Mathematics Colloquia and Seminars

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Helioseismology is the study of the interior of the sun from its acoustic vibrations, which have a characteristic period of about 5 minutes. Infering solar structure and kinematics from the frequencies of solar oscillations is an inverse problem that can be addressed with a number of statistical tools. I will give an overview of helioseismology, focusing on statistical problems in estimating the oscillation frequencies from the fundamental observations. The basic data are the intensities of light at various frequencies in each pixel of a CCD camera, measured once a minute. These spatio-temporal series have gaps, caused by malfunctions, birds in the field of view, routine maintenance, the use of the telescope for other kinds of observations, etc. I will present an approach to mitigating the effect of the gaps on estimates of the spectrum of oscillations: multitaper spectrum estimates using gap-adapted tapers. The approach is computationally efficient, and improves the reliability of estimates of the oscillation frequencies and allows the frequencies of more solar modes to be estimated, compared with methods used previously. The approach was adopted recently by the Global Oscillations Network Group (GONG), a network of six solar telescopes that span the globe at mid-latitudes, for their standard data-reduction pipeline. This work is joint with Imola Fodor (Lawrence Livermore National Laboratory) and the GONG project team (National Solar Observatory, Tucson).