Abstract
We derive a number of rough theoretical estimates for the precision of a geoid model computed from a local gravimetric survey combined with global reference model information. Example calculations for Finland and Estonia are presented.
Highlights
It is possible to give a number of theoretical estimates for the precision of a gravimetric geoid computed using gravimetric survey data obtained from a bounded area and having a finite density of measurement points
The aliasing error, due to the finite spatial density of the survey, where error patterns with halfwavelengths shorter than this spacing are misrepresented as geoid error patterns with longer wavelengths
Estimating the out-of-area error requires knowledge of the signal covariance function, either of the full gravity field, or of the part of gravity not described by the reference model
Summary
It is possible to give a number of theoretical estimates for the precision of a gravimetric geoid computed using gravimetric survey data obtained from a bounded area and having a finite density of measurement points. The derivations presented below have in the past appeared in different form and in small pieces in the nonreviewed literature, often in connection with practical geoid determination projects [1,2,3]. The average „error of prediction“ in the form of a mean error for an arbitrary point somewhere in the terrain, when predicting its gravity anomaly from those of nearby points This error is in principle computable if we know two quantities defining the gravity anomaly field’s signal covariance function: its signal covariance C0 and its correlation length l. One of us (KK) after discussing with Tõnis Oja, concluded that the value 3 mGal is probably more realistic
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