ALBERT

Description / Table of Contents: PREFACE There are problems, when applying statistical inference to the analysis of data, which are not readily solved by the inferential methods of the standard statistical techniques. One example is the computation of confidence intervals for variance components or for functions of variance components. Another example is the statistical inference on the random parameters of the mixed model of the standard statistical techniques or the inference on parameters of nonlinear models. Bayesian analysis gives answers to these problems. The advantage of the Bayesian approach is its conceptual simplicity. It is based on Bayes' theorem only. In general, the posterior distribution for the unknown parameters following from Bayes' theorem can be readily written down. The statistical inference is then solved by this distribution. Often the posterior distribution cannot be integrated analytically. However, this is not a serious drawback, since efficient methods exist for the numerical integration. The results of the standard statistical techniques concerning the linear models can also be derived by the Bayesian inference. These techniques may therefore be considered as special cases of the Bayesian analysis. Thus, the Bayesian inference is more general. Linear models and models closely related to linear models will be assumed for the analysis of the observations which contain the information on the unknown parameters of the models. The models, which are presented, are well suited for a variety of tasks connected with the evaluation of data. When applications are considered, data will be analyzed which have been taken to solve problems of surveying engineering. This does not mean, of course, that the applications are restricted to geodesy. Bayesian statistics may be applied wherever data need to be evaluated, for instance in geophysics. After an introduction the basic concepts of Bayesian inference are presented in Chapter 2. Bayes' theorem is derived and the introduction of prior information for the unknown parameters is discussed. Estimates of the unknown parameters, of confidence regions and the testing of hypotheses are derived and the predictive analysis is treated. Finally techniques for the numerical integration of the integrals are presented which have to be solved for the statistical inference. Chapter 3 introduces models to analyze data for the statistical inference on the unknown parameters and deals with special applications. First the linear model is presented with noninformative and informative priors for the unknown parameters. The agreement with the results of the standard statistical techniques is pointed out. Furthermore, the prediction of data and the linear model not of full rank are discussed. A method for identifying a model is presented and a less sensitive hypothesis test for the standard statistical techniques is derived. The Kalman-Bucy filter for estimating unknown parameters of linear dynamic systems is also given. Nonlinear models are introduced and as an example the fit of a straight line is treated. The resulting posterior distribution for the unknown parameters is analytically not tractable, so that numerical methods have to be applied for the statistical inference. In contrast to the standard statistical techniques, the Bayesian analysis for mixed models does not discriminate between fixed and random parameters, it distinguishes the parameters according to their prior information. The Bayesian inference on the parameters, which correspond to the random parameters of the mixed model of the standard statistical techniques, is therefore readily accomplished. Noninformafive priors of the variance and covariance components are derived for the linear model with unknown variance and covariance components. In addition, informative priors are given. Again, the resulting posterior distributions are analytically not tractable, so that numerical methods have to be applied for the Bayesian inference. The problem of classification is solved by applying the Bayes rule, i.e. the posterior expected loss computed by the predictive density function of the observations is minimized. Robust estimates of the standard statistical techniques, which are maximum likelihood type estimates, the so-called M-estimates, may also be derived by Bayesian inference. But this approach not only leads to the M-estimates, but also any inferential problem for the parameters may be solved. Finally, the reconstruction of digital images is discussed. Numerous methods exist for the analysis of digital images. The Bayesian approach unites some of them and gives them a common theoretical foundation. This is due to the flexibility by which prior information for the unknown parameters can be introduced. It is assumed that the reader has a basic knowledge of the standard statistical techniques. Whenever these results are needed, for easy reference the appropriate page of the book "Parameter Estimation and Hypothesis Testing in Linear Models" by the author (Koch 1988a) is cited. Of course, any other textbook on statistical techniques can serve this purpose. To easily recognize the end of an example or a proof, it is marked by a A or a t~, respectively. I want to thank all colleagues and students who contributed to this book. In particular, I thank Mr. Andreas Busch, Dipl.-Ing., for his suggestions. I also convey my thanks to Mrs. Karin Bauer, who prepared the copy of the book. The assistance of the Springer- Verlag in checking the English text is gratefully acknowledged. The responsibility of errors, of course, remains with the author.

Description / Table of Contents: The study of calcareous bedding rhythms has become an important field in Geology. Often these bedding rhythms are simply interpreted as representations of primary climatic cycles without showing the effects of any appreciable diagenetic overprinting. This study, however, deals predominantly with the diagenetic processes which are usually large and affect both the amplitude and rhythm of carbonate oscillations. The purpose of this textbook is two fold. First, it intends to provide a better understanding of the processes of diagenetic bedding. Secondly, this new approach allows one to quantify and to understand diagenesis in terms of mass exchanges. This is possible through the development of methods which combine chemical data with compaction measurements. These methods can be also used independent of the marl-limestone alternation problem.

