The reduction correction in North America

An inverse Poisson integral technique was used to determine a gravity field on the geoid which, when continued by analytic free space methods to the topographic surface, agrees with the observed field. The computation is performed in three stages, each stage refining the previous solution using data at progressively increasing resolution (1 x 1 deg, 5 x 5', 5/8 x 5/8') from a decreasing area of integration. Reduction corrections are computed at 5/8 x 5/8' granularity by differencing the geoidal and surface values, smoothed by low-pass filtering and sub-sampled at 5' intervals. The 1 x 1 deg averages of the reduction corrections thus obtained for 172 1 x 1 deg squares in western North America are discussed. The 1 x 1 deg mean reduction corrections are predominantly positive, varying from -3 to +15 mgal, with values in excess of 5 mgal for 26 squares. Their mean and rms values are +2.4 and 3.6 mgal respectively and they correlate well with the mean terrain corrections. The mean and rms contributions from the three stages of computation are: 1 x 1 deg stage +0.15 and 0.7 mgal; 5 x 5' stage + 1.0 and 1.6 mgal; and 5/8 x 5/8' stage +1.3 and 1.8 mgal. These results reflect a tendency for the contributions to become larger and more systematically positive as the wavelengths involved become shorter. The results are discussed in terms of two mechanisms; the first is a tendency for the absolute values of both positive and negative anomalies to become larger when continued downwards and, the second, a non-linear rectification, due to the correlation between gravity anomaly and topographic height, which results in the values continued to a level surface being systematically more positive than those on the topography.