Accession Number : AD0728688

Title :   A Study of Covariance Functions Related to the Earth's Disturbing Potential.

Descriptive Note : Scientific rept.,

Corporate Author : OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE

Personal Author(s) : Meissl,Peter

Report Date : APR 1971

Pagination or Media Count : 96

Abstract : The following quantities are considered: geoidal undulations, gravity anomalies, deflections of the vertical, a fictitious surface density, the vertical gradient of gravity anomalies. These quantities are interrelated by linear operators having the spherical harmonics as eigen-functions. If the covariance of one of these quantities is specified, that of the others can be computed. Thereby rigorous bounds for the ratios of the different variances can be established. Though the earth's disturbing potential can be represented by any of the above quantities, there are differences in the stability of the resulting solutions. Attention is focused on potentials obtained from a combination of satellite information and gravimetry. In that case the introduced quantities are considered as residuals with respect to a geoid resulting from the adjusted lower degree harmonic coefficients. It is shown that the covariance of any one of the residual quantities tends to have certain theoretical properties. These are a predetermined number of zeros as well as negative correlation at certain predetermined distances. A comparison has been performed between the gravity anomaly residuals with respect to a low order geoid and mean 5(o) degree x 5 degree block anomalies having uncorrelated errors. Compared are the resulting errors in geoidal undulations and deflections of the vertical. (Author)

Descriptors :   (*GRAVITY, ANOMALIES), POTENTIAL THEORY, HARMONIC ANALYSIS, OPERATORS(MATHEMATICS), STOCHASTIC PROCESSES

Subject Categories : Geodesy

Distribution Statement : APPROVED FOR PUBLIC RELEASE