Improved harmonic development of the Earth tide-generating potential

Kudryavtsev, S. M.

doi:10.1007/s00190-003-0361-2

Cited by 46 publications

(34 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We made harmonic development of the TGP for the three terrestrial planets with help of a new modification of the spectral analysis method (Kudryavtsev 2004(Kudryavtsev , 2007. According to this method, the development is directly made to Poisson series where both amplitudes and frequencies of the series' terms are high-degree polynomials of time (as opposite to the classical Fourier analysis where both amplitudes and frequencies of the resulting series' terms are constants).…”

Section: Development Of Tgp For the Terrestrial Planetsmentioning

confidence: 99%

“…The latest long-term numerical planetary/lunar ephemerides DE/LE-406 (which are the extension of DE/LE-405 over 6,000 years) are used as the source of the Sun, Moon and major planets' coordinates. The expansion of the planetary TGP is made with use of a new modification of the spectral analysis method (Kudryavtsev 2004(Kudryavtsev , 2007.…”

mentioning

confidence: 99%

“…[A development of the Earth TGP is done in Kudryavtsev (2004).] The latest long-term numerical planetary/lunar ephemerides DE/LE-406 (which are the extension of DE/LE-405 over 6,000 years) are used as the source of the Sun, Moon and major planets' coordinates.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Harmonic development of tide-generating potential of terrestrial planets

Kudryavtsev

2008

Celest Mech Dyn Astr

View full text Add to dashboard Cite

The aim of this study is to obtain high-accurate harmonic developments of the tide-generating potential (TGP) of Mercury, Venus and Mars. The planets' TGP values have been first calculated on the base of DE/LE-406 numerical planetary/lunar ephemerides over a long period of time and then processed by a new spectral analysis method. According to this method the development is directly made to Poisson series where both amplitudes and arguments of the series' terms are high-degree polynomials of time. A new harmonic development of Mars TGP is made over the time period 1900 AD-2100 AD and includes 767 second-order Poisson series' terms of minimum amplitude equal to 10 −7 m 2 s −2 . Analogous series composing both Mercury and Venus TGP harmonic models are built over the time period 1000 AD-3000 AD and include 1,061 and 693 terms, respectively. A modification of the standard HW95 format for representation of the terrestrial planets' TGP is proposed. The number of terms in the planets' TGP models transformed to the modified HW95 format is 650 for Mercury, 422 for Venus, and 480 for Mars. The quality of the new developments of the terrestrial planets' TGP is better than that of the similar developments obtained earlier.

show abstract

Section: Development Of Tgp For the Terrestrial Planetsmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Harmonic development of tide-generating potential of terrestrial planets

Kudryavtsev

2008

Celest Mech Dyn Astr

View full text Add to dashboard Cite

show abstract

“…The Non-Harmonic method was initiated by Sir John Lubbock (1831). This method is based on the direct computation of the tidal potential using as-Tide, with the total number of 26753 known frequencies (Kudryavtsev 2004) is a dynamic system with well established frequency content. Some of the known constituents in this phenomenon are given in Table 1.…”

Section: Introductionmentioning

confidence: 99%

Analyzing the tidal frequency content using Karhunen-Loeve Expansion technique

Yousefi¹,

Hossainali²

2013

Journal of Geodetic Science

View full text Add to dashboard Cite

Abstract:The Karhunen-Loeve Expansion (KLE) technique has been recently applied by geophysicists for analyzing the temporal variations of dynamic systems such as the ocean-atmosphere interface, crustal deformation and fault systems. The application of this method to tidal data can provide a direct insight into the efficiency and reliability of this method in reconstructing a periodic signal. The comparison of the obtained results to those proposed by the least squares harmonic estimation (LSHE) as a newly developed method which is widely used in geodetic community for analyzing the GPS time series can be of signi cant interest for both geodesists and geophysicists. This paper applies the KLE method to the tidal time series of the Workington station in United Kingdom and compares the given results to those suggested by the LSHE method. The detection of the majority of the expected long period constituents and the larger number of the detected low frequency components by KLE as compared to the least squares harmonic estimation emphasizes on the efficiency and the predominance of this method to the LSHE technique.

show abstract

“…This approach leads to an essential improvement in accuracy of harmonic development of a function tabulated over a long-term interval and to reduction of the series' length. The details of the method are given in the next section (see also Kudryavtsev 2004).…”

Section: Introductionmentioning

confidence: 99%

Long-term harmonic development of lunar ephemeris

Kudryavtsev¹

2007

A&A

Self Cite

View full text Add to dashboard Cite

Aims. The aim of this study is to develop new analytical series representing lunar coordinates to accuracy compatible with the accuracy of the modern numerical ephemeris of the Moon.Methods. An improved method of spectral analysis of tabulated function is used to make harmonic development of the latest long-term numerical ephemeris of the Moon LE-406 which covers a six thousand-year interval. A feature of the method is that the development is made directly to Poisson series where both amplitudes and arguments of the series' terms are high-degree polynomials of time.Results. The new analytical development includes 42 270 Poisson series' terms of minimal amplitude equivalent to 1 cm and is valid over 1500-2500. A simplified version of the development includes 7952 series' terms of minimal amplitude equivalent to 1 m and is valid over 3000BC-3000AD. Over 1500-2500 the maximum difference between lunar coordinates calculated by means of the new analytical series and numerical ephemeris LE-406 is 3.2 m in geocentric distance, 0. 0056 in ecliptic longitude, and 0. 0018 in ecliptic latitude. This is 9-70 times better than the accuracy of the latest analytical theory of lunar motion ELP/MPP02, and the number of terms in the new development is less than that in ELP/MPP02.

show abstract

Improved harmonic development of the Earth tide-generating potential

Cited by 46 publications

References 0 publications

Harmonic development of tide-generating potential of terrestrial planets

Harmonic development of tide-generating potential of terrestrial planets

Analyzing the tidal frequency content using Karhunen-Loeve Expansion technique

Long-term harmonic development of lunar ephemeris

Contact Info

Product

Resources

About