Generalizing the Harmonic Reduction Procedure in Residual Topographic Modeling

Abstract

In gravity field modeling measurements are usually located on or above the terrain. However, when using the residual topographic modeling (RTM) method, measurements may end up inside the masses after adding the mean topography. These values do not correspond to values evaluated using a harmonic function. A so-called harmonic correction has been applied to gravity anomalies to solve this problem. However, for height anomalies no correction has been applied. To generalize the correction to e.g. height anomalies we interprete that the vertical gravity gradient inside the masses multiplied by height equals the correction. In principle the procedure is applicable to all gravity field functionals. We have tested this generalization of the procedure which consist in determining equivalent quantities in points Q on the mean surface if this surface is in free air. The procedure has as data the reduced values in P inside the masses but considered as being located at the mean surface. Numerical tests with height anomaly data from New Mexico and Norway as control data show that for gravity anomalies the general procedure is better than using the original harmonic correction procedure.