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Santosa, Fadil 2014-12-14T14:42:21Z 2014-12-14T14:42:21Z 10000-01-01 1980 1980 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). No. of bitstreams: 1 8108650.pdf: 2202453 bytes, checksum: 4d8b8014e6c9596d730fd81c0bc42dd8 (MD5) Previous issue date: 1980 Embargo set by: Seth Robbins for item 68692 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 81 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980. http://hdl.handle.net/2142/68514 (UMI)AAI8108650 eng Applied Mechanics Geological Survey Scattering Techniques for the Geophysical Inverse Problem text Dissertation Ph.D. Theoretical and Applied Mechanics Theoretical and Applied Mechanics University of Illinois at Urbana-Champaign