THE SOLUTION OA10 OF EARTH ORIENTATION PARAMETERS BY OPTICAL ASTROMETRY,
1899.7-1992.0

June 2010 

Jan Vondrak and Cyril Ron, Astronomical Institute
Bocni II, 141 31 Praha 4, Czech Republic
e-mail: vondrak@ig.cas.cz, ron@ig.cas.cz

The observations of latitude and universal time variations made at 33
observatories all over the world with 47 instruments of different types
are used to derive Earth Orientation Parameters (EOP) in the interval
1899.7-1992.0.  To this end, all available results (latitude, universal
time, star altitude) based on individual star or star pair observations
(that were originally referred to local star catalogs) are re-reduced to
the Earth Orientation Catalog 4 (EOC-4) and the present IAU standards.
The apparent places of the observed stars are calculated using relevant
parts of the IERS Conventions.  More than four thousand different objects
(stars, photocenters of multiple systems) were observed throughout
the interval in question.  Additional corrections are applied before
the solution is made, such as the secular motions of the instruments
(due to plate tectonics, using the geophysical model NNR NUVEL1), certain
instrumental constants (plate scale, micrometer value), deformations
of the apparent almucantar (due to anomalous refraction), oceanic
tide-loading effects in the direction of the local verticals of the
observatories.  Short-periodic zonal tide variations in the speed of
rotation of the Earth (due to deformations of the solid Earth) are
removed from the observed values of universal time but they are added
back to the values of UT1-TAI estimated from the solution.

From about four and half million observations, 16445 unknown parameters
are estimated in a single least-squares solution with constraints.
Such a large system of linear equations is solved using a modified
Cholesky decomposition of the sparse matrix of normal equations, taking
into account their specific form.  The estimated parameters comprise
polar motion (i.e. motion of the spin axis in terrestrial reference
frame); after 1956, when the International Atomic Time scale (TAI)
became available, the differences between universal time UT1 and TAI
are also determined, at five-day intervals in the whole time span.
Celestial pole offsets (motion of the same axis in celestial reference
frame) are represented by quadratic function of time, for the whole
interval. In addition to these, combinations of Love numbers Lambda=1+k-l
(governing the solid Earth tidal variations of the local verticals) are
estimated, together with the small corrections of station coordinates
and the seasonal effects in latitude/longitude (i.e. a constant, secular
trend, semi-annual and annual terms) at each observatory.  The latter
are mutually tied by 18 constraints (these are meant to fix the
terrestrial reference frame to the one defined by initially chosen
station coordinates and to reduce the systematic deviations of
individual instruments due to seasonal effects of refraction). These
constraints are applied only to the most stable stations, in order to
assure long-term stability of the solution in terrestrial frame. Biases
and seasonal effects were then esimated by comparing our solution with
the IERS C04 solution after 1978, when modern space techniques of
observation became dominant, and removed from the optical astrometry
solution.


References:

Vondrak J.:  1991, Calculation of the new series of the Earth
orientation parameters in the Hipparcos reference frame, Bull. Astron.
Inst. Czechosl. 29, 97-103.

Vondrak J., Pesek I., Ron C., Cepek A.:  1998, Earth orientation
parameters 1899.7-1992.0 in the ICRS based on the Hipparcos reference
frame, Publ. Astron. Inst. Acad. Sci. Czech R. No. 87, 1-56.

Vondrak J., Stefka V.: The Earth Orientation Catalog 4: An optical
reference frame for monitoring Earth's orientation in the 20th century,
Astron. Astrophys. 509, A3(2010), DOI: 10.1051/0004-6361/200912472

Vondrak J., Ron C., Stefka V.: Earth orientation parameters based on
EOC-4 astrometric catalog, Acta Geodyn. Geomat. 2010, in press

Vondrak J., Ron C.: Tying the terretrial reference frame of EOP measured
by optical astrometry to ITRF, Poster at Session G3, EGU General Aseembly,
Vienna, May 2010