{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/68514"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/68514","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Scattering Techniques for the Geophysical Inverse Problem","abstract":"We consider the inverse problem for the propagation of elastic waves in stratified media. The one-dimensional inverse problem for the propagation of shear waves is studied in the context of spectral theory. We generalize certain inverse scattering methods in quantum mechanics to determine the properties of the stratification from experimental knowledge gathered at the origin of the half-line. We further apply this method with some mathematical manipulations to arrive at a procedure to solve the inverse problem for a three-dimensional layered half space. This formulation of the problem lead to the complete and unique reconstruction of the depth dependences of the Lame parameters and the density from surface data. A discussion on the applicability of the proposed profile inversion method is given, and it is demonstrated with a numerical example.","abstract_html":"We consider the inverse problem for the propagation of elastic waves in stratified media. The one-dimensional inverse problem for the propagation of shear waves is studied in the context of spectral theory. We generalize certain inverse scattering methods in quantum mechanics to determine the properties of the stratification from experimental knowledge gathered at the origin of the half-line. We further apply this method with some mathematical manipulations to arrive at a procedure to solve the inverse problem for a three-dimensional layered half space. This formulation of the problem lead to the complete and unique reconstruction of the depth dependences of the Lame parameters and the density from surface data. A discussion on the applicability of the proposed profile inversion method is given, and it is demonstrated with a numerical example.","abstract_has_math":false,"creators":["Santosa, Fadil"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Theoretical and Applied Mechanics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-14T14:42:21Z","date_published":"2014-12-14T14:42:21Z","updated_at":"2026-07-22T22:25:59Z","subjects":["Applied Mechanics","Geological Survey"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8108650"],"render_values":[{"text":"(UMI)AAI8108650","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/68514","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Santosa, Fadil"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-14T14:42:21Z","10000-01-01","1980"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Theoretical and Applied Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied Mechanics","Geological Survey"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/68514","(UMI)AAI8108650"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider the inverse problem for the propagation of elastic waves in stratified media. The one-dimensional inverse problem for the propagation of shear waves is studied in the context of spectral theory. We generalize certain inverse scattering methods in quantum mechanics to determine the properties of the stratification from experimental knowledge gathered at the origin of the half-line. We further apply this method with some mathematical manipulations to arrive at a procedure to solve the inverse problem for a three-dimensional layered half space. This formulation of the problem lead to the complete and unique reconstruction of the depth dependences of the Lame parameters and the density from surface data. A discussion on the applicability of the proposed profile inversion method is given, and it is demonstrated with a numerical example.","Made available in DSpace on 2014-12-14T14:42:21Z (GMT). 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We generalize certain inverse scattering methods in quantum mechanics to determine the properties of the stratification from experimental knowledge gathered at the origin of the half-line. We further apply this method with some mathematical manipulations to arrive at a procedure to solve the inverse problem for a three-dimensional layered half space. This formulation of the problem lead to the complete and unique reconstruction of the depth dependences of the Lame parameters and the density from surface data. A discussion on the applicability of the proposed profile inversion method is given, and it is demonstrated with a numerical example.","Made available in DSpace on 2014-12-14T14:42:21Z (GMT). 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