ALBERT

Description / Table of Contents: OPENING ADDRESS On behalf of the Local Organizing Committee, I welcome you all to the first International Workshop on GPS-techniques in surveying and geodesy held at this university. This workshop is designed to bring together experts from various countries and also scientists who carry out, analyze and interpret such measurements with those who work on instrumental and theoretical problems. The workshop focuses hereby on high-precision applications with emphasis on monitoring time-dependent phenomena such as those relevant to geodynamics as well as men-made constructions as those in civil engineering and similar fields. It is astonishing to see how, in spite of all earlier satellite work over the last two decades, GPS-methods became so fast a relevant new technology, in its proper sense, in modern geodesy and surveying besides VLBI and Satellite Laser Ranging (SLR). With the recent development of new dual-frequency receivers the role of GPS-procedures in monitoring large-scale phenomena over big distances will still expand; and the application of kinematical GPS-approaches is of utmost interest in solving high-precision problems. It is indeed fascinating to realize how GPS-methods have become in such a short time a surprisingly efficient and effective, this means : fast, precise and easy to apply, tool which is able to replace already now, after a few years of existence and with an incomplete set of a few out of the 18 satellites (of the final stage), at least partially some expensive, slow and cumbersome classical surveying methods. On the other hand, it cannot be overemphasized that GPS-procedures are still at their beginning and the full spectrum of their capabilities still has to be explored. In Europe, for example, where excellent classical surveying systems do exist the situation is quite different from the situation in other countries such as Canada or the USA. Even within Europe the application types of GPS-methods will vary; for example, in Norway the situation is quite different from central European countries. It is often forgotten, that together with GPS we will have to introduce new concepts and a new thinking in combination with other modern satellite procedures. GPS itself can resolve only a small part of the problems to be solved by modern geodesy but it will open the way to a great variety of new applications and capabilities. Modern global tectonics is just one of the new disciplines of high interest and great practical impact. I could continue in citing other similarly important new fields. GPS is, however, of special importance because it replaces old technologies and fills gaps where modern and efficient tools are most needed. Consequently, also the optimal combination of GPS-methods with new auxiliary and also classical high-precision techniques is of great importance, mainly under the european conditions outlined above. Moreover, the real-time or almost-real-time use of GPS in combination with photogrammetry, inertial geodesy, gravity gradiometry or even classical surveying is of substantial interest. It is indeed important to realize the new concepts in modern satellite and space methods and I, therefore, spoke above of a new "technology" which should be optimally developed as there is a worldwide need of such capabilities and tools. In view of the few active NAVSTAR-satellites in sky in 1988 this is perhaps not the best year for GPS-applications but the right time for a review of the experience gained until now and using it as a base for the planning of the future...

