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 Analysis of Earth Orientation Parameter  time series updated: February 2021 Select a time series and pertaining EOP in the following table, then below the table select one the following options: ASCII file / plot / spectrum / least square fit / Vondrak filter / singular spectral analysis comparison of EOP series Time scale : Modified Julian Date Besselian Year    arcsecond/second for EOP (by default mas/ms) Begin     End   Remove tidal variations from UT1/LOD1  label in French   TT - UT12

 series IAU 19803 series IAU 20003 read starting date x y x-iy UT1-UTC UT1-TAI dψ sinε0UAI 1980 dε UAI 1980 dψ sinε0 +i dε dX UAI 2000 dY UAI 2000 dX +i dYUAI 2000 dx/dt dy/dt LOD mas mas mas ms ms mas mas mas mas mas mas mas/day mas/day ms Select EOP COMBINED EOP series of our service C04 C04 read 1962- 1 1 1 1 1 1 1 1 1 1 1 1 C0412h C0412h read 1984- 1 1 1 1 1 1 1 1 1 C01 C01 read 1846- 1 1 1 1956- 1900- 1900- 1900- 1984- 1984- 1984- C02 read 1830- 1 1 OPAC read 2000- 1 1 1 1 1 1 OPAC2 OPAC2 read 2000- 1 1 1 1 1 1 1 1 OTHER COMBINED EOP series SPACE read 1993- 1 1 1 1 1 1 1 1 BUL A BUL A read 1846- 1 1 1 1996- 1996- GNSS EOP series CODE 1993- 1 1 1 1 1 1 1 1 EMR 1996- 1 1 1 1 1 1 1 1 ESOC 1996- 1 1 1 1 1 1 1 1 GFZ 1996- 1 1 1 1 1 1 1 1 GRGS 2014- 1 1 1 1 1 1 1 1 IAA read 2000- 1 1 1 1 1 1 IGS Final 1996- 1 1 1 1 1 1 1 1 IGS Rapid 1996- 1 1 1 1 1 1 1 1 JPL 1996- 1 1 1 1 1 1 1 1 NOAA 1996- 1 1 1 1 1 1 1 1 SIO 1996- 1 1 1 1 1 1 1 1 VLBI EOP series AUS AUS read 1983- 1 1 1 1 1 1 1 1 1 1 1 BKG BKG read 1984- 1 1 1 1 1 1 1 1 1 1 1 1 CGS CGS read 1984- 1 1 1 1 1 1 1 1 1 1 1 1 GSFC GSFC read 1979- 1 1 1 1 1 1 1 1 1 1 1 1 IAA IAA read 1979- 1 1 1 1 1 1 1 1 1 1 1 IVS quaterly IVS read 1984- 1 1 1 1 1 1 1 1 1 1 1 1 IVS rapid IVS read 2005- 1 1 1 1 1 1 1 1 1 1 1 1 MAO MAO read 2000- 1 1 1 1 1 1 1 1 1 1 1 OPA OPA read 1984- 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SPBU SPBU read 1989- 1 1 1 1 1 1 1 1 1 1 1 USNO USNO read 1979- 1 1 1 1 1 1 1 1 1 1 1 1 BKG int. read 2000- 1 1 1 1 GSFC int. read 2000- 1 GSI int. read 2003- 1 IAA int. read 2006- 1 IAA rapid int. read 2006- 1 OPA int. read 2006- 1 PUL int. read 2000- 1 SPBU int. read 1997- 1 USNO int. read 2000- 1 SLR EOP series ASI read 2003- 1 1 1 1 CSR 1983- 1 1 1 1 1 DUT 1993- 1 1 1 1 1 IAA 1992- 1 1 1 1 1 1 ILRS (comb.) 2002- 1 1 1 1 MCC 1996- 1 1 1 1 OCA 1993-2007 1 1 1 1 1 DORIS EOP series IDS(comb) read 1993- 1 1 1 IGN 1993-2013 1 1 1 1 1 INASAN read 1993- 1 1 1 1 1 EOP series from optical observation AICAS read 1900-1992 1 1 1 1 1 1 1 1 AICAS read 1900-1992 1 1 1 1 1 JPL(LOD)* read 1832-1997 1 HMNAO* read 2000BC-2016 1 1 HMNAO 2021* read 2000BC-2019 1 1 series IAU 19803 series IAU 20003 read starting date x y x-iy UT1-UTC UT1-TAI dψ sinε0UAI 1980 dε UAI 1980 dψ sinε0 +i dε dX UAI 2000 dY UAI 2000 dX +i dYUAI 2000 dx/dt dy/dt LOD
