Geodesy
Description
The fifth edition of this textbook has been completely revised and significantly extended in order to reflect the revolution of geodetic technologies, methods and applications during the last decade. The Global Geodetic Observing System established by the IAG utilizes a variety of techniques to determine the geometric shape of the earth and its kinematics, the variations of earth rotation, and the earth's gravity field. The societal importance of geodetic products was highlighted by the UN resolution on the Global Geodetic Reference Frame. In this context, both space and terrestrial techniques play a fundamental role. Recent space missions are monitoring climate-relevant processes such as mass transport in the Earth system and sea level changes. The analysis of the time variation of the geodetic products provides the link to neighboring geosciences and contributes to proper modelling of geodynamic processes. New satellite mission concepts and novel technologies such as quantum gravimetry and optical clocks show great potential to further improve the geodetic observing system in the future. The book especially addresses graduate students in the fields of geodesy, geophysics, surveying engineering, geomatics, and space navigation. It should also serve as a reference for geoscientists and engineers facing geodetic problems in their professional work. The book follows the principal directions of geodesy, providing the theoretical background as well as the principles of measurement and evaluation methods, which is enriched with numerous figures. An extensive reference list supports further studies.
Reviews / Votes
"Aufgrund der umfassenden Darstellung der Geodäsie, von ihren historischen Wurzeln bis hin zu den neuesten Entwicklungen und Anwendungen, bietet 'Geodesy' einen unvergleichlichen Überblick über dieses wichtige und sich ständig weiterentwickelnde wissenschaftliche Feld. Damit eignet es sich sowohl als grundlegendes Handbuch für fortgeschrittene Studierende der Geodäsie als auch als Referenz für Wissenschaftler und Ingenieure auch aus benachbarten Fachdisziplinen." Dr. Rainer Fletling, Universität Kassel, Fachbereich Bauingenieur- und Umweltingenieurwesen
4. Edition
"The book is thoroughly revised and extended with the important results achieved in the years since the last edition (2001). The section on Satellite Observations has been extended with descriptions of the current missions like GRACE and GOCE. Geodynamics is well treated in an extended chapter on "Structure and Dynamics of the Earth". The book contains an extensive bibliography with 500 references added since the edition of 2001. [..] But what is extremely important is the index, which makes the book useful as a handbook for everyone. The book also includes many fine figures and illustrations, now also in color. [..] It is a wonderful book with so much important information covering all of modern geodesy." Carl Christian Tscherning in: Journal of Geodesy, 86, p.786 (2012)
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Other editions
Persons
__ Wolfgang Torge was born 1931 in Laubusch, Lower Silesia, Germany. In 1968 he was appointed full professor for geodesy at the (now) Leibniz University in Hannover, Germany. In the following thirty years he built up the Institute of Geodesy (Institut für Erdmessung), concentrating on three-dimensional geodesy, gravimetry and gravity field modeling including gravity variations with time. International and partly long-term research projects concentrated on Iceland, South America and China. His booklet "Geodäsie" (De Gruyter, 1975) was well accepted, followed by a textbook and since 1980 by five editions of the graduate textbook "Geodesy", now with the co-authors Jürgen Müller and Roland Pail. The monographs on "Gravimetry" (1989) and "Geschichte der Geodäsie in Deutschland" (2007/2009) indicate special areas of Torge´s interest.
Among Torge's manifold activities in national and international cooperation and management we have his 32 years lasting chief-editorship of the Zeitschrift für Vermessungswesen (recognized by the Helmert-medal in gold), the chairmanship of the National Committee of Geodesy and Geophysics and the presidency of the International Association of Geodesy (1991-1995).
__ Jürgen Müller is full Professor in Physical Geodesy at the Leibniz Universität Hannover, Germany, since 2001. He studied Geodesy at the Technical University of Munich where he also finished his doctoral degree in 1991 "with excellence" and his habilitation in 2001. His main research fields cover gravity field satellite missions, terrestrial gravimetry, including novel measurement concepts, related earth system research, lunar laser ranging and general relativity.
In the past years, he focused his research on elaborating the potential benefit of quantum technologies for geodetic applications. Examples are quantum accelerometers/gravimeters for ground and space use as well as optical clock networks for novel height systems and monitoring of mass variations. This research has been carried out in large collaboration programs together with physicists like the DFG CRC 1464 TerraQ of which Jürgen Müller is the speaker. This new research field has also been pushed by the International Association of Geodesy (IAG) by establishing the major project Novel Sensors and Quantum Technology for Geodesy (QuGe) with Jürgen Müller as its chair.
