Analysis of Earth Orientation Parameter  time series

updated: December 2015

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

Begin     End   Remove tidal variations from UT1/LOD1  label in French


series
IAU 1980
2
series
IAU 2000
2
read starting
date
x y x-iy UT1-
UTC
UT1-
TAI

sinε0
UAI 1980

UAI 1980

sinε0 +i dε
dX
UAI 2000
dY
UAI 2000
dX
+i dY
UAI 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
C01 C01 read 1846- 1 1 1 1962- 1962- 1900- 1900- 1900- 1984- 1984- 1984-
C02 read 1830- 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-
  GPS 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
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
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
CNES 1999- 1 1 1
IGN 1993- 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
series
IAU 1980
2
series
IAU 2000
2
read starting
date
x y x-iy UT1-
UTC
UT1-
TAI

sinε0
UAI 1980

UAI 1980

sinε0 +i dε
dX
UAI 2000
dY
UAI 2000
dX
+i dY
UAI 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    

Spectral analysis (FFT, complex for 2D signal)
Amplitude (Ampl.)2

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)

Weighted least square fit of periodic components (periods in unit of time)
Positive periods         Polynomial of degree
Negative periods  
(take negative periods only for 2 dimensional signal)
        Draw residuals and input data     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
(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 enveloppe / phase referred to 2πfct  
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- Reference precession-nutation model for celestial pole offsets: either IAU 2000 or IAU 1980


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