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: INTRODUCTION The International Summer School of Theoretical Geodesy on Satellite Altimetry in Geodesy and Oceanography was held in Trieste (Italy) from May 25 to June 6, igg2. It was organized by Prof. R. Rummel of the Delft University of Technology and by Prof. F. Sansò of the Politecnico di Milano and was attended by 63 participants and 7 lecturers from 17 countries. The School was hosted by the International Centre of Theoretical Physics of Trieste. Satellite altimetry provides a lot of data that require more and more sophisticated models in order to be interpreted and exploited. One of the main problems related to the practical treatment of the data can be summarized as follows: oceanographers would like to ask geodesists to compute precise orbits and a precise geoid in order to put into evidence the Sea Surface Topography that can be interpreted as an oceanographic signal related to currents and to several physical parameters; on the other hand, geodesists would like to ask oceanographers to a-priori determine the Sea Surface Topography, in order to be able to extract from the altimeter data the geoid and the orbit errors to be used in the gravity field modelling. The solution to this dilemma can only be found in a cooperative frame. An integrated model to be used for a single-step treatment of altimetry is probably far to be defined, so at present geodesists and oceanographers must cooperate to obtain step-wise and iterative modelling of the gravity field and of the oceanographic phenomena. This is precisely the reason why the school on Satellite Altimetry was organized on an interdisciplinary basis...

Description / Table of Contents: PREFACE Sedimentation as a Three-Component System describes the most common styles of deposition in marine environments as they relate to sediment composition. Three components, organic matter, carbonate, and siliciclastic sediment, may settle concurrently, but at different rates, intermixing on the sea floor to form a particular sediment composition. A change in the flux of one component is capable of relatively diluting or concentrating the other two components, which can be expressed in the characteristic ratio of organic carbon to carbonate in the resulting sediment. The basic concept of this book is to address organic carbon-carbonate associations in terms of depositional inputs and time spans. In addition, the three-component system describes organic carbon changes related to major facies transitions. Examples include models of the genesis of carbonaceous sediments, with their various laminated to bioturbated lithotypes, and numerical organic carbon prediction. I hope that this book will encourage stimulating discussions and promote a new approach to quantitative stratigraphy...

Description / Table of Contents: PREFACE Some of the major ecological and social problems of the present and future are the production, treatment, and disposal of anthropogenic wastes. Iaais is equally true for sparsely and densely populated industrial areas, including large countries in which sites for waste disposal would seem to be readily available. Especially nonradioactive hazardous wastes with their long-term toxicity need to be isolated from the biosphere just as effectively as radioactive substances. The long-term safety required of waste disposal sites can only be assured under specific geological and mineralogical conditions in certain parts of the lithosphere (underground repositories). The subjects related to the production, avoidance, treatment, and disposal of anthropogenic wastes cover a range of knowledge encompassing the natural sciences, engineering, medicine, and law. This work presents some fundamental situations and problems conceming the disposal of toxic hazardous wastes which have been dealt with in several research projects. The individual chapters are related scientifically. Long-term, effective solutions to our waste problems can only be found when interrelationships and possible future developments are considered. Only the current status of this rapidly developing field can be discussed here. The individual chapters contain scientifically founded data and observations. Other aspects for which there are still controversial opinions and arguments are also discussed, which should stimulate further thought. Further developments and scientific advances can only be achieved by constantly challenging previous theories, and not through static observation and narrow-mindedness. The most extensive quantification possible of the problems related to disposal of hazardous wastes is an essential aim of our work. This not only involves calculating the volume of waste and available repository space, but also compiling data on the long-term effects and the safe, long-term isolation of anthropogenic wastes from the biosphere. A simple description of conditions and processes without using concrete data, which is still widespread, is rejected since it frequently leads to pure speculation. The scientific fundamentals and results presented in this work are of general validity for many questions concerning waste disposal. One example is the amount of waste produced annually in Germany, in which toxic, hazardous wastes play a major role. FoIlowing this train of thought, available data are used to show how limited the possibilities are for the long-term safe underground deposition of hazardous wastes with respect to the current quantities of waste. Of utmost importance is information on the 10ng-term effects of toxic wastes, as well as criteria which have to be considered with respect to the long-term safe deposition of hazardous waste. The natural chemical cycles and material transport in the various zones of the earth are the focus of interest here. They are the scientific basis for assessing every repository for anthropogenic wastes in geological systems. Therefore the significance of material transport and geochemical cycles is emphasized regarding all questions concerning the long-term safety of repositories on the earth's surface and in the lithosphere. Thus, our concept for the scientific evaluation of the long-term safety of underground repositories in geological systems differs from all other models presently under discussion in Germany. In this work, marine evaporites are discussed with respect to the underground deposition of hazardous wastes and the long-term safety of underground repositories in salt rocks. The isolation of hazardous materials from the biosphere can above all be influenced by fluid phases. Fluid phases can mobilize and transport hazardous materials through rocks in the biosphere. This is true, without exception, for all magmatic, sedimentary, and metamorphic rocks, and for marine evaporites, too! In Germany evaporites have commonly been considered to be completely impermeable with respect to fluid phases (solutions and gases). This erroneous view stems from a complete lack of knowledge or misestimation of the dynamic evolution of the composition of evaporite bodies. Unfortunately, this is still true today for parts of some state agencies which deal with repositories. However, all observations of evaporite bodies made over the last more than 100 years have clearly shown that under certain conditions fluid and gaseous components are mobile in evaporites as well. Solutions in marine evaporites have been the object of personal interest and scientific research of A.G. Herrmann for 40 years. The occurrence and formation of salt solutions in the various salt mining districts of Germany are presently being restudied and reevaluated on an extended scientific basis (e.g., v. BORSTEL 1992). A presentation of the current knowledge on salt solutions is beyond the scope of this publication. However, in the interest of continuing research a research project proposed by A.G. Herrmann (1987b) will be introduced here. The direct quantitative analysis of the chemical composition (quatemary and quinary systems) of small fluid inclusions in rocks of the salt deposits of Hessen and Niedersachsen are the primary focus of this project. Information important to fundamental research on the formation and alteration of salt rocks and on the long-term safety of underground repositories should be gained from these studies (e.g., HERRMANN & v. BORSTEL 1991). In addition to salt solutions, gases are also fluid components which occur in practically all marine evaporite deposits. Hence, both salt solutions and gases must be carefully considered when planning underground repositories in an evaporite body and evaluating their long-term safety. This publication contains an up-to-date overview of the gas occurrences in the marine evaporites of Central Europe. Despite previous studies, there is still a considerable deficit in scientific information regarding the distribution and formation of gases in the evaporites occurring in Germany. A detailed research program on the geochemical relationships involving the formation of evaporites and gases will draw attention to this situation. One aspect must be emphasized in the planning and construction of repositories for anthropogenic wastes: their long-term safety. This publication deals precisely with this subject, and in Part III of this work we will present the concept that we have developed. This concept is based on the fact that evaporite bodies are subject to a dynamic evolution and that the chemical and mineralogical composition provides important information on the effect of fluid phases on salt rocks. Previous works contain the testing of methods and presented initial results using the Gorleben salt dome as an example. However, we are just at the beginning of our research project on the long-term safety of underground repositories (e.g., HERRMANN & KNIPPING 1989, HERRMANN 1992). The information contained in this publication is based on years of experience in evaporite research and underground repositories for anthropogenic wastes. Examples are presented which can be applied to similar situations and problems in other countries. Waste disposal is not just a national problem, it has long become an international one for all types of anthropogenic wastes...