A New Approach to the High-Resolution Linear Radon Transform based on Compressive Sensing Theory: Application on Teleseismic Wavefields

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dc.contributor.advisorLevander, Alan R.en_US
dc.contributor.committeeMemberNiu, Fenglinen_US
dc.contributor.committeeMemberBaraniuk, Richard G.en_US
dc.creatorAharchaou, Mehdien_US
dc.date.accessioned2014-09-18T13:31:36Zen_US
dc.date.available2014-09-18T13:31:36Zen_US
dc.date.created2013-05en_US
dc.date.issued2013-04-19en_US
dc.date.submittedMay 2013en_US
dc.date.updated2014-09-18T13:31:37Zen_US
dc.description.abstractThe development of new tools for high-resolution seismic imaging has been for many years one of the key challenges faced by earthquake and exploration seismologists. In order to make data amenable to imaging analysis, pre-processing steps are of great importance. This thesis proposes a new method for pre-processing teleseismic data based on the linear radon transform implemented according to compressive sensing theory – a novel theory about acquiring and recovering the sparsest signals (with minimum significant coefficients) in the most efficient way possible with the help of incoherent measurements. The LRT works by mapping data into a sparsity-promoting domain (called the radon domain) where the desired signals can be easily isolated, classified, filtered and enhanced; and where noise can be attenuated or completely removed. The performance of the LRT is enhanced in terms of both high-resolution and computational cost by formulating the problem as an inverse problem in the frequency domain. This work shows that, unlike the common wisdom, irregularity in spatial sampling of teleseismic wavefields can be beneficial because it provides the incoherency needed to solve the compressive sensing problem and therefore recover the sparsest solutions in the radon domain. The inverse problem formulation yields the added advantage of automatic spatial interpolation and phase isolation after data reconstruction, and enables to regularize the problem by imposing sparsity constraint (instead of smoothness, which is the constraint usually adopted). We discuss and investigate the resolving power and applicability of convex and non-convex types of regularizers inspired from compressive sensing theory, and we establish a lower bound on the number of measurements needed to resolve certain time dips related to signals of interest within the data. We finish by applying the method to synthetic and recorded datasets and show how we do signal extraction, noise removal and spatial interpolation on teleseismic wavefields.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationAharchaou, Mehdi. "A New Approach to the High-Resolution Linear Radon Transform based on Compressive Sensing Theory: Application on Teleseismic Wavefields." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/77208">https://hdl.handle.net/1911/77208</a>.en_US
dc.identifier.slug123456789/ETD-2013-05-581en_US
dc.identifier.urihttps://hdl.handle.net/1911/77208en_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.subjectEarthquake Seismologyen_US
dc.subjectComputational seismologyen_US
dc.subjectSeismic Data Processingen_US
dc.subjectPre-processingen_US
dc.subjectTeleseismic Wavefieldsen_US
dc.subjectSignal Extraction and Recoveryen_US
dc.subjectSignal Improvementen_US
dc.subjectLinear Radon Transformen_US
dc.subjectSlant Stacken_US
dc.subjectCompressive sensing theoryen_US
dc.subjectInverse problem theoryen_US
dc.subjectGeophysicsen_US
dc.titleA New Approach to the High-Resolution Linear Radon Transform based on Compressive Sensing Theory: Application on Teleseismic Wavefieldsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentEarth Scienceen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Scienceen_US
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