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Computer applications in the earth sciences. An update of the 70's
360
Book Reviews
concentrate on topics of their own choice in which there is current activity to report. The result is a much more lively (if more uneven) volume. Most of the papers are thonght-provoking, and many contain significant new ideas not yet published elsewhere in any detail. It is interesting, for example, to compare the approaches of These two volumes are collections of papers on mathe- Agterherg, Dnghert, and Whitten to handling spatiallydependent data, to those of Hipel and McLeod, and matical and computer applications in geology, but there Lahovitz (concentrating on Box-Jenkins modelling and the similarity effectively ends. "Computer Applications" geophysical data) on the one hand, and Cli~ and Ord is intended basically as a backward-looking set of his(spatial autocorrelation and geographical modelling). torical reviews of progress in the whole range of geoloAgterberg, Daghert, and Whitten, in their three papers, gical sciences. "Future Trends", in contrast, consists of a use the language of geostatistics (sensu stricto) to desselection of more advanced contributions in a few crihe similar theoretical ground to that covered by much fields chosen according to the interest areas of John of the other work in totally different languages. There Grittiths to whom the book is dedicated. seems to be scope for considerable integration and sim"Computer Applications" (17 papers plus one abstract) plitication of techniques among the different specialities. is the proceedings volume of the 8th Geochautauqua held There are only two papers on "Deductive methods"-in Syracuse, New York, in 1979. The 17 papers in both on sedimentology. Vistelius extends his weE-known "Future Trends" were written specially for the volume, work on Markov-chain analysis to the study of gravita. which commemorates the retirement of John Grittiths tional stratification. Dacey and Krumhein give an in= from active teaching at Pennsylvania State University. II teresting comparison of the application of basic probis interesting that there is little overlap in the authorship ability theory to particle size distribution and stream of the two books: only 5 authors (Whitten, Agterberg, channel network models. Davis, Merriam, and Reyment) have contributed to both. The papers in the "Resources" section contain less The "Computer Applications" volume is not subtheoretically stimulating material, but include two useful divided formally into sections; the papers subdivide reviews by Krige and by Drew and Root, covering mingeoscience into its broad interest areas and each author ing and petroleum respectively," and a fascinating case attempts (with varying degrees of success) to cover one study by Davis and Harbangh on the interplay between field of applications. This format is appropriate for a mathematical geology, exploration strategy, and review volume and the result is surprisingly consistent. economic poficy-making (and illustrating very well the There are a few outstanding papers in this book: notably the opening contribution from Gritfiths is an incisive points made by Harbangh in his paper in the "Computer Applications" volume). geophilosophical accmmt of geoscience prohlem-solving. The fourth section, on "Relations", contains papers In the remainder of the beok, the more successful papers which cover some of the expanding applications of are those which combine a re#Jew of'developments in the "new" or "advanced" mathematics in geology. Reyment 70s with some insight into the present frontiers of the field and a good reference list. Outstanding examples are and Banfield present the theory and demonstrate the use of a method for analyzing asymmetric relationships in the paper by Koch on developments in exploration and mining geology, by Mann on stratigraphic analysis, geology by means of matrix methods. Merriam and Robinson address the well-known but still unsolved and Sutterlin on information systems. Whitten, writing problem of comparison of maps, attempting a new on structural geology, includes an excellent bibliography. method, of cross-multiplication. Craig provides a simple Some of the other papers take a more selective and introduction to the use of graph theory in analyzing idiosyncratic approach, and concentrate on particular natural systems. The final two papers, by Wickman (on problems and methods within their chosen subject area. For example, Reyment concentrates on the combination order and randomness) and Gould (on a structural lanof paleontological, geochemical, and geophysical data by guage of relations) are patchy in style and content, but the methods outlined in his recently published book, to include many useful and stimulating ideas. It will have become obvious that the two volumes give paleoecological information of use to the petroleum industry; Agterberg, writing on mineral-resource evalua- serve rather different purposes. "Computer Aption, concerns himself mainly with map data processing; plications" will probably have a wide readership, prinand McIntyre in a good general paper on the man- cipally of students and newcomers to the field of mathematical geology hoping to gain an introduction to machine interface emphasises the potential role of the APL l a n g ~ . Perhaps the most significant paper in the the whole field; it should be regarded as a secondary volume is that by Harbangh on regional resource fore- source of information, and as such the bibliographies casting in which he argues powerfully that geomathema- which are generally good must be considered essential. ticians should be involved deeply in policy-making proThe "Future Trends" volume, in contrast, is a primary cesses. research publication (though with the ocasional review) and of more use to the initiate than the novice. Both The "Future Trends" volume is organized differently: books deserve a place on the library shelf, whether in it is divided into four sections, on "Spatially dependent data", "Deductive methods", Resources", and '~Rela- university or in industry. Neither, however, is likely to tions", but within these the authors have been free to find a wide private market, in competition with the many Campeter Applkaflens in the Earth Sciences. An Update of the 7O's, edited by D. F. Merriam. Plenum Press, New York, 1981, 385p.; and Future Trmds in Gcomathematks, edited by R. G. Craig and M. L. Labovitz. Pion Press, London, 1981, 318 p.