__ Roland Pail is full professor for Astronomical and Physical Geodesy at Technical University of Munich (TUM), Germany, since 2010. He studied geophysics at the University of Vienna, and received his doctorate in engineering sciences (sub auspiciis praesidentis) from TU Graz in 1999. Subsequently he was an assistant professor at TU Graz until 2009, where he received his habilitation in "theoretical geodesy" in 2002. His research activities focus on physical and numerical geodesy with the main emphasis on the global and regional modeling of the Earth's gravity field and its temporal changes, playing an important role in the definition of height systems and making significant contributions to the monitoring of climate-relevant mass transport processes, such as ocean circulation, sea level rise, ice mass melting, global water cycle.
He was principal investigator of the ESA gravity mission GOCE and has been leading several national and international research projects. He is spokesman of the Research Training Group UPLIFT dealing with the modelling of geophysical vertical motion processes. He is currently working on the development, design and numerical simulation of future gravity mission concepts, and is leading an ESA science study on the realization of the satellite constellation mission MAGIC. Together with Jürgen Müller, he is investigation novel technologies such as quantum sensors for gravimetry.
Content
1 Introduction
1.1 Definition of geodesy
According to the classical definition of Friedrich Robert Helmert (1880), "geodesy (?? = Earth, da?? = I divide) is the science of the measurement and mapping of the Earth's surface". Helmert's definition is fundamental to geodesy, even today. The surface of the Earth, to a large extent, is shaped by the Earth's gravity, and most geodetic observations are referenced to the Earth's gravity field. Consequently, the above definition of geodesy includes the determination of the Earth's external gravity field. Since ancient times, the reference system for the survey of the Earth has been provided by extraterrestrial sources (stars). This demands that the Earth's orientation in space be implied into the focus of geodesy. In recent times, the objective of geodesy has expanded to include applications in ocean and space research. Geodesy, in collaboration with other sciences, is also now involved in the determination of the surfaces and gravity fields of other celestial bodies, such as the moon (lunar geodesy) and planets (planetary geodesy). Finally, the classical definition has to be extended to include temporal variations of the Earth's figure, its orientation, and its gravity field.
With this extended definition, geodesy is part of the geosciences and engineering sciences, including navigation and geomatics (e.g., Nat. Acad. Sciences, 1978; Plag and Pearlman, 2009; Herring, 2015). Geodesy may be divided into the areas of global geodesy, geodetic surveys (national and supranational), and plane surveying. Global geodesy includes the determination of the shape and size of the Earth, its orientation in space, and its external gravity field. A geodetic survey deals with the determination of the Earth's surface and gravity field over a region that typically spans a country or a group of countries. The Earth's curvature and gravity field must be considered in geodetic surveys. In plane surveying (topographic surveying, cadastral surveying, and engineering surveying), the details of the Earth's surface are determined at a local level, and thus, curvature and gravity effects are most often ignored.
There is a close relation between global geodesy, geodetic surveying, and plane surveying. Geodetic surveys are linked to reference frames (networks) established by global geodesy, and they adopt the parameters for the figure of the Earth and its gravity field. On the other hand, the results of geodetic surveys contribute to global geodesy. Plane surveys, in turn, are generally referenced to control points established by geodetic surveys. They are used extensively in the development of national and state map-series, cadastral and geoinformation systems, and in civil engineering projects. The measurement and data evaluation methods applied in national geodetic surveys, nowadays, are mostly similar to those used in global geodetic work. In particular, space methods (satellite geodesy), which have long been a dominant technique in global geodesy, are now also commonly employed in regional and local surveys. This also requires a more detailed knowledge of the gravity field at regional and local scales.
With the corresponding classification in the English and French languages, the concept of "geodesy" (la géodésie, "höhere Geodäsie" after Helmert) in this text refers only to global geodesy and geodetic surveying. The concept of "surveying" (la topométrie, Vermessungskunde or "niedere Geodäsie" after Helmert) shall encompass plane surveying.
