Approximate inverse scattering using pseudodifferential scaling

This 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.

Name thesis:degree_name

Master of Arts

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

2009

Author dc:creator

• Nammour, Rami

Advisor dc:contributor.advisor

• Symes, William W.

• Geophysics
• Mathematics

Statement dc:rights

• Copyright 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.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/61837

OAI identifier oai:identifier

oai:repository.rice.edu:1911/61837