Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.gao.spb.ru/english/as/j2014/presentations/brzezinski.pdf Äàòà èçìåíåíèÿ: Thu Oct 2 15:41:41 2014 Äàòà èíäåêñèðîâàíèÿ: Sun Apr 10 05:55:58 2016 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: arp 220

On application of the complex demo dulation pro cedure for monitoring Earth rotation: comparison with the standard approach using the long perio dic EOP components estimated from VLBI data analysis by the VieVS CD software
Aleksander Brzezinski1,2, Agata Wielgosz2, and Sigrid B¨hm3 ´ o
1)

Institute of Geodesy and Geodetic Astronomy, Warsaw University of Technology 2) Space Research Centre, Polish Academy of Sciences, Warsaw, Poland 3) Institute of Geodesy and Geophysics, Vienna University of Technology alek@cbk.waw.pl

Presented at

Journ´es 2014 "Syst`mes de R´f´rence Spatio-Temporels" e e ee
"Recent developments and prospects in ground-based and space astrometry"
22­24 September 2014, Pulkovo Observatory, St. Petersburg, Russia

The first author expresses his thanks for the free accommodation offered by the Local Organizing Committee of the Journ´es 2014. e This work was supported by the Polish national science foundation NCN under grant No. DEC-2012/05/B/ST10/02132.


Intro duction In the recent works (B¨hm et al., J. Geodynamics, 62 (2012) 56­68; Brzezinski and B¨hm, o ´ o Proc. Journees 2011, 132­135) we demonstrated the application of the complex demodulation (CD) technique for VLBI estimation of the Earth orientation parameters (EOP). This technique enables simultaneous determination of the long period components of polar motion (x,y), universal time dUT1 (=UT1-UTC) and nutation (celestial pole offsets dX,dY) as well as the high frequency (diurnal, semidiurnal, ...) components of polar motion and dUT1. In this work we discuss advantages of this approach over the conventional procedures applied for the EOP estimation. We also show results of an analysis of the long periodic time series dX, dY and dUT1 derived by the complex demodulation algorithm implemented in the Vienna VLBI Software (VieVS CD). Results are compared to those based on the EOP series based on the combined EOP solutions provided by the IVS and the IERS. Paper contents · Brief description of the CD algorithm · Data analysis ­ VLBI parameter estimation using the VieVS CD algorithm ­ analysis of the nutation and dUT1 series · Conclusions
Brzezi´ski et al. n Journ´es 2014, St. Petersburg, 22­24 September 2014 e


Complex demo dulation metho d Complex demodulation (CD), general description · a method of extracting the high frequency signals from time series (Bingham et al., 1967); · the output `image' of the high frequency signal is a low frequency, complex valued time series which is easy to handle in analysis; · the procedure preserves power spectrum of the original series while moving it only along the frequency axis in such a way that the demodulation frequency becomes zero. Detailed description of the CD method and its application for modeling Earth rotation can be found in (Brzezinski, J. Geodynamics, 62(2012) pp. 74-82). A successful application of the CD ´ technique for VLBI estimation of the EOPs was demonstrated by B¨hm et al. (2012). o Parametrization of polar motion (PM) and universal time (UT) for complex demodulation
x(t ) = y (t )
N

=-N

x (t ) y (t) cos() + sin() , UT1(t) = y(t) - x (t )

N

[uc(t) cos() + us(t) sin()] , (1)
=0

where =GMST+ , GMST stands for Greenwich Mean Sidereal Time and x(t), y(t), us(t), c u(t) are assumed to not vary significantly in time. When estimated from the VLBI data these time dependent amplitudes are treated as constant during one 24-hr session.
Brzezi´ski et al. n Journ´es 2014, St. Petersburg, 22­24 September 2014 e


Complex demo dulation metho d Remarks · the terms = 0 of the expansion (1) are the long periodic components of PM and UT1 which are estimated in the standard adjustment; · the term = -1 of polar motion is an equivalent representation of the celestial pole offsets, i.e. [x-1, -y-1] = [ X, Y ] in the first order approximation; · the terms = ±1, ±2, . . . express quasi diurnal, semidiurnal, ...., variations in PM (retrograde/prograde for -/+) and in UT1. Data analysis · apply expansion (1) with N = 4 in VLBI data analysis by the modified VieVS software (B¨hm o et al., 2014); · perform analysis of the nutation (PM with = -1) and low frequency dUT1 ( = 0) series ­ the analysis has been done over the full period of data 1984.0­2010.5 as well as over the reduced period 1990.0­2010.5. · perform similar analysis of the dX, dY and dUT1 series from the combined solutions IVS 13q2X, IERS C04, and compare results to those derived from the VieVS CD series.
Brzezi´ski et al. n Journ´es 2014, St. Petersburg, 22­24 September 2014 e


Results: nutation
PM from VLBI data demodulated at -1 5 4 3
1 2

Nutation: smoothed, removed corrections to IAU2006/2000

1.5

2 PM x and -y (mas)
Nutation dX, dY [mas]

1 0 -1 -2

0.5

0

-0.5

-1

-3 -4 -5
-1.5 IERS IVS CD 1985 1990 1995 year 2000 2005 2010

1985

1990

1995 Time (years)

2000

2005

2010

-2

Nutation: smoothed, removed corrections to IAU2006/2000
1 0.8 0.6 0.4 Nutation dX, dY [mas] 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 2000 IERS IVS CD 2000.5 2001 2001.5 2002 2002.5 year 2003 2003.5 2004 2004.5 2005

