Harmonic Analysis as a Tool for Locating Errors in Terrestrial Gravimetry Data.
Abstract:Harmonic analysis of terrestrial gravimetry supports the computation of Earth Gravitational Models [EGMs]. Historically, incorporating terrestrial data into an EGM can be achieved by first gridding the data to form equi-angular gravity anomaly area-means. Each computed mean value typically estimates the average of the anomaly across the surface of an equiangular prism in a Digital Elevation Model [DEM]. Appropriate solid-harmonic analysis can then be applied to the gridded values. This yields a harmonic model which should ‘best’ reproduce these mean values via solid-harmonic synthesis across the surface of each DEM prism. Such nominally ‘terrestrial’ harmonic models can then be combined with satellite gravity information to yield a combination EGM.
Importantly, these terrestrial harmonic models also provide a useful tool for assessing the terrestrial gravimetry which supported them. Low degree (Nmax=200/250) discrepancies between the terrestrial models and their GRACE/GOCE ‘satgrav’ counterparts are already highlighting problem areas in U.S. gravimetry data holdings. However, also interesting are the residuals (mis-closes) between the derived harmonic models and their input anomaly data grids. This is because these equi-angular data grids can be usefully conceived as digital planimetric leveling traverses. They combine mean gravity estimates with mean changes in elevation, thereby necessarily yielding implied estimates for mean changes in geopotential from one DEM prism surface to the next. We consider a hypothetical closed ‘leveling’ loop, in which mean geopotential changes are digitally integrated around a circuit of data prims. If this gridded data correctly represents a conservative field, then the integrated geopotential differences should sum to zero, within the resolution of the data grid. However, for large data errors which deviate significantly from a conservative field, the digitally integrated geopotential will not close to zero. Here the purely harmonic model cannot reproduce the non-conservative data grid, and we will observe a large residual between the two. This provides for the possibility of detecting errors in the data grid, and in the supporting terrestrial gravimetry.
Here we present initial results from this approach, and look to future applications.