Gravity Field Approximation Using the Predictors of Bjerhammar and Hardy

摘要

Gravity field approximation using the predictors of Bjerhammer and Hardy is investigated. In the Bjerhammar method, a finite number of observations is given and it is required to compute a disturbing potential which is harmonic down to a sphere fully internal to the Earth, regular at infinity and it satisfies all the observations. In the Hardy method, a particular family of density anomaly functions is selected which, together with its normal derivatives, vanishes at the boundary. The resulting disturbing potential is non-singular at points that induce potential. Both methods can use any linear functional of the disturbing potential as observation and/or quantity to be predicted. Both predictors were tested with the White Sands test data. Reference field and residual terrain model effects were removed from the observations and they were restored at the control stations after the predictions were performed. The best gravity anomaly predictions with both methods were performed with only Delta g observations and the downward continuation onto the nadir points of the observations. The most important overall result of this work is that when reference field and residual terrain model effects are taken into account, there are at least five methods that can predict (xi,eta) from Delta g to the sub-second level, even in mountainous areas. Furthermore, the improvement of the predictions should not be anticipated from a theoretical breakthrough but from data type and coverage improvement. (JHD)