In this volume, geodesy is treated only in the more restrictive sense as explained above (excluding plane surveying), and is limited to the planet Earth. Among the numerous textbooks and handbooks on surveying, we mention Brinker and Minnick (2012), Kahmen (2006), Nadolinets et al. (2017), and Ghilani (2022). For lunar and planetary geodesy, see Nothnagel et al. (2010) and Wiezorek (2015), and also Petit and Luzum (2010) and Luzum et al. (2011).
1.2 The objective of geodesy
Based on the concept of geodesy defined in [1.1], the objective of geodesy with respect to the planet Earth may be described as follows:
The objective of geodesy is to determine the figure and external gravity field of the Earth, as well as its orientation in space, as a function of time, from measurements on and exterior to the Earth's surface.
This geodetic boundary-value problem incorporates a geometric (figure of the Earth) and a physical (gravity field) part; both are closely related.
By the figure of the Earth, we mean the physical and the mathematical surface of the Earth as well as a geodetic reference model (e.g., Moritz, 1990).
The physical surface of the Earth is the border between the solid or fluid masses and the atmosphere. The ocean floor may be included in this definition, being the bounding surface between the solid terrestrial body and the oceanic water masses. The irregular surface of the solid Earth (continental and ocean floor topography) cannot be represented by a simple mathematical (analytical) function. Continental topography is therefore described pointwise by coordinates of control (reference) points. Given an adequately dense control network, the detailed structure of this surface can be determined by interpolation of data from spatial and terrestrial topographic and photogrammetric surveying and from hydrographic surveys (e.g., Hake et al., 2001; McGlone, 2013; Konecny, 2014; Luhmann et al., 2019). On the other hand, the ocean surface (70 % of the Earth's surface) is easier to represent. If we neglect the effects of ocean currents and other "disturbances" like ocean tides [3.4.2], it forms a part of a level or equipotential surface of the Earth's gravity field (surface of constant gravity potential). We may think of this surface as being extended under the continents and identify it as the mathematical figure of the Earth, which can be described by a condition of equilibrium (Helmert, 1880/1884). J. B. Listing (1873) designated this level surface as geoid [3.4.1].
The great mathematician, physicist, astronomer, and geodesist Carl Friedrich Gauss (1777-1855) had already referred to this surface: "Was wir im geometrischen Sinn Oberfläche der Erde nennen, ist nichts anderes als diejenige Fläche, welche überall die Richtung der Schwere senkrecht schneidet, und von der die Oberfläche des Weltmeers einen Theil ausmacht . ", which reads in English translation: "What we call surface of the Earth in the geometrical sense is nothing more than that surface which intersects everywhere the direction of gravity at right angles, and part of which coincides with the surface of the oceans" (C. F. Gauss: Bestimmung des Breitenunterschiedes zwischen den Sternwarten von Göttingen und Altona, Göttingen 1828. C. F. Gauss Werke, Band IX, Leipzig 1903, p. 49, see also Moritz, 1977).
The description of the external gravity field including the geoid represents the physical aspect of the problem of geodesy. In solving this problem, the Earth's surface and the geoid are considered as bounding surfaces in the Earth's gravity field. Based on the law of gravitation and the centrifugal force (due to the Earth's rotation), the external gravity field of the Earth can be modeled analytically and described by a large number of model parameters. A geometric description is given by the infinite number of level surfaces extending completely or partially exterior to the Earth's surface. The geoid as a physically defined Earth's figure plays a special role in this respect.
Reference systems are introduced in order to describe the orientation of the Earth in space (celestial reference system) as well as its surface geometry and gravity field (terrestrial reference system). The definition and realization of these systems has become a major part of global geodesy; the use of three-dimensional Cartesian coordinates in Euclidean space is adequate in this context. However, due to the demands of users, reference surfaces are introduced. We distinguish between curvilinear surface coordinates for horizontal positioning and heights above some zero-height surface for vertical positioning. Due to its simple mathematical structure, a rotational ellipsoid, flattened at the poles, is well suited for describing horizontal positions, and consequently, it is used as a reference surface in geodetic surveying. In plane surveying, the horizontal plane is generally a sufficient reference surface. Because of the physical meaning of the geoid, this equipotential surface is well suited as a reference for heights. For many applications, a geodetic reference Earth (Earth model, normal Earth) is needed. It is realized through a mean-Earth ellipsoid that optimally approximates the geometry (geoid) and the gravity field of the Earth. Figure 1.1 shows the mutual location of the surfaces to be determined in geodesy.
The body of the Earth, its gravity field, and its...
