Study of the high‐frequency spectrum of the anomalous gravity potential

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Abstract
The analysis of the high‐frequency spectrum of the anomalous gravity potential is important for a number of current and emerging technologies in geodesy and geophysics. Among them is the precise determination of deflections of the vertical by inertial techniques, the development of data processing methods in airborne gradiometry, and the signal extraction methods for airborne gravimetry. The spectral information required can be obtained by analyzing dense gravity data by fast Fourier transform techniques. An attempt has been made to use available data files in Canada for this purpose. The data consisted of a rather uniform set of (5 arc min × 5 arc min) point anomalies in most of the continental areas of Canada and four sets of point gravity anomalies with an average data spacing of about 1 km in areas of limited extent. The analysis showed that the gravity spectrum has to be resolved to about degree and order 7000, i.e., to a point spacing of about 3 km, to resolve the gravity anomalies to 1 mGal. Thus a similar data spacing would be required in airborne gradiometry and gravimetry in order to get an equivalent resolution. The derived spectrum was used to determine suitable degree variance models and covariance functions for the above applications. The spectrum estimated from the 5 arc min × 5 arc min gravity anomalies covering the nonmountainous areas of Canada indicates that the degree variances of the anomalous potential decay as ℓ−3.6. This means that a number of currently used covariance models do not agree with the results of this analysis. A discussion on the choice of a more adequate model concludes the paper.