The Effect of Vertical Datum Inconsistencies on the Determination of Gravity Related Quantities.

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Abstract
Three different models of inconsistencies in the world vertical datum due to the Sea Surface Topography problem are constructed. A spherical harmonic decomposition of different models of global vertical datum inconsistencies into a set of potential coefficients up to degree and order 180 is described. The effect of datum inconsistency is found significant at low degree harmonics and negligible above degree 60. The maximum relative error (by degree variances of coefficients) is estimated as 1%. In terms of the error in geoid undulation the absolute cumulative effect of datum inconsistency can be of the order of 0.5 m which is of the order to the amplitude of Sea Surface Topography variation. In terms of the error in gravity anomaly, the cumulative effect can be of the order of 0.1 mgal. The effect of the internal distortion of the North Americal vertical datum due to the overconstrained adjustment of the 1929 levelling net is found to produce the cumulative error in geoid undulation of the order to 2 millimeters, and in terms of gravity anomaly this error is estimated as 0.0001 mgals. The secondary effect on the zero-degree undulation term when the gravity anomaly data in the spherical cap are used through the Stokes' equation to produce the geoid undulation field is found to be of the order of 1 cm for most practical applications.

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