Description / Table of Contents: PREFACE This volume comprises the main lectures delivered at the Fourth International Summer School in the Mountains on "Mathematical and Numerical Techniques in Physical Geodesy", held from August 25 to September 5, 1986 in Admont, Austria. The School was organized by the Institute of Theoretical Geodesy of the Technical University Graz, Austria under the auspices of the International Association of Geodesy. All five continents were represented by 70 participants from over 20 countries. The purpose of the Summer School was to provide an introduction to advanced techniques which represent the mathematical vehicle for the treatment of modern geodetic problems, to familiarize participants with the present state of the art of global and local gravity field determination methods, ranging from orbit theory, the key satellite techniques, to inertial and standard terrestrial methods, and to discuss future scientific developments. The arrangement of this volume matches the sequence of lectures given at the School. The theoretical PART A represents the mathematical framework of modern physical geodesy, the application PART B deals with the key satellite and surface techniques, providing the detailed structure of the earth's gravity field. PART A: One of the main goals in physical geodesy, global and local gravity field determination, is pursued by extensively applying functional analytic methods. Recently special attention is being given to the base function and norm choice problem, and to the establishment of a sound link between density distributions inside the earth as the source and observed or estimated gravity field quantities as the effect. The lectures by C.C. Tscherning focus on this topic. Space and time dependent problems of discrete and continuous type are encountered in modern geodesy nowadays and dealt with in the lectures by F. Sans6. Estimation theory either in its stochastic or statistic formulation plays a key role in the processing of processes like the earth's gravity field. The consistent processing of large structured data sets calls for equally structured numerical algorithms. Spectral analysis with its powerful fast Fourier transform has become a common tool for the treatment of such problems. An introduction to spectral methods, supplemented by numerous examples, is provided by B. Hofmann-Wellenhof and H. Moritz. PART B: The theory of orbit dynamics, tailored to the near circular orbits of most geodetic satellites, is fundamental to modern geodetic satellite techniques and discussed in the lectures by O.L. Colombo. Particular emphasis is put on the interplay between orbit perturbations and the earth's disturbing gravity field and its mapping by satellite techniques like satellite altimetry, satellite-tosatellite tracking and satellite gradiometry. Satellite gradiometry, which is discussed in the lectures by R. Rummel in detail, with regard to the geometric structure of the gravitational field, the observability of the gradients, and the mathematical model underlying the gravity field recovery problem, promises to provide particularly detailed information about the gravity field of our planet. The global structure of the earth's gravity field is described in terms of earth gravity field models which are derived from both satellite and surface data. The many delicate, mathematically as well as numerically challenging problems, related to the consistent processing of very large space distributed data sets, and proposed solutions are presented in the lecture by R.H. Rapp. For many years various attempts have been made to explain the shorter wavelength part of the earth's anomalous gravity field by isostatic phenomena. Recently several high resolution topographicisostatic earth models have been computed based on global digital terrain data using different techniques fo~ the estimation of the parameters of the chosen isostatic model. A declared goal is the maximum smoothing of the observed gravity field by removing the contribution of the topography and its isostatic compensation. This topic is discussed in the lectures by H. SUnkel. Inertial methods are steadily gaining importance, power and application. This is not only due to hardware improvements in terms of precision and reliability, but also due to recent advances in the mathematical and numerical modelling of the system's performance. An investigation of the error characteristics of inertial survey systems and their interaction with the anomalous gravity field, studied in the framework of dynamic system analysis, is the topic of the lectures by K.-P. Schwarz and the key issue for further improvements and possible integrations with other positioning systems. Geodetic data have both geometric and physical ingredients of various nature. Standard geodetic processing procedures aim at a separation of geometry from physics. Integrated geodesy, in contrast, has been designed as a very sophisticated melting pot which handles practically all available geodetic data in a consistent and optimal way.lt handles surface and satellite data with either geometrically or gravity field dominated content, and geophysical data in terms of density and seismic informatlon just as well and represents as such the great synthesis of mathematical modelling in connexion with geodetic data processing techniques; these advanced ideas are presented in the lectures by G. Hein. This volume presents highlights of modern geodetic activity and takes the reader to the frontiers of current research. It is not a textbook on a closed and limited subject, but rather a reference book for graduates and scientists working in the vast and beautiful, demanding but rewarding field of earth science in general and physical geodesy in particular. The editor expresses his appreciation to all authors of this volume for their advice and help in formulating and designing the scientific program of the Summer School, for providing typewritten lecture notes, and for their excellent cooperation.

Description / Table of Contents: PREFACE During the last decades, remarkable progress in heat flow studies has been made and a rough picture of the global surface heat flow density distribution can now be drawn. Simultaneously, the question of over which time period the surface heat flow is constant arose. There is a big field of model calculations, based on the changes in radioactive heat generation of the Earth, on plate motions, on stretching hypotheses or on other ideas, which result in geotherms in the geological past. Although these speculative paleogeotherms seem to be realistic especially in oceanic areas they do not belong to the scope of this book. In continental areas however, it is not possible to find a simple time dependence of the surface heat flow density. However, petroleum research and tectogenetic studies are very interested in the geothermal history of sedimentary basins and other continental areas. To obtain satisfactory results, a more or less direct determination of paleo heat flow density or geothermal gradient would be necessary to give more certain boundary conditions for calculating oil generation, and for controlling tectogenetic hypotheses. There are many methods available in the geosciences to determine temperatures in the geological past. Most of these models are able to estimate temperatures at which a mineral or a mineral assemblage was formed. These methods, however, are mostly unsuitable to reach the main goal of paleogeothermics in general, which is to determine the (regional) heat flow density variations during the geological past for bigger geological units, such as sedimentary basins. The methods applied most in sedimentary basins have been deduced from the degree of coalification of organic matter. Although much effort has been made to explain analytically the organic metamorphism, the results found up to now have been insufficient . However, the widespread application of this thermometer to estimate ancient thermal conditions is also reflected in the contents of this very volume where the interpretation of the degree of coalification of organic matter plays an important role. As well as this geothermometers, other methods are reviewed from a geophysical viewpoint which favours methods suitable to determine a paleothermal state of the upper crust. Further contributions of this book deal with - the history of the earth's surface temperature whose change provides an essential correction factor in heat flow density determinations, - isotope geothermometers and their application to various environments to evaluate thermal conditions in the past geological history, - an application of the radiometric dating method to retrace the paleothermal condition of the Central Alps. Most of the contributions were presented at the symposium "Paleogeothermics" which was held at the 18. General Assembly of the International Union of Geodesy and Geophysics, August 15-27, 1983 in Hamburg/FRG. It has been the first time that such a symposium has been organized by the International Heat Flow Commission, and this book presents an attempt to define paleogeothermics under the auspices of the International Heat Flow Commission.

