Terrain correction computations by spherical harmonics and integral formulas

This contribution investigates three methods for terrain correction computations. Two integral formulas proposed by Moritz and by Vanicek and Kleusberg and a spherical harmonics presentation developed to the third power of terrain elevation by Nahavandchi and Sjoberg have been used in this study. The comparison of these approaches shows large differences in a test area in Sweden. The range of the Vanicek and Kleusberg's direct terrain correction (-36 to 21 mGal) is substantially larger than Moritz (0 to 17 mGal) and spherical harmonics (-550 to 259 microGal) approaches. The indirect effect ranges from -4.8 cm to 0.7 cm in integral formula while it is found to be 4.2-6.9 cm by spherical harmonics presentation. Numerical results also show that some long- wavelength contributions might be missing in integral formulas while they are present in spherical harmonics method. However, some short wavelength features are obviously missing in spherical harmonics method. We conclude that a compromise between these two methods has to be in order. The new formula has to represent both local information and long-wavelength contributions.