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Inversion formulas for time-distance helioseismology
Thompson, Nathan L.
Thompson, Nathan L.
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2013-05
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Electronic dissertations
Electronic dissertations
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Abstract
In this thesis we examine the inverse kinematic problem presented in time-distance helioseismology.
Acoustic wave oscillations in the Sun travel along ray paths below the Sun's
surface. These ray paths are de ned by Fermat's principle of least time. Di erences from
the expected travel times of these oscillations to di erent points on the Sun's surface is
indicative of inhomogeneities in the solar structure. Measuring these perturbations in the
travel times allow the recovery of information about acoustic sources and
ows within the
Sun. Our goal is to accurately recover functions describing these perturbations, and hence
information about solar features. An inverse problem is solved using the transport equation
in conjunction with a rst order approximation of the ray path geometry. We obtain results
that show this inversion process is unique and stable, as well as explicit formulas for the
solutions to the scalar and vector tomography problems considered.
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Thesis (M.S.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
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Wichita State University
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Copyright Nathan Thompson, 2013. All rights reserved