REVISITING THE COMPUTATION OF NORMAL MODES IN SNREI MODELS OF PLANETS - close eigenfrequencies

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dc.contributor.advisorde Hoop, Maarten
dc.creatorYe, Jingchen
dc.date.accessioned2019-01-02T22:11:47Z
dc.date.available2019-12-01T06:01:10Z
dc.date.created2017-12
dc.date.issued2018-02-21
dc.date.submittedDecember 2017
dc.date.updated2019-01-02T22:11:48Z
dc.descriptionEMBARGO NOTE: This dissertation was originally published under a 2 year embargo. Embargo has been extended 24 months till 2021-12-01.
dc.description.abstractWe develop a robust algorithm to compute seismic normal modes in a spherically symmetric, non-rotating Earth. A well-known problem is the cross-contamination of modes near "intersections" of dispersion curves for separate waveguides. Our novel computational approach completely avoids artificial degeneracies by guaranteeing orthonormality among the eigenfunctions. We extend Buland’s work, and reformulate the Sturm-Liouville problem as a generalized eigenvalue problem with the Rayleigh-Ritz Galerkin method. A special projection operator incorporating the gravity terms proposed by de Hoop and a displacement/pressure formulation are utilized in the fluid outer core to project out the essential spectrum. Moreover, the weak variational form enables us to achieve high accuracy across the solid-fluid boundary, especially for Stoneley modes, which have exponentially decaying behavior. We also employ the mixed finite element technique to avoid spurious pressure modes arising from discretization schemes and a numerical inf-sup test is performed following Bathe’s work. In addition, the self-gravitation terms are reformulated to avoid computations outside the Earth, thanks to the domain decomposition technique. Our package enables us to study the physical properties of intersection points of waveguides. According to Okal's classification theory, the group velocities should be continuous within a branch of the same mode family. However, we have found that there will be a small “bump” near intersection points, which is consistent with Miropol'sky’s observation. In fact, we can loosely regard Earth’s surface and the CMB as independent waveguides. For those modes that are far from the intersection points, their eigenfunctions are localized in the corresponding waveguides. However, those that are close to intersections will have physical features of both waveguides, which means they cannot be classified in either family. Our results improve on Okal’s classification, demonstrating that dispersion curves from independent waveguides should be considered to break at intersection points. Moreover, intersection points have close relations with Stoneley-related modes observed from earthquakes data, which casts light on studying deep Earth's structures.
dc.embargo.terms2019-12-01
dc.format.mimetypeapplication/pdf
dc.identifier.citationYe, Jingchen. "REVISITING THE COMPUTATION OF NORMAL MODES IN SNREI MODELS OF PLANETS - close eigenfrequencies." (2018) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/104942">https://hdl.handle.net/1911/104942</a>.
dc.identifier.urihttps://hdl.handle.net/1911/104942
dc.language.isoeng
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.
dc.subjectNormal modes computation
dc.subjectCross-contamination
dc.subjectIntersection points
dc.titleREVISITING THE COMPUTATION OF NORMAL MODES IN SNREI MODELS OF PLANETS - close eigenfrequencies
dc.typeThesis
dc.type.materialText
thesis.degree.departmentApplied Physics
thesis.degree.disciplineNatural Sciences
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.majorAppl Physics/Comp & Appl Math
thesis.degree.nameMaster of Science
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