Abstract
The second-order derivatives of the Earth’s potential in the local north-oriented reference frame are expanded in series of modified spherical harmonics. Linear relations are derived between the spectral coefficients of these series and the spectrum of the geopotential. On the basis of these relations, recurrence procedures are developed for evaluating the geopotential coefficients from the spectrum of each derivative and, inversely, for simulating the latter from a known geopotential model. Very simple structure of the derived expressions for the derivatives is convenient for estimating the geopotential coefficients by the least-squares procedure, at a certain step of processing satellite gradiometry data. Due to the orthogonality of the new series, the quadrature formula approach can be also applied, which allows avoidance of aliasing errors caused by the series truncation. The spectral coefficients of the derivatives are evaluated on the basis of the derived relations from the geopotential models EGM96 and EIGEN-CG01C at a mean orbital sphere of the GOCE satellite. Various characteristics of the spectra are studied corresponding to the EGM96 model.
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Petrovskaya, M.S., Vershkov, A.N. Development of the second-order derivatives of the Earth’s potential in the local north-oriented reference frame in orthogonal series of modified spherical harmonics. J Geod 82, 929–944 (2008). https://doi.org/10.1007/s00190-008-0223-z
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DOI: https://doi.org/10.1007/s00190-008-0223-z