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In the gravity method of exploration geophysics, Bouguer is the name of a specific correction to measurements, and also the name of the anomaly remaining after that correction and other corrections...

The strict mathematical model of the mobile precise trigonometric levelling (MPTL) is deduced and its error sources are analysed in this paper. Some position sensors are added to instruments and observing reciprocal at the same time using two modified measuring robots so as to reduce the influence of atmospheric refraction, curvature of the earth and other factors. It is not necessary to measure the heights of instruments and targets by constructing the even numbers of observed edges to avoid errors of measuring heights. Experimental results indicate that MPTL has greatly increased the working efficiency and reduced the labour intensity compared with precise geometric levelling in the hills and mountains. A large number of experiments have proved that the standard deflection of measurement is less than and with an average speed of more than 7 kilometres per day in mountainous terrain.

To properly construct broad features of lithospheric magnetization structure derived through inversion of the regional magnetic anomaly data, the curvature of the Earth should be taken into conside...

Children's understandings of the shape and relative sizes of the Earth, Sun and Moon have been extensively researched and in a variety of ways. Much is known about the confusions which arise as young people try to grasp ideas about the world and our neighbouring celestial bodies. Despite this, there remain uncertainties about the conceptual models which young people use and how they theorise in the process of acquiring more scientific conceptions. In this article, the relevant published research is reviewed critically and in-depth in order to frame a series of investigations using semi-structured interviews carried out with 248 participants aged 3–18 years from China and New Zealand. Analysis of qualitative and quantitative data concerning the reasoning of these subjects (involving cognitive categorisations and their rank ordering) confirmed that (a) concepts of Earth shape and size are embedded in a ‘super-concept’ or ‘Earth notion’ embracing ideas of physical shape, ‘ground’ and ‘sky’, habitation of and...

In 1950 National Geographic published one of the first large-scale images of the curvature of the Earth. Clyde T. Holliday of the Applied Physics Laboratory at Johns Hopkins University constructed the mosaic, which was taken from a camera affixed to a V-2 rocket launched from White Sands Proving Ground, New Mexico. Holliday crafted the image as a bellwether for two contradictory yet inextricable ideas: the promise of Earth photography in making life easier for everyday peoples and the militarization of space. Examining one pre-1960 rocket-based Earth image this essay offers a reassessment of Earth photographs as only environmentalist texts.

The three-dimensional (3D) shape of the Earth is of major importance for many remote-sensing applications. Consequently, methodologies and techniques for generating digital surface models (DSMs), d...

Systems for landscape visualization and geographical data handling require methods for efficient data access. Retrieval of data from large geographical databases, ten to thousands of Gbytes, is usually optimized with spatial indexing mechanisms. The simplest form of spatial indexing is achieved by dividing the database into congruent grid cells. The subsequent subdivision of the grid cells can be based on so-called quadtrees. Quadtrees for two-dimensional division and subdivision are appropriate for cartographical data. A geographical database, with objects stored in geocentric or geodetic (geographical) co-ordinates, requires indexing mechanisms that take into account the shape of the Earth. In this paper, we present a method for indexing of geographical data, named Ellipsoidal Quadtrees (EQT). In contrast to other global indexing methods, EQT is based on the Earth ellipsoid and not a spherical approximation. EQT division and subdivision make it possible to divide the Earth surface into a mesh of quadran...

Since military planners must know the size and shape of the earth if they hope to track earth-orbiting satellites and to target missiles on distant lands, geodesy was an important concern of the two superpowers during the Cold War. The most important geodetic product in the United States was a series of increasingly powerful World Geodetic Systems, the first of which (WGS 60) was published for the Department of Defense in 1960. Although WGS 60 was created because of intense international rivalries, it reflected the intense rivalries between America's Army and its Air Force, and it introduced the notion of 'political geodesy'. My attention to American events does not indicate a lack of interest in the Soviet story; rather, I hope that historians with better language skills and better access to Soviet documents will examine geodetic research on the other side of the former Iron Curtain.

