The inverse problem of constructing a gravimetric geoid

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Abstract
Computation of a single geoidal height from gravity acceleration data formally requires that the latter be known everywhere on the earth. We present a computational procedure based on linear inverse theory for estimating geoidal heights from incomplete sets of data. The same scheme can be used to estimate gravity accelerations from altimetry‐derived geoids. The systematic error owing to lack of data and the choice of a particular inverse operator is described by using resolution functions and their spherical harmonic expansions. An rms value of this error is also estimated by assuming a spectrum for the unknown geoid. The influence of the size of the data region, the spacing between data, the filtering applied to the data, and the model weighting function chosen are all quantified in a spherical geometry. The examples presented show that when low degree spherical harmonic coefficients are available—from satellite orbit analysis—a band‐passed version of the geoid can be constructed from local gravity data, even with a relatively restricted data set.

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