ALBERT

Beschreibung / Inhaltsverzeichnis: 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.

Beschreibung / Inhaltsverzeichnis: 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.

Beschreibung / Inhaltsverzeichnis: PREFACE This volume presents results from members of the Project 216 "Global Biological Events in Earth History" of the International Geological Correlation Programme (IGCP). The project, initiated by the elder editor (O.H.W.) within the framework of the International Palaeontological Association (IPA) in the late 70s, was officially established in 1984. Subsequently, it led to the first three conferences on Global Bio-Events, and their respective symposia volumes: 1) In G6ttingen, West Germany in 1986 (WaUiser, O. H., Ed., 1986, Global Bio-Events, Springer-Verlag); in Bilbao, Spain in 1987 (Lamolda, M. A., Kauffrnan, E. G., and Walliser, O. H., Eds., 1988, Paleontology and Evolution: Extinction Events; Rev. Espafiola de Paleont., n. extraord.); and in Boulder, Colorado, U.S.A. in 1988 (this volume). The next meeting, on Innovations and Revolutions in the Biosphere, is planned in Oxford, England in 1990, to be hosted by Martin Brasier. During the history of this project, the focus of our research has shifted significantly. Initial focus was on specific global mass extinctions (e.g. the Precambrian/Cambrian, Frasnian/Fammenian, Cretaceous/Tertiary, and Eocene/Oligocene events) to a broader treatment of Phanerozoic mass extinctions, their differences or unifying factors, and their causal mechanisms. Subsequent meetings have attempted to focus attention on a fuller spectrum of global bio-events in Earth history. The Boulder Conference, and this volume, although still strongly influenced by the excitement of mass extinction research, expresses these new trends in bioevent studies. The Boulder conference, held on May 16-23, 1988, focused on a broad spectrum of Abrupt Changes in the Global Biota. Over 100 participants from 13 nations attended this meeting, representing diverse disciplines of palaeobiology, palaeoclimatology, palaeoceanography, sedimentology, geochemistry, and a broad spectrum of the stratigraphic and geological sciences. Four days of talks were supplemented by field trips to the continental Cretaceous/Tertiary boundary in the Raton Basin, New Mexico, and to the Cenomanian/Turonian mass extinction interval exposed near Pueblo, Colorado. The Conference itself was characterized by a great diversity of approaches to bio-event research, and the phenomenon of mass extinction. In particular, interactive causes involving both extraterrestrial and earthbound (tectonic, oceanographic, climatic) forces were discussed, and each major Phanerozoic mass extinction was treated by specialists in the field. In addition, many presentations focused on the causal mechanism and patterns of bio-event development that were not restricted to mass extinction intervals, but which could cause regional to global biotic response at any time in Earth history. Thus, both the conference, and this volume, focus attention on climatic and oceanic perturbations from anoxia, advection, rapid thermal change, toxic chemical enrichment, and energy shock from impacts and giant tsunamis as forcing mechanism for regional to global bio-events. The delicate balance of perched ocean/ctimate~fe systems under typical warm equable non-glacial Phanerozoic conditions, and their susceptibility to shock from even small perturbations, was a philosophical theme that ran throughout the meeting. The case for extraterrestrial forcing of tectonic, volcanic, and biological events was greatly strengthened by new data presented at this conference, with special concern for the effects of small comet/meteorite impacts in the oceans, and their chemical/physical/biological signature which might be used, in the absence of shocked minerals, microspheres or trace metals, to identify extraterrestrial events associated with global and regional bio-events. The conference benefitted from the introduction of much new data at high levels of resolution, especially from poorly studied mass extinction intervals. Interactive discussions, and many new ideas characterized the meeting. The new scientific results of this meeting are exciting; they are reviewed in the Conference Report published in Episodes (1988, v. 11, n. 4, p. 289-292). Most of the key papers presented at the Boulder meeting appear in this volume. What lies ahead in bio-event research? Clearly, a great deal of excitement and an age of discovery. We have only touched the surface of this new and dynamic field. We are starting to comprehend the dynamics of global mass extinctions, integrating detailed geochemical, physical and biological data into scenarios of cause and effect. But in the years ahead lies the job of understanding the whole spectrum of regional bioevents preserved in the ancient record, and especially the application of this research to solutions of the critical problems inherent in global change and the modern biotic crisis. Future directions for research at this conference include the investigation and modeling of abrupt chemical and thermal shifts in the ocean, the effects of impacts at deep ocean sites, the documentation of successful survival strategies and repopulation patterns following biotic crises, the deep ocean record of bio-events, and focus on alternative forces other than impacting to account for mass extinction events. This volume introduces some of these new pathways in bio-event research.

Beschreibung / Inhaltsverzeichnis: 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...

Beschreibung / Inhaltsverzeichnis: PREFACE The suggestion to compile and publish this volume dealing with some geoscientific problems of the Central Andes came up during a conference on "Mobility of Active Continental Margins" held in Berlin, February 1986. At this international conference, organized by the Berlin Research Group "Mobility of Active Continental Margins", colleagues from Europe, Southern and Northern America reported on their current investigations in the Central Andes. The Central Andes claim a special position in the 7000 km long Andean mountain range. In Northern Chile, Southern Bolivia and Northwest Argentina the Central Andes show their largest width with more than 650 km and along a Geotraverse between the Pacific coast and the Chaco all typical Andean morphotectonic units are well developed. Here, the pre-Andean evolution is documented by outcropping of Paleozoic and pre-Cambrian rocks. The characteristic phenomena of the Andean cycle can be studied along the entire geotraverse. The migration of the tectonic and magmatic activity starting in Jurassic and being active t i l l Quaternary is clearly evidenced. Besides the Himalaya, the Central Andes show with 70-80 km and -400 mgal the largest crustal thickness known in mountain ranges. These and many other interesting and exciting geoscientific features encouraged a group of geoscientists from both West-Berlin universities (Freie UniversitAt and Technische UniversitAt) to focus their studies along a geotraverse through the Central Andes. The realization of these studies would not have been possible without the active assistance and close cooperation of our colleagues from the geoscientific institutions in Salta (Argentina), La Paz and Santa Cruz (Bolivia) and Antofagasta and Santiago (Chile). Concerning the German participation, this joint and interdisciplinary project is financially supported since 1982 as Reserach Group" Mobility of Active Continental Margins" by the German Research Society and by the West-Berlin universities as well. A number of colleagues from universities in West Germany take part in this project, too. The papers presented here deal with the period from Late Precambrian up to the youngest phenomena in Quaternary. The contributions cover the whole spectrum of geoscientific research, geology, paleontology, petrology, geochemistry, geophysics and geomorphology. In conclusion, the data published here may help to improve the picture of Andean structure and evolution. The detailed investigations carried out in the past years show, that the first simple plate tectonic models proposed in the beginning of the seventies have to improved and modified. Furthermore, the results can be seen as contribution to the international Lithospheric Project and as a useful data base for the construction of a Central Andean Transect...