A new methodology for precise geoid determination with finest local details based on ellipsoidal approximation is presented. This methodology is formulated through the “fixed-free two-boundary value problem” based on the observable of the type modulus of gravity intensity, gravity acceleration and gravity potential at the GPS positioned stations, with support of the known geoid's potential value, W0.

Airy stated unequivocally that the dimensions of his Figure of the Earth, better known as the Airy 1830 ellipsoid, were given in “leet of the Shuckburgh standard”, further interpreted as feet of the first yard of the Shuckburgh scale. Because relation to the international metre was ill-defined, approximate metric equivalents have been used, e.g., by the geodetic datum of Great Britain. This article presents a definitive determination of thermal expansion of the Shuckburgh scale and of the length of its first yard.

Two adjacent Arcs of the Meridian were measured in Europe and in Africa close to the line of 30° longitude in the 19th and 20th Centuries. Both owed their existence to men of vision who could turn to Imperial Powers for the necessary funding. Both required dedication and hard physical labour for their completion. Although they were connected by others in the 1950's, the only computation of a long arc from Europe to Africa used other stations in Europe and did not reach the northernmost point. The European Arc made a major contribution to our knowledge of the shape of the earth in its time; the African Arc's contribution is less clear. They are both now part of history, superseded by the ubiquitous GPS, but it is a history that should be known and preserved.

The geoid is the fundamental surface that defines the figure of the Earth. It is approximated by mean sea-level and undulates due to spatial variations in the Earth's gravity field. The use of the geoid in regional geophysics is illustrated for the North West Shelf of Australia by removing long-wavelength geoid features, due predominantly to deep-Earth mass anomalies, in order to reveal near-surface structure. After this process, the residual geoid anomalies correlate well with known geological structures. Therefore, the geoid can provide information, complementary to other geophysical data, of the Earth's internal structure.

Significant systematic errors can result in precision surveying if the curvature of the earth is ignored in the adjustment of a survey network. The errors can become significant even for networks with very limited extent. An adjustment model for small-scale surveying networks such as precision threedimensional metrology networks is presented in this paper which uses a local Cartesian coordinate system and applies curvature corrections to all the observations in a network. The adjustment model is useful especially for precise industrial metrology networks such as those established using real-time electronic theodolite systems.

One class of surface water models is the shallow water models obtained by depth-averaging the microscale mass and momentum balances. Application of shallow water models to large scale problems (on the order of 1000's of km) requires the use of spherical coordinates. Traditionally, balance laws in spherical coordinates are derived by simply expanding the spatial operators in the standard depth-averaged equations. However, the equations themselves are based on an assumed planar surface so that an inconsistency exists between the derivation and the interpretation. In this article, a method is presented that properly accounts for the curvature of the Earth during the depth-averaging procedure. The derivation gives rise to new terms in both the continuity and momentum balances, terms that we refer to as curvature terms. A scaling analysis evaluates the magnitude of the terms. It is shown that the curvature term in the continuity balance is insignificant when the vertical velocity is small, i.e., at least four ...

The form of the Earth is much closer to a sphere than a flat slab, so why is gravity and magnetic modelling almost exclusively carried out within a flat Earth or Cartesian framework? The use of a Cartesian coordinate system can be attributed in part to the absence of alternatives in the commercial modelling and visualisation software packages and the need for additional computational resources if modelling is carried out in a spherical or ellipsoidal reference system. These are not sufficiently good reasons, however, to blindly continue with this practice. Gravity modelling is a particularly widespread activity, being used for basic gravity data processing (e.g., Bouguer and terrain corrections - e.g., LaFehr, 1991a, 1991b, 1998; Talwani, 1998; Hinze et al, 2005), geodesy applications (e.g., geoid calculations), and geological interpretation. To what degree are the outcomes of these activities affected by the choice of Earth representation? In the exploration geophysics community, there is a standard answer to the question ?when do curvature effects become significant? which is ?when the models are larger than 166.7 km in horizontal extent?. This criterion can be traced back to Hayford and Bowie (1912). What was the basis for choosing this distance? Is this a criterion that can be applied to all modelling applications or just the original application of Hayford and Bowie (1912)? Although there is general acknowledgment that the curvature of the Earth is important when performing gravity or magnetic modelling of long traverses or large regions, there are few studies of the errors involved if a Cartesian (or rectangular) coordinate reference system is used. Examples that demonstrate the magnitude of curvature effects on gravity response can be found in Hayford and Bowie (1912), Takin and Talwani (1966), Johnson and Litehiser (1972), Qureshi (1976), Miku?ka et al. (2006), and Cavsak (2008). In the following, results of simple calculations for a regular mesh of prismatic elements are presented to quantify the differences in vertical gravity and vertical gravity gradient response for equivalent representations of source elements in Cartesian or spherical coordinate reference systems. It is noted that outcomes for vertical gravity gradient response are the same as those that would be obtained for total magnetic intensity response (TMI). Although this work is based on models comprised of a regular array of prismatic mesh elements, the outcomes can be related to those that would be obtained for models based on arbitrary 3D polyhedra. There are clear extensions of methodology that would allow modellers to estimate the significance of curvature effects for any specific application. This will help to answer the question that is prompted by Figure 1, i.e., ?How significant are the differences if I carry out gravity or magnetic modelling for a portion of the Earth using a Cartesian framework rather than a spherical framework??

