Obtaining Earth Surface and Spatial Deflections of the Vertical From Free-Air Gravity Anomaly and Elevation Data Without Density Assumptions
Abstract
Moritz (1980) presents a density-free scheme allowing for the analytical or regular continuation of a given set of free-air gravity anomalies, referenced to the ground, to any desired level surface if a corresponding set of elevations (e.g., above mean sea level) is available. An efficient spectral implementation of this scheme is discussed by Sideris (1987). A subsequent spectral execution of the planar Vening-Meinez equation on the continued anomalies yields deflections of the vertical on the chosen level surface. The deflections are brought back to the Earth's surface via a spectrally implemented Taylor series. Deflections at a constant altitude above the level surface are obtained through a routine spectral execution of the planar upward continuation integral. Two sites, having diverse topographies, were surveyed for 1 arc min by 1 arc min mean free-air anomaly and elevation values and for smaller sets of astronomically determined deflections to serve as control or truth values. In a topographically tranquil but gravimetrically turbulent Oklahoma site the overall RMS of the differences between true and predicted deflections was 0.3 arc secs and in a rugged New Mexico site it was 0.6 arc sec. Accurate first derivative terms (in both continuation steps) require a 1 arc min data set as interpolation-free as possible. A 1 arc min data grid is shown to be insufficient for meaningful computations of the higher order series terms. Potential pitfalls of the two-dimensional fast Fourier transform pair are discussed with an emphasis on unwanted circular convolution effects which, if unaccounted for, can increase the error in individual predicted deflections by as much as 100%. Reprints.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 10, 1990
- Accession Number
- ADA228685
Entities
People
- David M. Gleason
Organizations
- Air Force Systems Command