Approximate inverse scattering using pseudodifferential scaling

dc.contributor.advisorSymes, William W.en_US
dc.creatorNammour, Ramien_US
dc.date.accessioned2011-07-25T01:38:34Zen_US
dc.date.available2011-07-25T01:38:34Zen_US
dc.date.issued2009en_US
dc.description.abstractThis thesis proposes a computationally efficient method for approximating the inverse of the normal operator arising in the linearized inverse problem for reflection seismology. The inversion of the normal operator using direct matrix methods is computationally infeasible. Approximate inverses estimate the solution of the inverse problem or precondition iterative methods. Application of the normal operator requires an expensive solution of large scale PDE problems. However, the normal operator approximately commutes with pseudodifferential operators, hence shares their near diagonality in a frame of localized monochromatic pulses. Estimation of a diagonal representation in this frame encoded in the symbol of the normal operator: (1) follows from its application to a single input vector; (2) suffices to approximate its inverse. I use an efficient algorithm to apply pseudodifferential operators, given their symbol, to construct a rapidly converging optimization algorithm that estimates the symbol of an inverse for the normal operator, thereby approximately solving the inverse problem.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. SCI. 2009 NAMMOURen_US
dc.identifier.citationNammour, Rami. "Approximate inverse scattering using pseudodifferential scaling." (2009) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/61837">https://hdl.handle.net/1911/61837</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/61837en_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.subjectGeophysicsen_US
dc.subjectMathematicsen_US
dc.titleApproximate inverse scattering using pseudodifferential scalingen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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