Book Reviews new textbooks in the field. There are papers in both which are too good to be missed and which are of broad interest, but apart from these it is likely that both volumes will age very quickly in a fast-developing field such as mathematical geology.
Mineral Industries Computing Ltd.
STEPHEN HENLEY
49 Harrow Road
Leighton Buzzard Bedfordshire LU7 8 UF England
Arithmetic Applied Mathematics, by Donald Greenspan. Pergamon Press, Oxford, 1981, 200 p. $12.00 (U.S.). This book describes a somewhat different approach to the deterministic theories of particle mechanics than that of continuum mechanics. The trajectories of individual particles are determined explicitly. As this technique requires the simultaneous solution of a large number of non-linear algebraic equations, it is only since the development of modern computers that it has been possible to do this. In the opening chapters, the gravitational and molecular forces of attraction and repulsion between particles, the so-called long and short range forces, are discussed and the equations for the N-body problem derived. The author shows that the definitions of energy and momentum for the discrete system are identical to those of continuum mechanics and the same laws of conservation
361
and symmetry apply. Then follows a large number of examples of the use of the technique in problems ranging from heat conduction to the evolution of planetary type bodies (an appendix contains a computer program for the creation of the earth!). The final chapters formulate the equations for special relativity using only arithmetic. Of most interest to geophysical scientists are the examples on fluid flows. These cover laminar, turbulent, and porous flows. The technique particularly is useful in determining free surface flows. The numerical techniques used for solving the continuum equations all suffer from the difficulty of defining where the free surface is. I was disappointed to discover that most of the examples are treated in a rather cursory way. There is no indication of the sensitivity of the various models to the number of particles included nor the time step used. Also the choice of the model parameters appears to be somewhat of a mystery. As someone more familiar with the Navier-Stokes equations, I had difficulty in relating how these parameters relate to the fluid properties such as viscosity. The book is aimed at undergraduates in mathematics and physics and as such should form a good basis for a short course on the subject. For someone wanting to apply these techniques, the book falls short on detail, although it does contain a large reference list for further reading.
Institute of Oceanographic Sciences Wormley Surrey England
K. J. PdCtIARDS
Book Reviews
concentrate on topics of their own choice in which there is current activity to report. The result is a much more lively (if more uneven) volume. Most of the papers are thonght-provoking, and many contain significant new ideas not yet published elsewhere in any detail. It is interesting, for example, to compare the approaches of These two volumes are collections of papers on mathe- Agterherg, Dnghert, and Whitten to handling spatiallydependent data, to those of Hipel and McLeod, and matical and computer applications in geology, but there Lahovitz (concentrating on Box-Jenkins modelling and the similarity effectively ends. "Computer Applications" geophysical data) on the one hand, and Cli~ and Ord is intended basically as a backward-looking set of his(spatial autocorrelation and geographical modelling). torical reviews of progress in the whole range of geoloAgterberg, Daghert, and Whitten, in their three papers, gical sciences. "Future Trends", in contrast, consists of a use the language of geostatistics (sensu stricto) to desselection of more advanced contributions in a few crihe similar theoretical ground to that covered by much fields chosen according to the interest areas of John of the other work in totally different languages. There Grittiths to whom the book is dedicated. seems to be scope for considerable integration and sim"Computer Applications" (17 papers plus one abstract) plitication of techniques among the different specialities. is the proceedings volume of the 8th Geochautauqua held There are only two papers on "Deductive methods"-in Syracuse, New York, in 1979. The 17 papers in both on sedimentology. Vistelius extends his weE-known "Future Trends" were written specially for the volume, work on Markov-chain analysis to the study of gravita. which commemorates the retirement of John Grittiths tional stratification. Dacey and Krumhein give an in= from active teaching at Pennsylvania State University. II teresting comparison of the application of basic probis interesting that there is little overlap in the authorship ability theory to particle size distribution and stream of the two books: only 5 authors (Whitten, Agterberg, channel network models. Davis, Merriam, and Reyment) have contributed to both. The papers in the "Resources" section contain less The "Computer Applications" volume is not subtheoretically stimulating material, but include two useful divided formally into sections; the papers subdivide reviews by Krige and by Drew and Root, covering mingeoscience into its broad interest areas and each author ing and petroleum respectively," and a fascinating case attempts (with varying degrees of success) to cover one study by Davis and Harbangh on the interplay between field of applications. This format is appropriate for a mathematical geology, exploration strategy, and review volume and the result is surprisingly consistent. economic poficy-making (and illustrating very well the There are a few outstanding papers in this book: notably the opening contribution from Gritfiths is an incisive points made by Harbangh in his paper in the "Computer Applications" volume). geophilosophical accmmt of geoscience prohlem-solving. The