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dc.contributor.advisorBukhgeym, Alexander L.
dc.contributor.authorThompson, Nathan
dc.date.accessioned2018-08-20T21:44:46Z
dc.date.available2018-08-20T21:44:46Z
dc.date.issued2018-05
dc.identifier.otherd18024s
dc.identifier.urihttp://hdl.handle.net/10057/15427
dc.descriptionThesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics and Physics
dc.description.abstractBeginning with the weighted transport equation, P u(x, ω) = hω, ∇xu(x, ω)i + µ(x)u(x, ω) = ρ(x, ω)a(x), x ∈ ω ⊂ R 2 , we examine the properties of acoustic waves that travel below the surface of a solid, such as the Earth or the Sun. According to the laws of geometric optics, these acoustic signals travel along ray paths which obey Fermat’s principle of least time. Every material has an optimal path and travel time and deviations from this travel time reveal features of the material hidden within. These optimal paths are encoded into our transport equation by the weight function ρ(x, ω). Using the Fourier series decomposition of u and ρ with respect to ω, we examine several approximations to an arbitrary weight function and solve for the perturbations to the expected travel time in both the scalar and vector tomography cases. Our results show that the solutions to the resulting systems of differential equations are unique and stable.
dc.format.extentvii, 85 pages
dc.language.isoen_US
dc.publisherWichita State University
dc.rightsCopyright 2018 by nathan Lee Thompson All Rights Reserved
dc.subject.lcshElectronic dissertations
dc.titleScalar and vector tomography for the weighed transport equation
dc.typeDissertation


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