Description / Table of Contents:
INTRODUCTION - WHY THIS BOOK? Why study Numerical Geology? Although geologists have dabbled in numbers since the time of Hutton and Playfair, 200 years ago (Merriam 1981e), geology until recently lagged behind other sciences in both the teaching and geological application of mathematics, statistics and computers. Geology Departments incorporating these disciplines in their undergraduate courses are still few (particularly outside the USA). Only two international geomathematical/computing journals are published (Computers & Geosciences; Mathematical Geology), compared with dozens covering, say, petrology or mineralogy. It also remains common practice for years (and $1000s) to be spent setting up computerized machines to produce large volumes of data in machine-readable form, and then for geologists to plot these by hand on a sheet of graph paper! Despite this, the use of numerical methods in geology has now begun to increase at a rate which implies a revolution of no less importance than the plate tectonic revolution of the 1960's -- one whose impact is beginning to be felt throughout the academic, commercial, governmental and private consultative geological communities (Merriam 1969, 1981c). Although a few pioneers have been publishing benchmark papers for some years, the routine usage of machine-based analytical techniques, and the advent of low-priced desk-top microcomputers, have successively enabled and now at last persuaded many more geologists to become both numerate and computerate. Merriam (1980) estimated that two decades of increasing awareness had seen the percentage of geomathematical papers (sensu lato) rise to some 15% of all geological literature; meanwhile, mineralogy-petrology and geochemistry had both fallen to a mere 5% each! In these Notes, geomathematics and numerical geology are used interchangeably, to cover applications of mathematics, statistics and computing to processing real geological data. However, as applications which primarily store or retrieve numbers (e.g. databases) are included, as well as those involving actual mathematical calculations, 'Numerical Geology' is preferred in the title. 'Geomathematics' in this sense should not be confused with 'geostatistics', now usually restricted to a specialised branch of geomathematics dealing with ore body estimation (§20). Reasons for studying Numerical Geology can be summarised as follows: (1) Volumes of new and existing numerical data: The British Geological Survey, the world's oldest, recently celebrated its 150th anniversary by establishing a National Geoscience data-centre, in which it is hoped to store all accumulated records on a computer (Lumsden & Flowarth 1986). Information already existing in the Survey's archives is believed to amount to tens or hundreds of Gb (i.e. = 1010-11 characters) and to be increasing by a few percent annually. The volumes of valuable data existing in the worM's geological archives, over perhaps 250 years of geological endeavour, must therefore be almost immeasurably greater. It is now routine even for students to produce hundreds or thousands of multi-element analyses for a single thesis, while national programs of geochemical sampling easily produce a million individual dement values. Such volumes of data simply cannot be processed realistically by manual means; they require mathematical and statistical manipulation on computers -- in some cases large computers. (2) Better use of coded/digitised data: In addition to intrinsically numerical (e.g. chemical) data, geology produces much information which can be more effectively used if numerically coded. For example, relatively little can be done with records of, say, 'limestone' and 'sandstone' in a borehole log, but very much more can be done if these records are numerically coded as 'limestone = 1' and 'sandstone = 2'. Via encoding, enormous volumes of data are opened to computer processing which would otherwise have lain dormant. More importantly, geological maps - perhaps the most important tool of the entire science - can themselves be digitised (turned into large sets of numbers), opening up vast new possibilities for manipulation, revision, scale-change and other improvements. (3) Intelligent data use: It is absurd to acquire large volumes of data and then not to interpret them fully. Field geologists observing an outcrop commonly split into two (or more) groups, arguing perhaps over the presence or absence of a preferred orientation in kyanite crystals on a schist foliation surface. The possibility of actually measuring these orientations and analyzing them statistically (§17) is rarely aired-- at last in this author's experience! Petrologists are equally culpable when they rely on X-Y or, at maximum 'sophistication', X-Y-Z (triangular) variation diagrams, in representing the evolution of igneous rocks which have commonly been analyzed for up to 50 elements! Whereas some geological controversies (especially those based on interpretation of essentially subjective field observations) cannot be resolved numerically, many others can and should be. This is not to say (as Lord Kelvin did) that quantitative science is the only good science, but qualitative treatment of quantitative data is rarely anything but bad science. (4) Literature search and data retrieval: Most research projects must begin with reviews of the literature and, frequently, with exhaustive compilations of existing data. These are essential if informed views on the topic are to be reached, existing work is not merely to be duplicated, and optimum use is to be made of available funding, The ever-expanding geological literature, however, makes such reviews and compilations increasingly time-consuming and expensive via traditional manual means. Use of the increasing number of both bibliographical and analytical databases (§3) is therefore becoming a prequisite for well-informed, high-quality research. (5) Unification of interests: In these days of inexorably increasing specialisation in ever narrower topics, brought about by the need to keep abreast of the exploding literature, numerical geology forms a rare bridge between different branches not only of geology but of diverse other sciences. The techniques covered in this book are equally applicable (and in many cases have been in routine use for far longer) in biology, botany, geography, medicine, psychology, sociology, zoology, etc. Within geology itself, most topics covered here are as valuable to the stratigrapher as to the petrologist. 