Modern geodesy can be said to have its origins in the expeditions to Peru and Lapland that finally determined that the earth was not an exact sphere and was in fact oblate. The 250th anniversary of those expeditions is being celebrated this year.Brief comments are given on the recorded measures of the figure of the earth up to 1735 and then details are given of the two major expeditions that resulted in the flattening of the earth.

This paper describes a recomputation of the classical determinations of the figure of the earth from arc measurements, made in the eighteenth century in ‘Peru’ and ‘Lapland’, under the auspices of the French Academy of Sciences. The recomputation was carried out by Christine Hudson using electronic computers, as part of the requirements for the M.Sc. in Surveying at University College London in 1984. The paper would have been easier to write if there had been only one set of measurements; but such was not the case. There are four different sets of data for the southern arc measurements, each of which has been re-computed, but one only for the northern arc. The data used have been gleaned from the various publications of the participants, as it has not been possible to use the actual field books.

The first sentence in a textbook dealing with photogrammetry may give the following definition: “Photogrammetry may be defined as the technology of obtaining reliable information about physical objects through the process of recording and measuring photographic images.” If this physical object is the surface of the earth, photogrammetry can be considered as a tool of surveying. In that case, photogrammetry is a part of geodesy, whose principal task is the determination of the shape of the earth and its field of gravitation. Up to the present, we have been accustomed to associating the different tasks in surveying either with what we would call conventional terrestrial methods or with photogrammetry

A brie/discussion o/the international and national background o/baseline measurement is presented. This discussion also includes a description of the equipment employed. The details o/the Victorian ba()e/ine measurement are given. demonstrating. via the comparison with the New South Wales 10 foot Standard. that the Victorian. New South Wales and Queensland baselines have a direct connection. Finally the history of the Victorian 10 foot rods ,from J 859 to J 986. is given along with a pictorial record of their physical construction. Introduction The origins of geodetic baselines may be traced back to 814ADI when astronomers were in pursuit of knowledge relating to the shape of the Earth. These baselines were an integral facet of geodesy and remained so until late in the 19th century. As the British Empire fanned out over the globe, its astronomers had the rare opportunity to measure meridian and parallel arcs in opposite hemispheres. England. India and South Africa were places where baselines were established in the early 1800's with the aim of resolving the shape of the Earth and the production of trigonometrically-controlled mapping. With baseline measurement (the probable error being± 0.8 to l.5ppm ) and angles ( the probable error being ± 0.2" ) surveyors had the precise 2 means to perform both of the above tasks. The new Colony of Victoria. by }860. was in great need of a systematic triangulation survey and the newly appointed Superintendent of Geodetic Survey saw that this presented a unique opportunity to provide additional scientific information on the Earth's shape and to map Victoria.lIistory shows that the former was never realised or acknowledged while the latter has been much maligned. Background

The professional surveyor, in the course of his training, is required to study certain problems of geodesy. He learns the significance of spherical excess; convergence of the meridian; the computation of the azimuth and distance between two stations, given their geographical latitudes and longitudes; and the relevant factors for the adopted Figure of the Earth.

