Refined least squares modification of Stokes' formula
LE Sjöberg - Manuscripta geodaetica, 1991 - Springer
Manuscripta geodaetica, 1991•Springer
The least squares modification of Stokes' formula reduces the impact of the errors stemming
from truncation, erroneous terrestrial gravity data and potential harmonics in a least squares
sense. A disadvantage of the method is that the modification requires a priori estimates of
gravity anomaly degree variances beyond the maximum degree and order (M) of available
potential coefficients (theoretically to infinity). In addition the solution is biased for each
degree. In contrast to the least squares method Molodensky's modification method accounts …
from truncation, erroneous terrestrial gravity data and potential harmonics in a least squares
sense. A disadvantage of the method is that the modification requires a priori estimates of
gravity anomaly degree variances beyond the maximum degree and order (M) of available
potential coefficients (theoretically to infinity). In addition the solution is biased for each
degree. In contrast to the least squares method Molodensky's modification method accounts …
Abstract
The least squares modification of Stokes’ formula reduces the impact of the errors stemming from truncation, erroneous terrestrial gravity data and potential harmonics in a least squares sense. A disadvantage of the method is that the modification requires a priori estimates of gravity anomaly degree variances beyond the maximum degree and order (M) of available potential coefficients (theoretically to infinity). In addition the solution is biased for each degree.
In contrast to the least squares method Molodensky’s modification method accounts only for the truncation error and requires no information on anomaly degree variances. This solution is unbiased to degree M.
The refined, “unbiased” least squares modification of Stokes’ formula combines some advantages of the methods above:
- The solution is unbiased through degree M, and
- the errors due to erroneous gravity anomalies and coefficients and truncation are reduced in a least squares sense. In fact the solution contains no truncation error to degree and order M.
Also, the least squares modification methods are considered for correlated data, and the solutions are extended to allow for more parameters sr than there are degrees M of potential coefficients available.
Springer
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