to the geophysicist some of his own prodigious reading. Reading this book will be the easiest way for a geophysicist to enter the field of
84
spectral analysis, both for the broad outline of the theory, and for the summary of applications of time-series analysis in the first decade or so of computer applications in geophysics. STUART
CRAMPIN
(Edinburgh)
The Structure of the Earth’s Crust, based on Seismic Data. S. Mueller (Editor). Elsevier, Amsterdam, 1974, 392 pp., 193 fig., Dfl. 100.00. This book is a collection of 33 papers dealing specifically with the structure of the earth’s crust in various regions of the world, including portions of the U.S.S.R., Europe, Africa, India, North and South:America, Hawaii, Australia, Japan, and both polar regions. The papers are those presented at a 1971 International Upper Mantle Committee Symposium on “Crustal Structure Based on Seismic Data”. Although predominantly seismic, as the title states, several of the papers incorporate gravity, magnetic, or other geophysical data to strengthen the interpretations. Editor Mueller, in the Foreword, succinctly emphasizes the importance of the book in which he states “the results . . . show that crustal structure cannot be considered separately from the structure of the mantle. The increasing complexity of the velocity-depth profiles makes it more and more difficult to sustain the simple motion of a lithosphere-asthenosphere model for the crust and upper mantle.” The truth of this statement is substantiated with little more than a cursory reading of the book; the diversity of measured seismic velocities and deduced structure even within a single region is so pronounced that the prevalent use of the terms “granitic” and “basaltic” to characterize a crustal section is an oversimplification at best and is misleading at worst. A significant implication of the book is that before any generalization is made concerning what might consitute a typical crust a far more complete program of crustal studies in new regions must be implemented. The selection of the particular papers is approximately representative of the levels of effort and support provided by various nations for geophysical studies. For example, the Soviet contribution is ten papers, reflecting in part the priority placed on crustal studies via the sustained and integrated Deep Seismic Sounding Program in the Soviet Union. Virtually all of the papers emphasize summary results of investigations, in the form of cross-sections or tables, and avoid discussing the details of accepted analysis techniques. However, if a discussion is desired of the various methods of analysis and interpretation, the generally excellent references included with the papers can be used to effectively pursue the subject. The amount of detail and completeness varies considerably between papers, from a single paragraph (with no references) on the central North American rift system to 34 pages with elaborate fold-outs and a rather com-