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D. E. Smylie - One of the best experts on this subject based on the ideXlab platform.

  • Spectral analysis of the VLBI pole path
    Journal of Geodynamics, 2009
    Co-Authors: Midhat Zuberi, D. E. Smylie
    Abstract:

    Abstract 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.

  • VLBI observations of free core nutations and viscosity at the top of the core
    Physics of the Earth and Planetary Interiors, 2004
    Co-Authors: Andrew K. Palmer, D. E. Smylie
    Abstract:

    Abstract Very long baseline interferometry (VLBI) nutation measurement series, both in excess of 23 years length, from Goddard Space Flight Center (GSFC) and the United States Naval Observatory (USNO), have been analyzed for free core nutation resonances. VLBI nutation observations can only be made when the radio sources being used are visible, rendering the data sequence inherently non-equispaced. This poses the problem of the approach to be taken with unevenly spaced sampling. Both the conventional Discrete Fourier Transform (DFT) and the Fast Fourier Transform Algorithm (FFT) for its computation strictly require a fixed sampling interval. Our approach is to find the Discrete Fourier Transform of the non-equispaced record by minimizing an objective function which weights the error between the DFT representation and the measured values in inverse proportion to the square of their standard errors. The resulting conditional equations have a coefficient matrix of Toeplitz form but the recursive Levinson algorithm has been found inadequate for their solution, even when implemented in double quad precision. Instead, we employ the Singular Value Decomposition technique to solve the least squares problem of fitting the Discrete Fourier Transform to the non-equispaced VLBI nutation observations. A novel feature of our procedure is to use the Parseval Relation to determine the number of singular values of the coefficient matrix to be eliminated. We report the observation for the first time of the prograde mode predicted by Jiang [Jiang, X., 1993. Wobble–nutation modes of the earth, Ph.D. thesis, York University, Toronto, Canada]. The long series of observations allow the determination of the time evolution of the free core nutations. We observe both the prograde and the retrograde modes to be in free decay. In addition to providing measures of the viscosity just below the core–mantle boundary (CMB), the free decays suggest impulsive excitations rather than continuous excitation by electromagnetic core–mantle coupling or the atmosphere. The average recovered viscosity at the top of the core is of the order 615 Pa s in contrast to the value of 8 × 1 0 − 3  Pa s found by Gans [Gans, R., 1972. Viscosity of the Earth’s core, J. Geophys. Res. 77, 360–366] from the extrapolation of laboratory measurements, and commonly used by dynamo theorists.

Akhilesh Prasad - One of the best experts on this subject based on the ideXlab platform.

Lokenath Debnath - One of the best experts on this subject based on the ideXlab platform.

S R Bandewar - One of the best experts on this subject based on the ideXlab platform.

Sumant Kumar - One of the best experts on this subject based on the ideXlab platform.