| Popis: |
Modern observations of polar motion, using techniques such as Very Long Baseline Interferometry (VLBI), have reduced error levels by as much as three orders of magnitude, compared to classical astronometric methods. Here we focus on VLBI observations which are characteristically unequally spaced. We develop a very effective method of spectral analysis for unequally spaced time sequences. First, the least squares fit to the representation of the sequence by the Discrete Fourier Transform (DFT) is calculated, weighting the observations by the inverse square of the accompanying standard error. The coefficient matrix of the normal equations of this fit is nearly singular. It is subjected to a Singular Value Decomposition (SVD). In the usual application of SVD singular values are eliminated in order to improve the stability of the numerical system but no criterion is given for how many singular values to eliminate. To overcome this shortcoming, we introduce the Parseval condition which relates the mean square in the time domain to that in the frequency domain. Singular values are eliminated until Parseval’s theorem is satisfied. Typically, the mean square in the frequency domain is many orders of magnitude too large. As singular values are eliminated, starting with the smallest and working upward, the mean square in the frequency domain appears to decrease monotonically until the Parseval relation is satisfied. Once the DFTs are found, spectral analysis and the estimation of confidence intervals proceed in the standard way. We perform a spectral analysis of the polar motion on 24.5 years of observations by using a Welch Overlapping Segment Analysis (WOSA) with four record segments of 14-year length with 75% overlap. Parameters of the Chandler wobble resonance are found as well as a detailed spectrum. |
Full Text from ScienceDirect