Knowledge Bank

Investigations on the upward continuation of gravity anomalies given on the surface of the earth's visible topography are reported. Results are compared for three upward continuation procedures: first, the direct Poisson integration of the original terrain-uncorrected surface anomalies; second, the direct Poisson integration of terrain-corrected (i.e., Faye) surface anomalies; and third, the so-called indirect method. In the indirect method the original anomaly field is basically split into three frequency ranges that are then modeled separately: the low frequencies are modeled by spherical harmonics; the medium frequencies are modeled by Poisson integration of residual surface anomalies with long-wavelength terrain correction applied; and the high frequencies are modeled by prism integration of the gravitational effects of certain shallow topographic masses of assumed constant density. Values of 5 'x 5' mean anomalies, 5' x 5' mean elevations, and 30" x 30" point elevations in a 7° x 9° area covering both mountainous and smooth topography in New Mexico are used in actual upward continuations. Upward continued values are obtained for test profiles at elevations 30, 10, and 5 km, as well as for points in the float section (30 km elevation) of a balloon-borne gravity measuring project being coordinated by the Air Force Geophysics Laboratory (AFGL). The test profiles resulting from the direct Poisson integration of terrain-uncorrected anomalies are negatively biased (i.e., too low) by about (0.6, 0.5, 0.7) mgal at elevation (30, 10, 5) km compared with the profiles resulting from the direct Poisson integration of terrain-corrected anomalies. There is no detectable bias between the latter set of profiles and those from the indirect method. The standard deviation of the differences among the three upward continuation methods reaches the order of (0.5, 0.6, 1.3) mgal at (30, 10, 5) km elevation, for the profiles tested. Also presented is an analysis of errors associated with upward continued anomalies and with computed normal gravity values. It is projected that values at the AFGL balloon points have been recovered with about 0.9 mgal total standard error in gravity anomaly with data error propagation as dominating error source, and about 0.7 mgal error in normal gravity with vertical position error as dominating error source. In a separate series of tests, it is shown that upward continuations using Fast Fourier techniques produce results that agree with Poisson integration on the level of (0.1, 0.3) mgal at (30, 10) km elevation.