Precise computation of the direct and indirect topographic effects of Helmert's 2nd method of condensation using SRTM30 digital elevation model

The direct topographic effect (DTE) and indirect topographic effect (ITE) of Helmert's 2nd method of condensation are computed using the digital elevation model (DEM) SRTM30 in 30 arc-seconds globally. The computations assume a constant density of the topographic masses. Closed formulas are used in the inner zone of half degree, and Nagy's formulas are used in the innermost column to treat the singularity of integrals. To speed up the computations, 1-dimensional fast Fourier transform (1D FFT) is applied in outer zone computations. The computation accuracy is limited to 0.1 mGal and 0.1cm for the direct and indirect effect, respectively. The mean value and standard deviation of the DTE are -0.8 and ±7.6 mGal over land areas. The extreme value -274.3 mGal is located at latitude -13.579◦ and longitude 289.496◦ , at the height of 1426meter in the Andes Mountains. The ITE is negative everywhere and has its minimum of -235.9 cm at the peak of Himalayas (8685 meter). The standard deviation and mean value over land areas are±15.6 cm and -6.4 cm, respectively. Because the Stokes kernel does not contain the zero and first degree spherical harmonics, the mean value of the ITE can't be compensated through the remove-restore procedure under the Stokes-Helmert scheme, and careful treatment of the mean value in the ITE is required.