Description / Table of Contents: Cellular growth is an important crystal growth process and offers an interesting example of natural pattern formation. The present work has been undertaken to study cellular growth, especially its pattern formation, both experimentally and numerically. In situ observations of faceted cellular growth clearly revealed cellular interactions in the array of cells. Cell tip splitting and loss of cells were observed to be the two main mechanisms for the adjustment of cell spacings during growth. For the first time, the true time-dependent faceted cellular growth has been modelled properly. The time evolution of faceted cellular growth has demonstrated the dynamical features of cellular growth processes. It was shown that the pattern formation was determined by cellular interactions in the array, either transient or persistent depending on the growth condition. The cellular structures were irregular when persistent interactions occurred, whereas relatively regular structures could be formed once the transient interactions had stopped. As a result of cellular interactions, a finite range of stable cell spacings was found under a given growth condition. Numerical experiments were carried out for k 〉 1 and k 〈 1 (where k is the solute partition coefficient), under a number of different growth conditions. It was found that these two cases were not symmetric as far as solute distribution is concerned; however the pattern formation behaviours were similar. For k 〉 1 shallow cells were retained, while for k 〈 1, the formation of liquid grooves along the cell boundary depended on the growth condition. The solute effect plays an important role in the cellular interactions in the array. The results were compared with experimental observations in thin film silicon single crystals. It is felt that a general behaviour of pattern formation is found and should be expected for other processes such as non-faceted cellular or eutectic growth. In addition, the solute flow in steady state cellular array growth was studied using the point source technique. Preliminary work was carried out to measure steady state non-faceted cell shapes. Heat flow in zone melting was studied numerically.

Description / Table of Contents: PREFACE This monograph is a compendium of revised papers which were originally presented at the "Ron Mather Symposium on Four-Dimensional Geodesy", 28-31 March, 1989, held at the University of New South Wales, Sydney, Australia. The symposium had the enthusiastic support of the International Association of Geodesy and the Australian Academy of Sciences. The symposium served two purposes: to honour the achievements of the late Professor Ron S. Mather, the distinguished Australian geodesist who died in 1978, and to review and report on the latest developments in four-dimensional geodesy. Four-dimensional geodesy is a convenient term for those geodetic principles and techniques which yield position, gravity and their time variations. In the past geodesists have tended to think of the earth as a static body, save from occasional savage earthquakes or volcanic eruptions. So, why the need to coin the term "four-dimensional geodesy") Because it explicitly recognises that time is an integral part of understanding geodetic measurements. But let's first identify the scope of modern geodesy. Geodesy has traditionally been concerned with two separate, though closely related, topics: accurate positioning of objects on the earth's surface, and mapping the earth's external gravity field. These are still the fundamental tasks of geodesy, although the spheres of application have now extended into space. However, present and emerging geodetic measurement technologies for gravity field mapping and positioning are sensitive to defolTnations of the earth's surface and gravity field. Within the geodetic community, this new emphasis on accounting for the time-varying characteristics of position and gravity has fundamental principles; in particular the establishment and maintenance of appropriate global reference systems for geodesy. At the same time, there has been a growing recognition by the earth sciences in general of the important role of geodesy in studying earth deformations, as well as atmosphere and ocean dynamic phenomena. The geodetic measurements, for example, are taken over time scales of hours to decades, and occasionally to a century or longer. Though this is only a small part of the whole deformation spectrum, it is a very important one. Geodesy bridges the low frequency part of the spectrum available from geological observations, with the high frequency end observed from, for example, seismic instrumentation. It's role in atmospheric and oceanographic studies is as a unique, high precision remote sensing tool. The revolution in geodesy is not, however, restricted to the measurement technology only. It is true that without the advances of space geodesy and terrestrial metrology, the notion of four-dimensional geodesy is a rather academic one. These advances, which now reveal time-variable signals above the measurement noise level, have important implications for all geodetic activities. The geodetic activities we refer to can be identified as: experiment design and measurement processes; definition and maintenance of highly stabie geodetic reference systems; data analysis; and interpretation of position and gravity results. Ultra high precision measurements are of little use without sophisticated analysis tools to extract the small signals in the data. The interpretation of geodetic results will be in error if insufficient attention is paid to ensuring that the reference systems to which the results relate are themselves stable. Clearly four-dimensional geodesy is as much about concepts and principles, as about computers and geodetic equipment. This diversity is reflected in the papers selected for this book. They range over topics related to the modem measurement tools, the reduction and analysis techniques, to the interpretation of geodetic results within the context of problems currently being investigated in the earth sciences. We would like to thank the International Association of Geodesy and the Australian Academy of Sciences for sponsorship of the Symposium. Unisearch Ltd., the commercial arm of the University of New South Wales, was the managing agent, and staff members of the School of Surveying and of Unisearch Ltd. were involved in the organisation of the Symposium. We would like to gratefully acknowledge these excellent contributions. Let us express also our gratitude for the useful guidance which we received from Prof. K. Lambeck, A. Prof. A. Stolz and Dr. R. Coleman of the Scientific Advisory Committee and the continuous support given by Prof. E.W. Grafarend. Sincere thanks are due to the authors of the selected papers for agreeing to contribute to this Monograph, and for their positive cooperation during the production of this volume.

