Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical Implied by Anomaly Degree Variance Models.

This report first develops a new anomaly degree variance model by considering potential coefficient information to degree 20, and updated values of the point anomaly variance (1795 mgal2), the 1° block variance (920 mgal2) and the 5° block variance (302 mgal2), the variances being given with respect to the Geodetic Reference System 1967. This new model was computed assuming that anomaly information was given on a sphere of radius 6371 km with the radius of the best fitting Bjerhammer sphere found to be 6369.8 km. This new model and several other models were used to develop closed express ions for the covariance and cross-covariance functions between gravity anomalies, geoid undulations (or height anomalies), and deflections of the vertical. It is shown how these global covariance expressions can be modified for use as local covariances and for use when mean anomalies are being considered. A Fortran subroutine is provided for the determination of the covariance values implied by the recommended anomaly degree variance model. [Some mathematical expressions are not fully represented in the metadata. Full text of abstract available in document.]