Statistical and harmonic analysis of gravity

Markov theory is developed in terms of two correlated functions, the free-air gravity anomaly and the elevation of the topography. The Markov methods are applied to the mean anomalies of 1°×1° blocks to extrapolate from all available observations to obtain estimates of mean anomalies of 10°×10° blocks world-wide. These estimates are adjusted so that the even-degree zonal harmonics are consistent with the precession of the node of satellite 1958β and so that the inadmissible first-and second-degree harmonics are absent. Spherical harmonic coefficients up to the eighth degree (P8,8 terms) for free-air gravity are computed. An independent autocorrelation analysis is made in order to estimate the variance of mean anomalies of blocks and the variance of each degree of the spherical harmonics. This analysis is utilized as a control on the error variances and covariances of the mean anomaly estimates made by the Markov method. The results are used in conjunction with the zonal harmonics derived from satellite motions to obtain a best estimate of the exterior potential in spherical harmonics from terrestrial gravimetry up to June 1958 and satellite data up to December 1958. It is planned to revise this estimate periodically as new observational data become available.