## Testing a Method for Excluding a Slow Trend from Measurements of the Earth's Orientation Parameters Using a Double Wavelet Transform

Transactions of IAA RAS, issue 66, 29–36 (2023)

**DOI**: 10.32876/ApplAstron.66.29-36

**Keywords**:
UT1, polar motion, wavelet, trend

### Abstract

When studying variations in the parameters of the Earth's rotation, it is necessary to correctly exclude a slow trend from the measurement results. As a rule, this is done by applying the appropriate filter or direct wavelet trans-form. However, the result of such an operation depends on the shape of the filter or the basis functions used (in the case of a wavelet) and is not unambiguous. This article discusses the results of testing one of the methods for excluding a trend – the double wavelet trans-form method, which allows you to exclude a slow trend (consisting of both the secular and long-period parts) from the measurement results without significant distortion of the shape of the high-frequency part of the original signal. This method was applied to exclude the slow trend from the observed values of the Earth's orientation parameters (coordi-nates of the terrestrial polar motion and variation of the Earth’s angular velocity) and to further refine the coefficients of the averaged models of seasonal variations in the angular velocity of the Earth's rotation, universal time and terrestrial polar motion. The Earth's orientation parameters data of International Earth Rotation Service and Reference Systems were used for analysis as measurement data. After the trend was eliminated, the residuals were analyzed using the least squares method, as a result of which the coefficients of the averaged models of the seasonal components of these variations were refined. The quality of the constructed models was evaluated by residual residuals using the fast Fourier transform method. The results showed the effectiveness of the method and the high quality of models with refined coefficients.

### Citation

`S. L. Pasynok. Testing a Method for Excluding a Slow Trend from Measurements of the Earth's Orientation Parameters Using a Double Wavelet Transform // Transactions of IAA RAS. — 2023. — Issue 66. — P. 29–36.`

```
@article{pasynok2023,
abstract = {When studying variations in the parameters of the Earth's rotation, it is necessary to correctly exclude a slow trend from the measurement results. As a rule, this is done by applying the appropriate filter or direct wavelet trans-form. However, the result of such an operation depends on the shape of the filter or the basis functions used (in the case of a wavelet) and is not unambiguous.
This article discusses the results of testing one of the methods for excluding a trend – the double wavelet trans-form method, which allows you to exclude a slow trend (consisting of both the secular and long-period parts) from the measurement results without significant distortion of the shape of the high-frequency part of the original signal. This method was applied to exclude the slow trend from the observed values of the Earth's orientation parameters (coordi-nates of the terrestrial polar motion and variation of the Earth’s angular velocity) and to further refine the coefficients of the averaged models of seasonal variations in the angular velocity of the Earth's rotation, universal time and terrestrial polar motion. The Earth's orientation parameters data of International Earth Rotation Service and Reference Systems were used for analysis as measurement data. After the trend was eliminated, the residuals were analyzed using the least squares method, as a result of which the coefficients of the averaged models of the seasonal components of these variations were refined.
The quality of the constructed models was evaluated by residual residuals using the fast Fourier transform method. The results showed the effectiveness of the method and the high quality of models with refined coefficients.},
author = {S.~L. Pasynok},
doi = {10.32876/ApplAstron.66.29-36},
issue = {66},
journal = {Transactions of IAA RAS},
keyword = {UT1, polar motion, wavelet, trend},
pages = {29--36},
title = {Testing a Method for Excluding a Slow Trend from Measurements of the Earth's Orientation Parameters Using a Double Wavelet Transform},
url = {http://iaaras.ru/en/library/paper/2161/},
year = {2023}
}
```

```
TY - JOUR
TI - Testing a Method for Excluding a Slow Trend from Measurements of the Earth's Orientation Parameters Using a Double Wavelet Transform
AU - Pasynok, S. L.
PY - 2023
T2 - Transactions of IAA RAS
IS - 66
SP - 29
AB - When studying variations in the parameters of the Earth's rotation,
it is necessary to correctly exclude a slow trend from the
measurement results. As a rule, this is done by applying the
appropriate filter or direct wavelet trans-form. However, the result
of such an operation depends on the shape of the filter or the basis
functions used (in the case of a wavelet) and is not unambiguous.
This article discusses the results of testing one of the methods for
excluding a trend – the double wavelet trans-form method, which
allows you to exclude a slow trend (consisting of both the secular
and long-period parts) from the measurement results without
significant distortion of the shape of the high-frequency part of the
original signal. This method was applied to exclude the slow trend
from the observed values of the Earth's orientation parameters
(coordi-nates of the terrestrial polar motion and variation of the
Earth’s angular velocity) and to further refine the coefficients of
the averaged models of seasonal variations in the angular velocity of
the Earth's rotation, universal time and terrestrial polar motion.
The Earth's orientation parameters data of International Earth
Rotation Service and Reference Systems were used for analysis as
measurement data. After the trend was eliminated, the residuals were
analyzed using the least squares method, as a result of which the
coefficients of the averaged models of the seasonal components of
these variations were refined. The quality of the constructed
models was evaluated by residual residuals using the fast Fourier
transform method. The results showed the effectiveness of the method
and the high quality of models with refined coefficients.
DO - 10.32876/ApplAstron.66.29-36
UR - http://iaaras.ru/en/library/paper/2161/
ER -
```