Ellipsoidal Corrections to Potential Coefficients Obtained from Gravity Anomaly Data on the Ellipsoid

摘要

The spherical harmonic coefficient C sub nm of the disturbing potential T is expressed as an integral of gravity anomaly data delta g sub f assumed to refer to the surface of the reference ellipsoid, plus ellipsoidal correction terms. The ellipsoidal correction terms are intended to remedy the spherical approximations made in the principal integral term regarding the boundary condition relating T and delta g and the shape of the boundary surface. Specifically, two corrections are employed to reflect the use of a boundary condition that now accounts for terms on the order of the earth eccentricity square. In addition three corrections are employed to account respectively for the first, second, and third radial derivative effect in reducing the gravity anomaly from the ellipsoidal boundary surface to the equatorial sphere where the desired spectrum C sub nm applies. Global maps are given to shown the effect of the various ellipsoidal correction terms on geoid undulations. The total correction has a global RMS value of about 34 cm in geoid undulation and 3.3 mgals in gravity anomaly, cumulative for degrees n = 2 to 180.