Description / Table of Contents: INTRODUCTION Theoretical modelling and the use of mathematical methods are presently gaining in importance since progress in both geology and mathematics offers new possibilities to combine both fields. Most geological problems are inherently geometrical and morphological, and, therefore, amenable to a classification of forms from a "Gestalt point of view". Geometrical objects have to possess an inherent stability in order to preserve their essential quality under slight deformations. Otherwise, we could hardly conceive of them or describe them, and today's observation would not reproduce yesterday's result (DANGELMAYR & GÜTTINGER, 1982). This principle has become known as "structural stability" (THOM, 1975), i.e. the persistence of a phenomenon under all allowed perturbations. Stability is also, of course, an assumption of classical Newtonian physics, which is essentially the theory of various kinds of smooth behavior (POSTON &STEWART, 1978). However, things sometimes "jump". A new species with a different morphology appears suddenly in the paleontological record (EI.DREDGE & GOULD, 1972), a fault develops, a landslide moves, a computer program becomes unstable with a certain data configuration, etc. It is, surprisingly, the topological approach which permits the study of a broad range of such phenomena in a coherent manner (POSTON & STEWART, 1978; LU, 1976; STEWART, 1982). The universal singularities and bifurcation processes derived from the concept of structural stabiIity determine the spontaneous formation of qualitatively similar spatio-temporal structures in systems of various geneses exhibiting critical behavior (DANGELMAYR & GÜTTINGER, 1982; THOM, 1975; POSTON & STEWART, 1978; GÜTTINGER & EIKEMEIER, t979; STEWART, 1981). In addition, this return to a "geometrization of phenomena"-- after decades of algorithmization-- comes much closer to the geologist's intuitive geometric reasoning. It is the aim of this study to elucidate, by examples, how the qualitative geometrical approach allows one to classify forms and to control the behavior of complex computer algorithms...

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!

Description / Table of Contents: INTRODUCTION While the complex mechanical properties of rocks and soils are studied for quite a while, it is only in the last decades that sound established mathematical models were developed based on accurate experimental data. Some rheological properties of geomaterials as for instance creep, were studied for a long time but the experimental data reported were incomplete and, as a consequence, the models developed have missed either the generality necessary for the solving of engineering problems or some of the major specific mechanical properties possessed by these materials as for instance dilatancy and/or compressibility , long term damage etc. Generally, these very particular empirical models were made for a specific test only and therefore are not appropriate for solving problems involving general loading histories. Let us remind that due to the presence of a great number of cracks and/or pores existing in roks and soils, the mechanical behaviour of geomaterials is quite distinct from that of other materials as for instance metals or plastics. That is why rock and soil rheology has some specific aspects. It must also be mentioned that the solving of various problems of rock and soil mechanics posed by modern technology was not possible by using time-independent models, thus the study and development of rehological models become absolutely necessary. In the last decade or so, very accurate experimantal data became available as a result of the development of experimental techniques and of the growing interest for this field of research in the scientific community. These data, in turn, have made possible the development of genuine models for geomaterials, mainly rheological models, able to describe such properties as creep, dilatancy and/or compressibility during creep, long term damage and failure occurring after various time intervals, slip surface formation etc. Today it is clear that no accurate constitutive equation for rocks can be formulated unless the dilatancy phenomena and the time effects are not included. Another idea is the need of a better description of the concepts of damage and failure of rocks, again using in someway the concepts of irreversible dilatancy or another related notion. In soil rheology it is clear that the scale effect may be taken into consideration in order to obtain a corect information from the routine tests. Also in writing the constitutive equations for soils it is neccessary to take into account the microscopic or local phenomena, because there is a great variety of types of saturated or nonsaturated soils, granular or cohesionless soil etc. The aim of the Euromech Colloquium 196 devoted to Rock and Soil Rheology and therefore that of the present volume too, is to review some of the main results obtained in the last years in this field of research and also to formulate some of the major not yet solved problems which are now under consideration. Exchange of opinions and scientific discussions are quite helpful mainly in those areas where some approaches are controversial and the progress made is quite fast. That is especially true for the rheology of geomaterials, domain of great interest for mining and petroleum engineers, engineering geology, seismology, geophlsics, civil engineering, nuclear and industrial waste storage, geothermal energy storage, caverns for sports, culture, telecommunications, storage of goods and foodstuffs (cold, hot and refrigerated storages), underground oil and natural gas reservoirs etc. Some of the last obtained results are mentioned in the present volume...