Methods for the computation of detailed geoids and their accuracy

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1975-11

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Ohio State University. Division of Geodetic Science

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Two methods for the computation of geoid undulations using potential coefficients and 1° x 1° terrestrial anomaly data are examined. It was found that both methods give the same final result but that the method suggested by Molodenskii allows a more simplified error analysis than the method used by Vincent and Marsh. Specific equations were considered for the effect of the mass of the atmosphere and a cap dependent zero-order undulation term was derived. Although a correction to a gravity anomaly for the effect of the atmosphere is only about -0.87 mgal, this correction causes a fairly large undulation correction (e.g. 2.3 m with a cap size of 20°) that has not previously been considered. The accuracy of a geoid undulation computed by these techniques was estimated considering anomaly data errors, potential coefficient errors, and truncation (only a finite set of potential coefficients being used ) errors. It was found that an optimum cap size of 20° should be used. The geoid and its accuracy were computed in the Geos - 3 calibration area using the GEM6 potential coefficients and 1° x 1° terrestrial anomaly data. The accuracy of the computed geoid is on the order of ±2 m with respect to an unknown set of best earth parameter constants. This geoid was compared to that computed by Vincent and Marsh where we found a systematic difference of 3.9 m, an undulation difference variance of (2.6 m), and a maximum difference of 12 meters.

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