On the interpolation of high-frequency gravity field signals in mountainous areas

Abstract

The paper presents a comparison among different techniques in interpolating
high-frequency gravity field signals in mountainous areas. A gap of 1◦ ×1◦ has been artificially
created within the free-air gravity anomalies data set for Austria. The remaining
data set has been used to interpolate the free-air gravity anomalies at the gap points;
then a comparison between the interpolated and the data values has been carried out
to determine the accuracy of the used interpolation technique. The following interpolation
techniques have been used: Kriging interpolation technique from free-air gravity
anomalies, traditional remove-restore technique and window technique (Abd-Elmotaal and
K¨uhtreiber, 2003). For the latter two techniques, the reduced anomalies have been used to
interpolate gravity anomalies at the data points of the gap using a least squares collocation
technique. The effect of the topographic-isostatic masses has been restored using both
techniques. A comparison between the data and interpolated values of free-air anomalies
at the gap points has been carried out. The results show that the Kriging technique
cannot be used for interpolating high-frequency gravity field signals in mountainous areas
and the window technique gives the best results with an interpolation standard deviation
of about 11 mgal. The range difference and the standard deviation of the residuals in
case of the window technique are smaller than those of the traditional remove-restore
technique by about 25%.