'Numerical geologists' are thus in the unique (and paradoxical) position of being both specialists and non-specialists; they may have their own interests, but their numerical and computing knowledge can often help all of their colleagues. (6) Employment prospects: There is a clear and increasing demand for computerate/numerate geologists in nearly all employment fields. In Australia, whose economy is dominated by geology-related activities (principally mining), a comprehensive national survey (AMIRA 1985) estimated that A$40M per annum could be saved by more effective use of computers in geology. Professional computer scientists are also of course in demand, but the inability of some of their number to communicate with 'laymen' is legendary! Consequently, many finns have perpetual need for those rare animals who combine knowledge of computing and mathematics with practical geological experience. Their unique bridging role also means that numerical geologists are less likely to be affected by the vaguaries of the employment market than are more specialised experts. Rationale and aims of this book This is a highly experimental book, constituting the interim text for new (1988) courses in 'Numerical Geology' at the University of Western Australia. It is published in the Springer Lecture Notes in Earth Sciences series precisely because, as the rubric for this series has it, "the timeIiness of a manuscript is more important than its form, which may be unfinished or tentative." Readers are more than welcome to send constructive comments to the author, such that a more seasoned, comprehensive version can be created in due course. Readers' indulgence is meanwhile craved for the number of mistakes which must inevitably remain in a work involving so many citations and cross-references. Emphasis is particularly placed on the word Notes in the series rifle: this book is not a statistical or mathematical treatise. It is not intended to stand on its own, but rather to complement and target the existing literature. It is most emphatically not a substitute for sound statistical knowledge, and indeed, descriptions of each technique are deliberately minimized such that readers shouM never be tempted to rely on this book alone, but should rather read around the subject in the wealth of more authoritative statistical and geomathematical texts cited. In other words, this is a synoptic work, principally about 'how to do', 'when not to do', 'what are the alternatives' and 'where to find out more'. It aims specifically: (1) to introduce geologists to the widest possible range of numerical methods which have already appeared in the literature; and thus (2) to infuse geologists with just sufficient background knowledge that they can: (a) locate more detailed sources of information; (b) understand the broad principles behind interpreting most common geological problems quantitatively; (c) appreciate how to take best advantage of computers; and thereby (d) cope with the "information overload" (Griffiths 1974) which they increasingly face. Even these aims require the reader to become to some extent geologist, computer scientist, mathematician and statistician rolled into one, and a practical balance has therefore been attempted, in which just enough information is hopefully given to expedite correct interpretation and avoidance of pitfalls, but not too much to confuse or deter the reader. Despite the vast literature in mathematics, statistics and computing, and that growing in geomathematics, no previous book was found to fulfill these alms on its own. The range of methods covered here is deliberately much wider than in previous geomathematical textbooks, to provide at least an introduction to most methods geologists may encounter, but other books are consequently relied on for the detail which space here precludes. These Notes adopt a practical approach similar to that in language guidebooks -- at the risk of emulating the 'recipe book' abhorred in some quarters. Every Topic provides a minimum of highly condensed sketch-notes (fuller descriptions are included only where topics are not well covered in existing textbooks), complemented by worked examples using real data from as many fields of geology as space permits. Specialists should thereby be able to locate at least one example close to their problems of the moment. In the earlier (easier) topics, simple worked examples are calculated in full, and equations are given wherever practicable (despite their sometimes forbidding appearance), to enable readers not only to familiarise themselves with the calculations but also to experiment with their own data. In the later (multivariate) topics (where few but the sado-masochistic would wish to try the calculations by hand!), the worked examples comprise simplified output from actual software, to familiarise readers with the types of computer output they may have to interpret in practice. Topics were arranged in previous geomathematical textbooks by statistical subject: 'analysis of variance', 'correlation', 'regression', etc., while nonparametric (rank) methods were usually dealt with separately from classical methods (if at all). Here, topics are arranged by operation (what is to be done), and both classical and rank techniques are covered together, with similar emphasis. When readers know what they want to do, therefore, they need only look in one Topic for all appropriate techniques. The main difficulty of this work is the near impossibility of its goal-- though other books with similarly ambitious goals have been well enough received (e.g.J.Math.Geol. 18(5), 511-512). Some constraints have necessarily been imposed to keep the Notes of manageable size. Geophysics, for example, is sketchily covered, because (i) numerical methods are already far more integrated into most geophysics courses than geology courses; (ii) several recent textbooks (e.g. Cantina & Janecek 1984) cover the corresponding ground for geophysicists. Structural geology is less comprehensively covered or cited than, say, stratigraphy, because (a) it commands many applications of statistics and computing unto itself alone (e.g. 3-D modelling, 'unravelling' of folds), whereas these Notes aim at techniques equally applicable to most branches of geology; (b) excellent comprehensive reviews of structural applications are already available (e.g. Whitten 1969,1981). Remote sensing is also barely covered, since comprehensive source guides similar in purpose to the present one already exist (Carter 1986). For the sake of brevity, phrases throughout this book which refer to males are, with apologies to any whose sensitivities are thereby offended, taken to include females!
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