Mathematics
Scientific paper
Jul 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984rpesc.......57b&link_type=abstract
In its USSR Rept.: Earth Sciences (JPRS-UES-84-005) p 57-58 (SEE N84-28132 18-42) Transl. into ENGLISH from Geod. i Kartogr. (U
Mathematics
Earth (Planet), Earth Gravitation, Geodesy, Geology, Gravity Anomalies, Lagrange Coordinates, Mathematical Models, Statistical Analysis
Scientific paper
In computing gravity anomalies at altitudes of hundreds of kilometers or greater it is customary to use a model of the Earth's potential in the form of an expansion in spherical function. At lesser altitudes a surface gravity survey under the particular point is also used. Gravity, however, must sometimes be determined at altitudes of tens of kilometers or less in the absence of a gravity survey in the region. The following procedure is used under these conditions: gravity is measured at the surface and it is reduced upward using the vertical gravity gradient delta (2) u/delta r (2) of the model field. The accuracy of this reduction decreases with altitude and its critical value must be computed. The measured g sub o value is reduced to the altitude H using the Lagrange formula. Proceeding along these lines, a formula is derived for the critical altitude h. The solution will be unstable because the derivatives are dependent on local peculiarities of the anomalous field. A statistically more valid solution can be obtained by replacing the real derivatives with their dispersions. The dispersion of the first derivative is denoted G (2) (H) and the dispersion of the second derivative is designated E(2)(H). Then a more effective formula is obtained for h.
Brovar V. V.
Tadzhidnov K. G.
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