fourth section, on "Relations", contains papers In the remainder of the beok, the more successful papers which cover some of the expanding applications of are those which combine a re#Jew of'developments in the "new" or "advanced" mathematics in geology. Reyment 70s with some insight into the present frontiers of the field and a good reference list. Outstanding examples are and Banfield present the theory and demonstrate the use of a method for analyzing asymmetric relationships in the paper by Koch on developments in exploration and mining geology, by Mann on stratigraphic analysis, geology by means of matrix methods. Merriam and Robinson address the well-known but still unsolved and Sutterlin on information systems. Whitten, writing problem of comparison of maps, attempting a new on structural geology, includes an excellent bibliography. method, of cross-multiplication. Craig provides a simple Some of the other papers take a more selective and introduction to the use of graph theory in analyzing idiosyncratic approach, and concentrate on particular natural systems. The final two papers, by Wickman (on problems and methods within their chosen subject area. For example, Reyment concentrates on the combination order and randomness) and Gould (on a structural lanof paleontological, geochemical, and geophysical data by guage of relations) are patchy in style and content, but the methods outlined in his recently published book, to include many useful and stimulating ideas. It will have become obvious that the two volumes give paleoecological information of use to the petroleum industry; Agterberg, writing on mineral-resource evalua- serve rather different purposes. "Computer Aption, concerns himself mainly with map data processing; plications" will probably have a wide readership, prinand McIntyre in a good general paper on the man- cipally of students and newcomers to the field of mathematical geology hoping to gain an introduction to machine interface emphasises the potential role of the APL l a n g ~ . Perhaps the most significant paper in the the whole field; it should be regarded as a secondary volume is that by Harbangh on regional resource fore- source of information, and as such the bibliographies casting in which he argues powerfully that geomathema- which are generally good must be considered essential. ticians should be involved deeply in policy-making proThe "Future Trends" volume, in contrast, is a primary cesses. research publication (though with the ocasional review) and of more use to the initiate than the novice. Both The "Future Trends" volume is organized differently: books deserve a place on the library shelf, whether in it is divided into four sections, on "Spatially dependent data", "Deductive methods", Resources", and '~Rela- university or in industry. Neither, however, is likely to tions", but within these the authors have been free to find a wide private market, in competition with the many Campeter Applkaflens in the Earth Sciences. An Update of the 7O's, edited by D. F. Merriam. Plenum Press, New York, 1981, 385p.; and Future Trmds in Gcomathematks, edited by R. G. Craig and M. L. Labovitz. Pion Press, London, 1981, 318 p.
Book Reviews new textbooks in the field. There are papers in both which are too good to be missed and which are of broad interest, but apart from these it is likely that both volumes will age very quickly in a fast-developing field such as mathematical geology.
Mineral Industries Computing Ltd.
STEPHEN HENLEY
49 Harrow Road
Leighton Buzzard Bedfordshire LU7 8 UF England
Arithmetic Applied Mathematics, by Donald Greenspan. Pergamon Press, Oxford, 1981, 200 p. $12.00 (U.S.). This book describes a somewhat different approach to the deterministic theories of particle mechanics than that of continuum mechanics. The trajectories of individual particles are determined explicitly. As this technique requires the simultaneous solution of a large number of non-linear algebraic equations, it is only since the development of modern computers that it has been possible to do this. In the opening chapters, the gravitational and molecular forces of attraction and repulsion between particles, the so-called long and short range forces, are discussed and the equations for the N-body problem derived. The author shows that the definitions of energy and momentum for the discrete system are identical to those of continuum mechanics and the same laws of conservation
361
and symmetry apply. Then follows a large number of examples of the use of the technique in problems ranging from heat conduction to the evolution of planetary type bodies (an appendix contains a computer program for the creation of the earth!). The final chapters formulate the equations for special relativity using only arithmetic. Of most interest to geophysical scientists are the examples on fluid flows. These cover laminar, turbulent, and porous flows. The technique particularly is useful in determining free surface flows. The numerical techniques used for solving the continuum equations all suffer from the difficulty of defining where the free surface is. I was disappointed to discover that most of the examples are treated in a rather cursory way. There is no indication of the sensitivity of the various models to the number of particles included nor the time step used. Also the choice of the model parameters appears to be somewhat of a mystery. As someone more familiar with the Navier-Stokes equations, I had difficulty in relating how these parameters relate to the fluid properties such as viscosity. The book is aimed at undergraduates in mathematics and physics and as such should form a good basis for a short course on the subject. For someone wanting to apply these techniques, the book falls short on detail, although it does contain a large reference list for further reading.
Institute of Oceanographic Sciences Wormley Surrey England
K. J. PdCtIARDS