The Effect of Noise on Geoid Height in Stokes-Helmert Method

摘要

Noises are an inevitable part of gravity observations and they can affect the accuracy of the height datum if they are not treated properly in geoid determination. To provide data for geodetic boundary value problems, surface gravity observations must be transferred harmonically down to the geoid, which is called Downward Continuation (DC). Fredholm integral of the first kind is one of the physically meaningful ways of DC, where the Poisson kernel is used to evaluate the data on the geoid. DC behaves inherently as a high pass filter so it magnifies existing noise in Helmert gravity anomalies on geoid (free air anomalies after applying the Helmert's second condensation method); although the results on the geoid will be later smoothed by evaluating the Stokes's integral so the noise is less pronounced in the final geoid heights. The effect of noise in Stokes-Helmert geoid determination approach is numerically investigated in this study. The territory of Iran, limited to 44-62° longitude and 24-40° latitude, is considered as the area of interest in this study. The global gravity model EGM2008, up to degree/order 2160, is used to synthesize the free air gravity anomalies on a regular grid on topography and are then transferred to Helmert space using available Digital Elevation Models (DEMs). Different levels of noise are added to the data and the effects of noise are investigated using the SHGeo software package, developed at the University of New Brunswick (UNB). Results show that if the downward continuation of 5*5 arcmin surface points is required, the standard deviation of differences between "noisy" and "clean " data on the geoid will increase by 15% with respect to the corresponding standard deviation on topography. These differences will increase for denser grid resolutions. For example, the noise of Ag on geoid will increase up to 100% if 1*1 arc-min points are used. The results of evaluating the Stokes integral show smoother results in terms of noise in the d