Transparency Property of One Dimensional Acoustic Wave Equations

dc.contributor.advisorSymes, William W.en_US
dc.contributor.committeeMemberRiviere, Beatrice M.en_US
dc.contributor.committeeMemberWarburton, Timen_US
dc.creatorHuang, Yinen_US
dc.date.accessioned2013-07-24T19:32:34Zen_US
dc.date.accessioned2013-07-24T19:32:36Zen_US
dc.date.available2013-07-24T19:32:34Zen_US
dc.date.available2013-07-24T19:32:36Zen_US
dc.date.created2012-12en_US
dc.date.issued2013-07-24en_US
dc.date.submittedDecember 2012en_US
dc.date.updated2013-07-24T19:32:37Zen_US
dc.description.abstractThis thesis proposes a new proof of the acoustic transparency theorem for material with a bounded variation. The theorem states that if the material properties (density, bulk modulus) is of bounded variation, the net power transmitted through the point z = 0 over a time interval [−T,T] is greater than some constant times the energy at the time zero over a spatial interval [0,Z], provided that T equals the time of travel of a wave from 0 to Z. This means the reflected energy of an input into the earth will be received. Otherwise, the reflections may not arrive at the surface. A proof gives a lower bound for material properties (density, bulk modulus) with bounded variation using sideways energy estimate. A different lower bound that works only for piecewise constant coefficients is also given. It gives a lower bound by analyzing reflections and transmissions of the waves at the jumps of the material properties. This thesis also gives an example to illustrate that the bounded variation assumption may not be necessary for the medium to be transparent. This thesis also discusses relations between the transparency property and the data of an inverse problem.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationHuang, Yin. "Transparency Property of One Dimensional Acoustic Wave Equations." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/71661">https://hdl.handle.net/1911/71661</a>.en_US
dc.identifier.slug123456789/ETD-2012-12-299en_US
dc.identifier.urihttps://hdl.handle.net/1911/71661en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectAcoustic wave equationen_US
dc.subjectTransparencyen_US
dc.subjectEnergy estimateen_US
dc.subjectInverse problemsen_US
dc.titleTransparency Property of One Dimensional Acoustic Wave Equationsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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