Mathematics – Logic
Scientific paper
Nov 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999phdt.........4f&link_type=abstract
Thesis (PhD). UNIVERSITY OF CALIFORNIA, BERKELEY, Source DAI-B 60/05, p. 2202, Nov 1999, 170 pages.
Mathematics
Logic
Solar Oscillation, Bootstrap Percentile, Multitaper
Scientific paper
Acoustic oscillations of the solar surface carry information about the interior structure and dynamics of the Sun. Accurate estimation of the oscillation power spectrum is of considerable scientific interest in order to map the inner Sun, to test theories of stellar evolution, and to understand physics at high temperatures and pressures. Instrumental problems and geometrical limitations in the observing strategy result in temporal and spatial missing values in helioseismological observations, and complicate the oscillation spectrum estimation. The periodogram is notorious in the statistical community for its limitations even for gapless data, yet it is the spectrum estimate of choice of helioseismologists. We propose alternative solar oscillation power spectrum estimates that improve on the periodogram and lead to more accurate oscillation mode parameter estimates. The estimates are designed to minimize the effects of the incomplete temporal coverage, and extend one-dimensional multitaper spectrum estimates to observations with gaps. We show how to construct favorable collections of orthogonal tapers tailored to the gap structure of a particular time series. The resulting multitaper spectrum estimates suppress the artifacts of the temporal gaps, have less broad band bias and variance than the periodogram, and, unlike the periodogram, are consistent. We also introduce a novel statistical resampling technique, the iterated bootstrap percentile method, to calculate realistic uncertainty estimates for multitaper spectrum estimates. We demonstrate the superiority of multitaper estimates over certain parametric spectrum estimates. In simulated and actual solar oscillation times series, more frequencies can be more accurately estimated from the proposed spectrum estimates than from the periodogram. Our procedure was recently adopted in the data reduction pipeline of the Global Oscillation Network Group (GONG), a state-of-the-art helioseismological experiment. The proposed methodology can be applied in the spectral analysis of any one-dimensional time series observed with incomplete temporal coverage, and can be extended to the spectral analysis of arbitrary spherical data observed with incomplete spatial coverage. The two-dimensional generalization can in turn be used to further improve the solar oscillation mode parameter estimates by minimizing the effects of the spatial missing values in helioseismic observations.
Fodor Imola K.
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