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Obenson 1983
Obenson, G. (1983). Direct integration of Stokes’ undulation and Vening Meinesz’s deflection equations for geographically defined gravity anomaly blocks. Journal of Geophysical Research 88: doi: 10.1029/JB088iB01p00665. issn: 0148-0227.

We give here a direct solution of this problem by converting, in an indirect way, the relevant integral equations over each block to their equivalent line integrals taken along and around the boundary curves of the block. Results of sample computations given clearly demonstrate the convergence and stability of these line integrals. We also computed geoidal parameters due to a 30¿¿30¿ inner zone alone at 71 grid locations in Cameroon, using 1¿¿1¿ anomalies and integration steps of 30¿ for the four innermost blocks and 180¿ for the rest of the blocks and compared these with equivalent values from the midpoint method. This comparison yielded significant differences-rms ΔN=2.2 m, ΔNmax=4 m; rms Δ&xgr;=2.9″, Δ&xgr;max=10.5″; rms Δ&eegr;=20¿, Δ&eegr;max=6.7″-that reflect the poor accuracy of the center point method, especially for 1¿¿1¿ blocks near the computation point.

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Journal of Geophysical Research
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American Geophysical Union
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