Description / Table of Contents: PREFACE Following the economical and social development of the local communities, mountain regions of temperate climates are increasingly becoming the site of valuable infrastructures and important urban and industrial settlements. As the catastrophic events of last years in the European Alps have clearly shown, the vulnerability of these territories has correspondingly increased, in terms of both property damage and losses of human life. Until recently, the hydraulic scientific community has paid little attention to mountain watersheds, except perhaps during the period if the hydropower development. Nevertheless attention was then focused on problems and methodologies somewhat different from the issues of actual environmental concern. More recently, however, hydraulic engineers have joined their colleagues from forest and rural engineering, who have traditionally dealt with erosion control in mountain areas, to bring in their own methodology, already experienced in lowland rivers. At the same time, academic people focused an interest in some phenomena, like massive transport, which is typical of mountain environment. To bring together all these contributions and to make the state of the art of the mountain river science (oropotamology) and technology, an International Workshop was called at the University of Trent (Italy), on October 1989, under the sponsorship of Fluvial Hydraulic Section of the IAHR. Three main topics have been recognized as particularly relevant from the point of view of both research and professivnal people: a) Hydrodynamics of steep channels and local scale process; b) Sediment movement and sediment training, with special emphasis on massive transport; c) Particular features of sediment transport related to non-uniform grain-size. However, as it is the case in these circumstances, the contest of several contributions often spread over more than one topic. In the following Introduction to papers, the three topics were split into 11 Sections, each one devoted to a more particular aspect recurrently addressed during the discussion. The same paper, thus, may be mentioned in different Sections of the Introduction.

Description / Table of Contents: The subject of the book is an indepth description of the theory and mathematical models behind the application of the Global Positioning System in geodesy and geodynamics. The text has been prepared by leading experts in the field, contributing their particular points of view. Unlike a collection of disjoint papers, the text provides a continous flow of ideas and developments. The mathematical models for GPS measurements are developed in the first half of the book, followed by the description of GPS solutions for geodetic applications on local, regional and global scales.

Description / Table of Contents: INTRODUCTION The awareness that mankind is able to influence and modify not only the local but also the global climate has led to a strongly growing interest in climate research. Strengthened research activities, which also made use of improved and novel experimental techniques, have yielded a wealth of information on climatic patterns in the past. At the same time, climate modelling has made much progress. While some questions have been answered, new problems have been recognized. One question related to anthropogenio climatic change is about the nature and causes of natural variations, against the background of which man-made changes must be viewed. The contributions to this volume all deal with the variabilitY of climate. Some papers are reviews of the knowledge to a current topic, others have more the character of an original contribution. The obseryational studies cover the range from year-to-year variations up to glacial-interglacial contrast, thereby going from instrumental data to results from proxy records...

Description / Table of Contents: PREFACE The papers contained in the present volume were prepared from the contributions presented during an international Advanced Workshop held in Santander, Cantabria, Spain between 1-5 November 1989. The workshop was a joint activity of the Working Group on Geology and Land-Use Planning (program "Geology and Environment", UNESCO), the Commission on Applied Quaternary Research (INQUA), the Sub-Commission on Maps of Environmental Geology (Commission of the Geological Map of the World) and the Grupo Españiol de Geología Ambiental y Ordenación del Territorio (Spanish Association for Environmental Geology and Land-Use Planning). The aims of the meeting were to discuss a series of topics in which the four participating scientific bodies share an interest, to analyze the existing problems and trends and to identify certain lines along which work and/or actions will be particularly necessary in the near future. It was expected that the discussions and the conclusions of the meeting would provide useful guidelines for earth scientists working on environmental problems and for other professionals and officials who deal with environmental analysis, planning and management, either on a scientific basis or in a decision-making capacity...