A wavelet thresholding technique for local geoid and deflection of the vertical determination using a planar approximation

A computational scheme using the wavelet transform is employed for local geoid determination, where wavelet multiresolution analysis (MRA) is introduced as an alternative approach to the well-established fast Fourier transform (FFT). The Stokes and Vening Meinesz integrals are approximated in finite MRA subspaces. The algorithm is built using an orthogonal wavelet base function. The characteristics of the base function and its effect on the final result are investigated. Hard and soft thresholding are tested in the compression of the kernel as well as global thresholding is compared to level-wise thresholding to optimize the compression level with an acceptable accuracy. Both global and level-wise thresholding are combined in order to achieve the maximum compression level, with acceptable geoid accuracy. The compression rate depends on the degree of singularity of the kernel. In the case of Stokes, a 94 per cent compression level is achieved with 1 cm (rms) accuracy in comparison to FFT and numerical integration approaches. Due to its stronger singularity, in the case of the Vening Meinesz kernel, 97 per cent compression rate is achieved with a 0.07 arc-second (rms) accuracy. The compression percentages achieved in this study are higher than those reported in pervious studies, which shows that this algorithm is very suitable for use in local geoid determination.