Figure 1: Nutation component (PM with = -1) estimated by VieVS CD, original series with error bars (top left). After applying empirical corrections to the conventional p-n model and the weak smoothing, the VieVS CD series is compared to the IVS and IERS celestial pole offsets (top right - overall view, and bottom - zoom).
Brzezi´ski et al. n Journ´es 2014, St. Petersburg, 22­24 September 2014 e


Results: nutation
Nutation retrograde 18.6 years
90 120 60 150 40 20 180 0 180 30 150 10 80 60 120 20 30 150

Nutation retrograde 9.3 years
90 30 60

Nutation retrograde 1/2 year
90 120 15 10 5 0 180 0 180 30 150 20 60

Nutation retrograde 13.7 days
90 120 20 30 10 30 60

0

210

330

210

330

210

330

210

330

240 270

300

240 270

300

240 270

300

240 270

300

Nutation prograde 18.6 years
90 120 60 150 40 20 180 0 180 30 150 80 60

Nutation prograde 9.3 years
90 120 20 30 10 150 30 60

Nutation prograde 1/2 year
90 120 15 10 5 0 180 0 180 30 150 20 60

Nutation prograde 13.7 days
90 120 20 30 10 30 60

0

210

330

210

330

210

330

210

330

240 270

300

240 270

300

240 270

300

240 270

300

Figure 2: Estimated corrections to the selected nutation terms with standard deviations of the amplitudes shown as circles. Reference precession/nutation model: IAU 2000/2006, units: microarcseconds, input time series: CD VieVS (red), IVS 13q2X (green) and IERS C04 (blue), period of analysis: 1984.0­2010.5.
Brzezi´ski et al. n Journ´es 2014, St. Petersburg, 22­24 September 2014 e


Results: low frequency dUT1
dUT1 - oryginal series
-20 CD IVS IERS

-22

-24

-26 dUT1 [s]

-28

-30

-32

-34

-36

1985

1990

1995 year

2000

2005

2010

Figure 3: Low frequency component of dUT1 estimated by VieVS CD (dUT1 with = 0), compared to the IVS and IERS series. Shown are the original series with error bars.
Brzezi´ski et al. n Journ´es 2014, St. Petersburg, 22­24 September 2014 e


Results: low frequency dUT1
dUT1: removed 4th degree polynomial
400 300 200 100 dUT1 [ms] 0 -100 -200 -300 -400 1985 1990 1995 year 2000 2005 IERS IVS CD 2010 dUT1 [ms] 400 300 200 100 0 -100 -200 -300 -400 1985 1990 1995 year 2000 2005 IERS IVS CD 2010

dUT1: removed 4th degree polynomial and 11.2a oscillation

dUT1: removed 4th degree polynomial and 11.2a oscillation
80 60 40 20 0 -20 -40 -60 -80 1995 IERS IVS CD 1995.5 1996 1996.5 1997 1997.5 year 1998 1998.5 1999 1999.5 2000

Figure 4: Low frequency component of dUT1 after removal of the 4th order polynomial (top left), 4th order polynomial and the 11yr sinusoid (top right) and its zoom (bottom).
Brzezi´ski et al. n Journ´es 2014, St. Petersburg, 22­24 September 2014 e

dUT1 [ms]


Results: low frequency dUT1

Figure 5: Error correlation matrix of the estimated parameters of the polynomial-sinusoidal model.
Brzezi´ski et al. n Journ´es 2014, St. Petersburg, 22­24 September 2014 e


Results: low frequency dUT1
dUT1 11.2 yr
90 120 200 150 150 100 50 180 0 180 30 150 10 5 0 30 250 60 120 15

dUT1 biennial
90 20 60

210

330

210

330

240 270

300

240 270

300

dUT1 annual
90 120 20 15 150 10 5 180 0 180 30 150 25 60 120

dUT1 semiannual
90 15 60 10 30 5 150 120

dUT1 terannual
90 8 60 6 4 2 0 180 0 30

210

330

210

330

210

330

240 270

300

240 270

300

240 270

300

Figure 6: Estimated parameters of the periodical components of dUT1 with standard deviations of the amplitudes shown as circles. Units: milliseconds, input time series: CD VieVS (red), IVS 13q2X (green) and IERS C04 (blue), period of analysis: 1984.0­2010.5.
Brzezi´ski et al. n Journ´es 2014, St. Petersburg, 22­24 September 2014 e


Conclusions General: · The complex demodulation algorithm is an efficient tool for extracting the high frequency signals in Earth rotation from the VLBI observations. Its application to the EOP determination by other space geodetic techniques is also possible. Nutation component: · The = -1 term of polar motion in the CD scheme is an equivalent representation of the celestial pole offsets. · The early nutation data is very noisy and contains variability which is not consistent with the rest of the series. When analysis of data does not include weighting it is recommended to remove data prior to 1990. · The VieVS CD series yields the results which are consistent with those following from the IVS and IERS combination series. · More detailed analysis shows closer agreement of the results based on the VieVS CD and IVS series, as expected. Exceptions are only the retrograde semiannual and fortnightly nutations where the VieVS CD estimates agree better with those of the IERS.
Brzezi´ski et al. n Journ´es 2014, St. Petersburg, 22­24 September 2014 e


Conclusions Low frequency dUT1: · Analysis of the VieVS CD dUT1 series shows good overall agreement with the two combination series, but also high correlation at seasonal frequencies. · The polynomial-sinusoidal model is not appropriate for separating the long periodic trend and the decadal variability. · There is also quite good agreement of te parameters of the periodical terms. The largest difference is found for the biennial and terannual terms for which the IERS results are not consistent with those based on the VieVS CD and IVS.

Brzezi´ski et al. n

Journ´es 2014, St. Petersburg, 22­24 September 2014 e