On the inversion of geodetic integrals defined over the sphere using 1-D FFT

• Published in: Journal of geodesy Vol. 79; no. 6-7; pp. 331 - 340
• Main Authors: GARCIA, R. V, ALEJO, C. A
• Format: Journal Article
• Language: English
• Published: Berlin Springer 01-08-2005; Springer Nature B.V
• Subjects: Algorithms; Convolution; Earth sciences; Earth, ocean, space; Exact sciences and technology; Fourier transforms; Geodetics; Internal geophysics; Solid-earth geophysics, tectonophysics, gravimetry; iterative methods; inverse problem; Deconvolution,Cyclic-convolution error; gravity field; efficiency; Fourier transformation; Spherical integral inversion 1D-FFT; geoid undulation; least-squares; global; case studies; Earth; deconvolution; noise; errors; geodesy
• ISSN: 0949-7714; 1432-1394
• DOI: 10.1007/s00190-005-0468-8

An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine's integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.[PUBLICATION ABSTRACT]