Reconciliation of Stokes' function and astro-geodetic geoid determinations

Abstract

The combined application of astronomic, geodetic, and gravimetric data to computations of the geoid is discussed. The general principle observed is that any adjustment should weight all observations inversely as their variances. Two conditions are imposed: (1) Geoid heights and deflections computed by Stokes' theorem from gravity data must equal those derived by astrogeodetic means. (2) The five harmonics P1, P11 sin λ, P11 cos λ, P21 sin λ, and P21 cos λ must be absent from the adjusted gravity field. The ideal case is discussed, including provision for separate determinations of parameters by independent astronomic methods. Practical modifications are then introduced in turn: treating gravity anomalies as representative of areas; holding geodetic or astronomic observations constant; using a reduced number of astronomic stations; and comparing interpolated points of the astro‐geodetic and gravimetic geoids. The most significant discrepancy from the ideal case of most practical solutions made heretofore appears to be in the weighting of the gravimetric data.

The latest achievements of physical geodesy

“…To mention some examples' Bornford and his group prefer to use only the classic astrogeodetic method; the satellite men seem to be inclined to overestimate the geodetic significance of the information obtained from the period of the satellite revolution and the precession of the node and perigee of the satellite orbits. Some scientists try to combine the results of the astrogeodetic method, satellite geodesy, and the gravimetric method [Kaula, 1959a]. Other scientists are inclined to fill even continent-wide gravimetrically unsurveyed areas with gravity anomalies estimated by the methods of statistical mathematics.…”

“…The Army Map Service has since computed other geoids using a different extrapolation method, somewhat different material, and different flattening values a. The computed geoids differ from one another, of course, because we have used the flattening value of the international ellipsoid, a --1:297.0, and the Army Map Service [Kaula, 1959a] has used the value a --1:298.49, or a --1:298.3. It is relatively simple to convert the N values from one flattening value to another.…”