Statistics – Computation
Scientific paper
Dec 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002agufmmr72b1026p&link_type=abstract
American Geophysical Union, Fall Meeting 2002, abstract #MR72B-1026
Statistics
Computation
1015 Composition Of The Core, 1025 Composition Of The Mantle, 3672 Planetary Mineralogy And Petrology (5410), 7207 Core And Mantle, 8124 Earth'S Interior: Composition And State (Old 8105)
Scientific paper
VLBI nutation measurements offer a unique opportunity to evaluate very small relative motions of the Earth's axis of rotation. This, in turn, can allow us to deduce properties of the Earth's deep interior. However, since VLBI nutation measurements can only be taken when the radio sources being observed are visible, the data is inherently non-equispaced. One of the fundamental problems posed in spectral analysis is the approach one should take when dealing with unevenly spaced sampling - the conventional Discrete Fourier Transform and the Fast Fourier Transform Algorithm for its computation, for example, strictly require a constant interval between successive data points. It is shown that a Discrete Fourier Transform can be obtained directly from a non-equispaced record by minimizing an objective function which weights the error energy terms in inverse proportion to the square of their standard deviations. The conditional equations have a coefficient matrix of Toeplitz form, and can be solved by any of a variety of linear algebra routines, including the Levinson algorithm. By its nature the fitting matrix can be highly ill-conditioned. This problem can be overcome by re-evaluating the result after setting the reciprocal of the smallest singular values in the fitting matrix to zero using the Singular Value Decomposition technique. The sampling in the non-equispaced case is modelled by multiplication of the record in the time domain by a Dirac comb with non-equispaced teeth. The effect of this sampling in the frequency domain is to convolve the Fourier Transform of the comb with the true frequency spectrum. Correction of the effect of non-equispaced sampling can be accomplished by convolving the computed spectrum with the frequency domain inverse of the Fourier Transform of the sampling comb. Using synthetic non-equispaced time series the results are shown to compare highly favorably with the traditional approach to non-equispaced data, a polynomial interpolation onto an evenly spaced time grid. The forgoing methods are used to provide a spectral analysis of a 16 year long VLBI nutation residual sequence in the search for the Retrograde Free Core Nutation and the numerically predicted Prograde Free Core Nutation. The results are then used to obtain a reappraisal of the viscosity of the outer core at the core-mantle boundary by determining the Q factor of the Free Core Nutation resonance.
Palmer Alice
Smylie Douglas E.
No associations
LandOfFree
Analysis of Non-Equispaced VLBI Nutation Measurements does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Analysis of Non-Equispaced VLBI Nutation Measurements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analysis of Non-Equispaced VLBI Nutation Measurements will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1892532