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in other words immediate vicinity under consideration

Undulation and Deflections by the Gravimetric Method

The method providing the basis from which the undulations of the geoid may be determined from gravity data was published in 1849 by a British scientist, Sir George Gabriel Stokes. However, the lack of observed gravity data prevented its application until recent years. In 1928, the Dutch scientist, Vening Meinesz, developed the formulas by which the gravimetric deflection of the vertical (Figure 22) can be computed.

The computation of the undulations of the geoid and the deflections of the vertical require extensive gravity observations. The areas immediately surrounding the computation point require a dense coverage of gravity observations and detailed data must be obtained out to distances of about 500 miles. A less dense network is required for the remaining portion of the earth. While the observational requirements for these computations appear enormous, the results well justify the necessary survey work.

Figure 23 shows how the mass surplus of the mountains and the mass deficiency of the oceans cause the deflections of the vertical and the undulations of the geoid. A mountain mass attracts the plumb line from the normal of the ellipsoid. Likewise the mass deficiency of the ocean does not attract the plumb line. These effects of the mass anomalies contribute to the deflection of the vertical. However, both deflections of the vertical and undulation values result from density variations throughout the earth. In the area of mass surplus, the observed gravity (reduced to sea level considering only the elevation) is generally greater than the theoretical value, and the anomalies are positive. In the areas of mass deficiency, the observed (reduced in the same manner) is generally smaller than the theoretical value and the anomalies are negative (Figure 24).

The deflections and undulations computed with sufficient gravity information are considered absolute values referred to an earth-centered reference ellipsoid. In other words, the axis of rotation for the ellipsoid passes through the earth's center of gravity.

Effective use of the gravimetric method is dependent only of the availability of anomalies in sufficient quantity to achieve the accuracy desired. Successful use of Stoke's integral and Vening-Meinesz formulas depends on a good knowledge of gravity anomalies in the immediate vicinity of the point under consideration and a general knowledge of anomalies for the entire earth.

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by no means

Geophysical Gravity Predictions

Measured gravity coverage is by no means complete. There are many large regions on the continents where gravity measurements are lacking or available only in small quantities. Gravity data for ocean areas has always been sparse; however, Satellite Altimetry (Chapter VII) has overcome this deficiency. In regions where an insufficient number of gravity measurements exists, some other approach must be used to obtain or predict the mean gravity anomalies for the areas.

Correlations exist between variations in the gravity anomaly field and corresponding variations in geological, crustal, and upper mantle structure, regional and local topography and various other types of related geophysical data. In many areas where gravity information is sparse or missing, geological and geophysical data is available. Therefore, the various prediction methods take into account the actual geological and geophysical cause of gravity anomalies to predict the magnitude of the anomalies.