# GEODESY THE CONCEPTS VANICEK PDF

J. E. Jackson; Geodesy: the Concepts Petr Vaníček and Edward Krakiwsky, North Holland, This content is only available as a PDF. Download. download Geodesy - 2nd Edition. Authors: P. Vanícek E.J. Krakiwsky Geodesy: The Concepts, Second Edition focuses on the processes, approaches, and. Geodesy. Petr Vanıˇcek. University of New Brunswick. I. Introduction. II. Positioning. III. further quantitative improvements of their conceptual model of the earth.

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Krakiwsky, you could download in the web link that we offer. One of the researches done in the country regarding physical geodesy is entitled Research and Development in Support of the Implementation of the Philippine Reference System of Results and Recommendations done by Enrico C.

Paringit, Diony A.

Ventura, and Jose Galo P. Isada published in October This local geoid model must be developed and validated from the global geopotential models. The whole survey that was done made use of the PRS92 as its single reference frame.

One particular and practical impact the project had was through the standardization of surveys on land parcels throughout the country. Prior to PRS92, land parcels in the country were surveyed through either triangulation from the previously determined Luzon datum of found in Balanacan, Marinduque or through azimuth derived from astronomic observation.

Because they are obtained from two different reference systems, the azimuth obtained from astronomic observation and the azimuth obtained from GNSS-based geodetic measurements have their own differences. The project provided a comparative analysis between the azimuths obtained from the two different reference systems.

## New views of the spherical Bouguer gravity anomaly

The analysis showed adjustments or transformations that can be done to relate the old data astronomic to the newer reference system geodetic. This made it possible to relate the old azimuths to more popular reference systems with the use of both GNSS and PRS92 which is a more practical and accurate approach to land parcel surveying.

According to results and findings of the 8-month long period of field observations, the geodetic control network of the Philippines is not as accurate as how the country needs it to be. A static network, especially for the Philippines, is highly undesirable. Also, for a more accurate and efficient reference system, it was highly recommended that gravity anomaly and deflection of the vertical must be verified to the quantities obtained through field observations.

The project also recommended to increase the number of control stations to be used in the new reference system as it is quite obvious that the increase in the number of control stations also increases the accuracy of the whole reference system. Two more concepts that are used in physical geodesy, and consequently, important to introduce, are the concepts of level surfaces and plumb lines.

Level surfaces are surfaces whose potential is constant. Level surfaces are sometimes referred to as equipotential surfaces. An example of an equipotential surface or a level surface is the geoid. Two vectors, whose scalar product is computed to be 0, are said to be orthogonal to one another. This is true to the relationship of the gravity vector and the equipotential surfaces such as the geoid.

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The imaginary lines orthogonal to the geoid are called the plumb lines. Plumb lines are important because their intersections with points on the surface of the Earth are computed to be the orthogonal height H of these points.

The orthogonal height is the difference in elevation computed from the geoid. The figure below shows the relationship between level surfaces, the geoid, orthogonal height and the gravity vector. Figure 3: Level surfaces and plumb lines Moritz, There are other types of gravity calculations and the experimentation and procedures that govern them.

These calculations vary from one procedure to the other in terms of approximations in the values of the gravity field, geoid model, and other concepts that rely on these data with measurements.

For example, for gravity computations, the level ellipsoid is more often used. Level ellipsoids or reference ellipsoids are, unlike other geometric models, geocentric.

Geocentric models have their centers coincided with the mass center of the Earth. This is because the gravity vector, from our basic Science courses, points directly towards the mass center of the Earth. The ellipsoid takes the place of the geoid and, consequently, is assumed to be a level surface with constant potential. Mathematical calculations involving this ellipsoid is much easier and to conduct and formulas can be understood and formulated more clearly.

## Geodesy: The Concepts

Gravity, height, and potential calculations are done with respect to this level ellipsoid using the same concepts of level surfaces and plumb lines. The gravity obtained from the level ellipsoid is called the normal gravity. This ellipsoid and the normal gravity field are determined by four constants: Reference Ellipsoid constants These four constants, again, vary from one calculation procedure to the other.

Calculations using these varied constants also have their own differences.

The GRS80 has a semi major axis a of 6,, Significant deviations from the GRS80 included information that was due to new data from Doppler, satellite laser ranging and satellite radar altimetry, among others. The figure below shows a simplified model of reference systems in general Figure 4: Simplified version of WGS84 These references systems mentioned above are two of the reference systems used for basic physical geodesy calculations and theories.

For more practical and more accurate data, geodesists and other scientists use local reference frames to establish controls and survey points within a local setting.

One example of a local reference system is the PRS92 discussed above. Local reference systems calculate for the best-fitting ellipsoid for a given local setting. Calculations tailor the reference ellipsoid into an ellipsoid that best fits the topography of the local area.

Figure 5: Best-fit ellipsoid IV. Application Physical geodesy has numerous applications, through various fields of earth sciences, mathematics, and other related fields such as the ones listed above.

One interesting application of physical geodesy in the field of geology is the theory of isostasy. This said to be idealized state isostasy is disturbed due to the continuous changes the Earth below and above its surface is perpetually undergoing.

## Petr Vaníček

Data from physical geodesy suggests that the outermost layers of the Earth are the ones adapting and adjusting to these changes so that isostasy can be restored. However, more drastic advances on the theory of isostasy made use of the concepts in geodesy, more specifically in physical geodesy.

These concepts include gravity, plumb lines, geoid, and global reference systems. One example of these studies of isostasy that made use of physical geodesy concepts was G. Airy argued that the outer layers of the earth consisted of thin crust over a fluid layer of much greater density.

The figure below shows the astronomic and geodetic observations that Airy did to support his argument.

He made his observations between the Himalays and the Ganges Plains, two areas whose elevations are largely different. The deflection angles calculated were due to the differences of gravity calculations using different mass densities and the deviations that come from it.

The deflection angles observed by Airy prove the continuous changes supported by the general theory of isostasy. The deviations in the gravitational field, both direction and magnitude, shows that the mass under higher elevated regions is much greater. Moreover, modern evidence of isostasy heavily relies on physical geodesy.

Latitudes nearer the pole have greater theoretical gravity measurement and, consequently, latitudes nearer the equator have less. Gravity is then assumed to be weaker than the theoretical values over mountain ranges. In regions where isostasy has had time to manifest itself without geological disturbances, the correlation between local elevation and gravity anomalies are more clearly seen. These types of data show how isostasy is present.

The GNSS is a product of both physical geodesy and satellite geodesy. The foundations of GNSS heavily rely on the concepts of elevation, and reference systems. Geometrically, GNSS satellites and receivers use a version of triangulation to determine the exact position of the receiver.Return to Book Page.

## Geodesy: The Concepts

Also, gravity is one of the most important sources of information used in geophysics. Calculations using these varied constants also have their own differences. Physical geodesy is the branch of geodesy that deals with the physical properties of the gravitational field of the earth. Observables and their Properties