Ellipsoidal Corrections to Potential Coefficients Obtained from Gravity Anomaly Data on the EllipsoidDepartment of Geodetic Science and Surveying, The Ohio State University, 1986 - Ellipsoid - 33 pages 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. |
Common terms and phrases
account for terms Ag(mgal bnmCnm boundary condition C(XN,XM Cảm Cam Cam Cam CCDEF CCOEF Chm and Chm CIMENSION cm from Chm Cn+2 Cnmnm COEF COEFIC Contour Interval cumulative DCCEF degree variances Department of Geodetic disturbing potential coefficients e²sin EAM(XN,XM ellipsoidal correction coefficients ellipsoidal correction formulas ellipsoidal correction terms equation equatorial sphere fully normalized geocentric geocentric latitude Geodetic Science geoid undulation gravity anomaly Age Gravity Anomaly Correction gravity anomaly data gravity potential harmonic degree IMPLICIT FEAL integral J.Y. CRUZ JCEPARM latitude m²-n maximum degree mgals in gravity n+k+2 nmax O(e² Ohio State University OSU86D solution plumb line potential coefficients obtained priori set PROCL Program radial derivative effect radius reference ellipsoid Science and Surveying space domain expressions spherical harmonic third radial derivative undulation and 3.3 Undulation Correction Implied VIXN WRITE 20 XN-XM XN,XM XN+4.DO XN+XM XN=DFLCAT Εγ әт