If g is the gravity value observed at point P at an elevation of H(m),
[g] + [corrections for topography] + [0.3086×H]-[normal gravity at point 0 on the geoid right under point P]
is usually taken to be the BOUGUER anomaly at point 0. This can be written as [g] + [corrections for topography] - [(normal gravity at point 0 ) - (0.3086 × H)]
Since the third term is the normal gravity at point P, this is equal to [g] + [corrections for topography] - [normal gravity at point P]
and is therefore more properly to be called the BOUGUER anomaly at point P, or the station BOUGUER anomaly, rather than the BOUGUER anomaly at point 0. The neglect of this differentiation between the BOUGUER anomaly at P and 0 in the customary procedures of reduction will sometimes cause no small errors in ravity interpretations.
In two-dimensional cases, if ΔG
0, ΔG
1, …BG
6 are station BOUGUER anomalies observed at horizontally equal intervals, 2π/6, but at various elevations, h
0, h
1, …h
6 (in radian), the real BOUGUER anomaly at χ=π on the geoid is given by the formula (8) in the text, where φ
0, φ
1, φ
2, φ
3, represent the respective coefficients of Δg3, Δg2, Δg1, Δg2 in the formula (6).
The formula (8) contains unknown Δg
8's on its right hand side. The value of Δg
3 in various degrees of approximation can be obtained by replacing these Δg
8's by their approximate values. In the formula (13), the innermost frame represents the zero-th approximation, the middle frame the first approximation, and the outermost frame the second approximation. Numerical values of 1/φ
0, φ
1 /φ
0, φ
2 /φ
0, φ
3 /φ
0 are given in Table I.
Model calculations have shown that this method works satisfactorily, especially by the second apporoximation.
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