Approximate Inverse Scattering Using Pseudodifferential Scaling

dc.contributor.authorNammour, Ramien_US
dc.date.accessioned2018-06-19T17:45:06Zen_US
dc.date.available2018-06-19T17:45:06Zen_US
dc.date.issued2009-04en_US
dc.date.noteApril 2009en_US
dc.descriptionThis work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/61837en_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.extent62 ppen_US
dc.identifier.citationNammour, Rami. "Approximate Inverse Scattering Using Pseudodifferential Scaling." (2009) <a href="https://hdl.handle.net/1911/102114">https://hdl.handle.net/1911/102114</a>.en_US
dc.identifier.digitalTR09-09en_US
dc.identifier.urihttps://hdl.handle.net/1911/102114en_US
dc.language.isoengen_US
dc.titleApproximate Inverse Scattering Using Pseudodifferential Scalingen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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