1. Introduction 1.1 The prime object of a national geodetic survey is the determination of the coordinates of a fairly close network of inter-connected survey stations distributed over the whole area of the survey.

Summary Small changes in the orbits of satellites near to the earth have revealed new information about the earth's gravitational field and atmosphere. This article explains the main properties of satellite orbits and describes the discoveries which have been made with their help in the following branches of geophysics: the figure of the earth and the gravitational field; the density of the upper atmosphere and its variations, which have proved to be linked with solar activity; and, finally, other properties of the atmosphere, such as temperature and winds.

(1818). XIX. Observations relating to the operations undertaken to determine the figure of the earth. The Philosophical Magazine: Vol. 52, No. 244, pp. 119-131.

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(1862). LV. Tests of the truth of the fluid theory of the figure of the earth. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 24, No. 163, pp. 409-417.

Human error concerning the geography of the earth has been recurrent throughout historic time. Some kinds of error arise because of the problems of dealing with phenomena in the three-dimensional zone forming earth-space. The broad curvature of the earth, the sheer diversity of earth-space, and the patterns of change through time all form pitfalls for the geographer who is, thereby, liable to error in his descriptive analyses. The problems of placing percepts (things perceived) against concepts (mental abstractions) make for difficulties in analyzing the three-dimensional spatial zone in which geographers work. Among the kinds of error committed there are avoidable varieties, such as the inexact use of descriptive and analytical language, the uncritical use of statistical data, the acceptance of unreliable data, and the confusion of the several kinds of spatial distributions. Less avoidable error derives from the formulation of hypotheses accounting for phenomena which, when critically examined a...

(1823). LXI. Proposal for a new method of determining a fixed unit of measure, by deducing the same from the curvature of the earth. The Philosophical Magazine: Vol. 61, No. 300, pp. 266-269.

1. The Secondary and Tertiary Triangulations of the six counties of Northern Ireland which were observed about 1900 were computed county by county each on its own meridian on a Cassini projection using Airy's figure of the earth. Although a number of points common to two or more counties were fixed no attempt was made to bring the separate counties into sympathy either with each other or even with the old Primary triangulation as adjusted by Clarke in 1856.

The present paper is an attempt to evolve a practical method of determining the geodetic azimuth of a referring mark close to the observer's horizon, and the η- and e-components of the deviation of the vertical from observations of only three stars of which two constitute a pair of north and south stars and the third lies close to the prime vertical. The method is applicable in higher latitudes as well. The geodetic azimuth is used as azimuth control for a survey while the deviation of the vertical is required for the astronomical levelling to determine the general figure of the earth.

I. INTRODUCTION The present investigation is a feasibility study of a spatial triangulation scheme covering the Australian continent, using the geometric satellite geodesy method. This method is a highly accurate means of relative-position determination of points on the Earth's surface that are separated by thousands of kilometers. As the method is independent of gravity and of any assumptions concerning the shape of the Earth, it is a most powerful means of precise-position fixation on a global scale.

Most text-books on surveying limit their discussion of the correction of vertical angles for curvature of the earth and atmospheric refraction to the correction of angles taken with a theodolite during triangulation and omit any reference to those taken with a clinometer. This is rather illogical, as in well-observed triangulation, with all vertical angles measured in both directions, no correction for these effects is necessary, whilst in plane-tabling on small scales where sketching at considerable distances is frequently employed the application of corrections for these effects is essential.

1. For both geodetic and geophysical reasons it is desirable that a method of determining the curvature of the earth at a large number of points, as well as the heights of these points, should be developed. The fact that these two quantities are intimately related in the process of height determination by reciprocal vertical angles has in general been ignored. The present paper does not profess to provide a complete solution; but rather to set forth the requirements and to make some suggestions towards meeting them; and to stress the need for research in the matter of terrestrial refraction, which is certainly long overdue.

The Figure of the Earth used by the Ordnance Survey for its work in Great Britain is that given by Sir George Airy in the “Encyclopaedia of Astronomy” in an article on the Figure of the Earth. It is universally known as Airy's Figure.