Iteration Procedure for Evaluating High Degree Potential Coefficients from Gravity Data

Earlier a solution of the gravimetric free scalar boundary value (BV) problem was derived with respect to the potential coefficients C _n,m , taking into account the correction terms due to both the earth’s ellipticity and surface topography. In the present paper the behavior of this solution is studied for large values of degree n. It is shown that the absolute value of the ellipsoidal correction to the spherical approximation $$ _{n,m}^{(0)} $$ , having the sign opposite to the latter, becomes of the same order for n ≈ 360, is equal to it at n ≈ 600 and then exceeds it, increasing with growing n. A similar situation is observed for the ellipsoidal correction in{152-2} derived by other authors, in particular by Pellinen, Rapp and Cruz. In the present paper, proceeding from the same BV solution, an alternative iteration procedure for evaluating $$ _{n,m} $$ is elaborated. The initial approximation in it is not $$ _{n,m}^{(0)} $$ but a modified quantity $$ _{n,m,}^{(1)} $$ depending on e2. The new formulas are well-suited for evaluating the potential coefficients of any degree n and order m.