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Wavelet evaluation of the Stokes and Vening Meinesz integrals
Abstract. The wavelet transform is a powerful tool in evaluating some singular geodetic integrals. Due to its localization properties in both the time (space) and frequency (scale) domains, and because the kernels of some geodetic integrals have singular points and decay smoothly and quickly away from the singularities, many wavelet transform coefficients of the kernels become zeros or negligible, and only a small number of wavelet transform coefficients are significant. It is thus possible to significantly compress the kernels of these integrals on a wavelet basis by neglecting the zero coefficients and the small coefficients below a certain threshold. Therefore, wavelets provide a convenient way of efficiently evaluating these integrals in terms of fast computation and savings of computer memory. A modified algorithm for the wavelet evaluation of Stokes' integral is presented. The same modified algorithm is applied to the evaluation of the Vening Meinesz integral, whose kernel has a stronger singularity than does Stokes' kernel. Numerical examples illustrate the efficiency and accuracy of the wavelet methods.
Wavelet evaluation of the Stokes and Vening Meinesz integrals
Abstract. The wavelet transform is a powerful tool in evaluating some singular geodetic integrals. Due to its localization properties in both the time (space) and frequency (scale) domains, and because the kernels of some geodetic integrals have singular points and decay smoothly and quickly away from the singularities, many wavelet transform coefficients of the kernels become zeros or negligible, and only a small number of wavelet transform coefficients are significant. It is thus possible to significantly compress the kernels of these integrals on a wavelet basis by neglecting the zero coefficients and the small coefficients below a certain threshold. Therefore, wavelets provide a convenient way of efficiently evaluating these integrals in terms of fast computation and savings of computer memory. A modified algorithm for the wavelet evaluation of Stokes' integral is presented. The same modified algorithm is applied to the evaluation of the Vening Meinesz integral, whose kernel has a stronger singularity than does Stokes' kernel. Numerical examples illustrate the efficiency and accuracy of the wavelet methods.
Wavelet evaluation of the Stokes and Vening Meinesz integrals
Liu, Q. (author) / Sideris, M.G. (author)
Journal of Geodesy ; 77
2003
Article (Journal)
English
BKL:
38.73
Geodäsie
On the integral formulas of Stokes and Vening Meinesz
| Online Contents | 1968
F. A. Vening Meinesz (1887–1966)
| Online Contents | 1966
The Stokes and Vening-Meinesz functionals in a moving tangent space
| Online Contents | 1996
Vening Meinesz inverse isostatic problem with local and global Bouguer anomalies
| Online Contents | 2000
Methods for computing deflections of the vertical by modifying Vening-Meinesz' function
| Online Contents | 1982