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

Abstract

S U M M A R YA 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.

FIR, IIR and Wavelet Algorithms for the Rigorous Filtering of GOCE SGG Data to the GOCE MBW

“…Wavelet MRA, both one dimensional (1-D) and two dimensional (2-D), has been extensively used since its introduction in applications of geodesy and gravimetry as a significant analysis tool [30]. WL-MRA has been used in local geoid determination employing gravity anomalies and deflections of the vertical [31] for the evaluation of the Stokes and Vening Meinesz integrals [32], for terrain correction [33], in analysis of GOCE and GRACE based global geopotential models [34], and in GOCE SGG data processing [35]. The localization parameters of the method are its distinctive characteristic, compared to the Fourier transforms which is the standard tool used in signal processing, given the fact that they analyze the signal in both the space and time domains.…”