 Lagrange Interpolation with time interval of day(s)       First date (optional) Produce file of the selected parameters       Draw data   Dynamic graph   Show errors Spectral analysis (FFT, complex for 2D signal) Amplitude PSD min. frequency or period       max. frequency or period x linear scale x log scale y linear scale y log scale frequency spectrum (in cycle / unit of time) period spectrum (in unit of time) First derivative Produce data Plot Weighted least square fit of periodic components (periods in unit of time) Positive periods         Polynomial of degree Negative periods       Weighted least square (take negative periods only for 2 dimensional signal)         Draw residuals     Draw fit and input data     Print residuals In-phase and out-of-phase terms (a, b) are estimated, as well as amplitude A and phase φ : 1-D :$$\small X = A \cos[2\pi/T (t-t_0) + \phi] = a \cos[2\pi/T (t-t_0)] + b \cos[2\pi/T (t-t_0)]$$ 2-D : $$\small X +i Y = A e^{i [2\pi/T (t-t_0) + \phi]$$ with the reference epoch $$\small t_0$$ = 1/1/2000 0hUT that is : $$\small X = a \cos[2\pi/T (t-t_0)] - b \sin[2\pi /T (t-t_0)$$    $$\small Y = b cos[2\pi/T (t-t_0)] + a sin[2\pi/T (t-t_0) ]$$ with $$\small a = A \cos\phi$$      $$\small b = A\sin\phi$$ Vondrak low/high pass filter Remove parabolic trend Produce data file Draw   with input data Select band above Select band below (P0) time unit     Transfer coefficient for P0:T0= % The Vondrak filter transfer function at another period P is given by T=1/(1+(P0/P)6 (1-T0)/T0) For the case "Select band around" the periods in [P0-0.1*P0, P0+0.1*P0] are transmitted with the rate > T0%. For the case "Remove band around" the periods outside [P0-0.1*P0, P0+0.1*P0] are transmitted with the rate > T0 %. Panteleev band pass filter (for 2D signal) Produce data file Draw filtered data and envelope / phase referred to 2πfct   Select band around fc= cycle/time unit     Band width f0= cycle/time unit This band pass filter was designed by Russian astronomer and gravimetrist V. L. Panteleev. Its frequency transfer function is given by $$\small T(f) = \frac{f_0^4}{ ( f - f_c)^4 + f_0^4 }$$. At the edges of the window $$\small |f - f_c| = f_0$$ and $$\small T = 0.5$$. Singular Spectral Analysis (SSA) -  Zoom between and    The extracted components are decorellated over time windows of (in the time unit) with the interpolation lag (in the time unit). Firt step consists in the determination of the eigenvalues and eigenvectors printed by decreasing weight. Then 5 singular components are reconstructed according to the following combinations of eigenvectors, to be stated from the analysis of the eigenvalues . RC1 Reconstructed Component (RC) based upon eigenvectors N1 and N2 RC2 RC3 RC4 RC5    produce time series (date, signal, RC1,RC2,RC3,RC4,RC5,residuals) draw Graphic dimension x   output graphics png   pdf   ps       Partial Interface with the C-Fortran Libraries SLAVA (C. Bizouard) & MIMOSA (S. Lambert). Thank you for bringing to our knowledge any possible mistake, mail to : christian.bizouard at obspm.fr 1 Variations produced by the solid Earth zonal tides (IERS 2000 model) 2 TT=TAI+32.184 s (for parameter UT1-TAI) 3 Reference precession-nutation model for celestial pole offsets: either IAU 2000 or IAU 1980