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Harmonic variations in the Earth Rotation determined using VLBI

The Earth rotation has harmonic variations caused by external
torques exerted directly and directly with the Sun, the Moon, and
the planets. Atmospheric and ocean circulation and variations
in continental water storage cause additional excitation in the Earth
rotation. While excitation due to external torques can be predicted
very precisely, excitation due to air and water mass redistribution
is not predictable. Layered non-rigid Earth response to the excitation
differently than an absolutely rigid body. For instance a boiled egg
rotates differently than a raw egg. Comparing observed variations
in the Earth rotation with the excitation we can make inference about
properties of the Earth's inferior that described by a number of parameter
called compliances or basic Earth parameters.
As the first step of studying the response of the Earth to forcings,
we have developed a procedure of estimating the spectrum of the Earth
rotation by analysis of the time series of VLBI group delays since
1984.0 through present. I estimate close to 1000 constituents in
a single least square analysis of 13 million VLBI group delays
without resorting to intermediate time series. The frequencies
of the estimated constituents are selected to cover

- all major nutation constituents with theoretical amplitude
about 10 prad;

- all 2nd order tides with amplitudes greater 0.1% of M2 tide
amplitude;

- all frequencies with a step 1/Δt within the retrograde
free core nutation and hypothetical prograde under core
nutation. Δt is the interval of observations.
- a number of ad hock frequencies within ter-diurnal band.

For close tidal and nutation constituents with frequency separation less
than 1/Δt constraints are imposed on the ratio of complex
amplitude estimates to be close to the radio of theoretical complex
amplitudes.
Since the Free core nutation is the unpredictable process, we have to
repeat the estimation procedure every 2–4 months. In a time
domain this is equivalent to a trigonometric extrapolation of the
free core nutation and updating the time series every 2–4 months.

## Numerical tables of the results of analysis of VLBI observations.

The tables below contain the estimates of the expansion of the vector
of small perturbations of the Earth rotation with respect to the empirical
nutation series MHB and empirical precession expression Capitaine_2003
taken as the reference into Fourier series from processing all suitable
geodetic VLBI observations. The components of the vector of the small
perturbations correspond to Euler angles. The expansion includes so-called
nutations and sub-diurnal variations in the Earth orientation parameters.
This project is supported by NASA
Earth Surface & Interior program, grant This NNX17AE02G.

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*
This web page was prepared by Leonid Petrov
() *

Last update: 2018.01.12_00:39:03