S U M M A R YDirect Global Positioning System measurement of geoid undulations on accurately levelled stations, usually tens of kilometres apart, can be interpolated by taking advantage of denser surveys of free-air gravity anomalies covering the same area. Using either a spherical or a planar earth model, a two-layer equivalent source is constructed, with the deepest masses located under the geoid stations and the shallower ones under the gravity stations, in such a way that the effect of the masses fits simultaneously, with different precisions, the anomalous potential related to the geoid and its vertical gradient or gravity anomaly. This poses a linear Bayesian problem, whose associated system of equations can be solved directly or by iterative procedures.The ability of the described method to predict the geoid elevation over the gravity stations is assessed in a synthetic example; and in the application to a real case, a gravity-enhanced geoid is mapped for an area of Buenos Aires province, Argentina, where local features are put in evidence.
The separation of regional and residual potential field anomalies, regarded as a spectral problem, can be greatly facilitated when a spectrum estimate shows a clear break between low‐ and high‐frequency components, a feature that normal fast‐Fourier‐transform (FFT) methods fail to present. In this work, we model the discrete Fourier transform of a potential field, measured at stations irregularly distributed on a surface, by means of a high‐resolution sparse estimate derived originally for seismic signal processing. The coefficients of this estimate, which are distributed according to the Cauchy probability law, produce a model with only few components having a significant value. A steepest‐descent algorithm gives a computing alternative to large matrix multiplications and inversions. Advantages of taking this approach are twofold. First, the high‐resolution transform can be used as a gridding tool to evaluate the potential field either on a horizontal plane or on the topographic surface. The enhancement of the spectral peaks and the virtual absence of sidelobes prevents oscillations and edge effects in the result. Secondly, the sparse distribution of the spectral elements allows the interpreter to locate clearly the low‐frequency components related to the regional field. After a second and faster pass, the values of those coefficients can be redefined in order to obtain a more robust separation, ajusting the residuals by the Cauchy criterion. A theoretical noise‐free example to separate the magnetic anomaly of a prism from a polynomial background illustrates well the difference between sparse and FFT spectra. An example with real Bouguer anomalies in the Interserrana basin, Argentina, shows that gridding results, in this case reduced to sea level, compare well with those obtained by other gridding methods, and that the separation procedure is able to outline well defined areas of positive and negative residual anomalies.
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