ALBERT

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.