An abstract analysis of differential semblance optimization

Simple item page
dc.contributor.advisorSymes, William W.en_US
dc.contributor.advisorTapia, Richard A.en_US
dc.creatorGockenbach, Mark Stevenen_US
dc.date.accessioned2009-06-04T00:02:23Zen_US
dc.date.available2009-06-04T00:02:23Zen_US
dc.date.issued1994en_US
dc.description.abstractDifferential Semblance Optimization (DSO) is a novel way of approaching a class of inverse problems arising in exploration seismology. The promising feature of the DSO method is that it replaces a nonsmooth, highly nonconvex cost function (the Output Least-Squares (OLS) objective function) with a smooth cost function that is amenable to standard (local) optimization algorithms. The OLS problem can be written abstractly as a partially linear least-squares problem with linear constraints. The DSO objective function is derived from the associated quadratic penalty function. It is shown that one way to view the DSO objective function is as a regularization of a function that is dual (in a certain sense) to the OLS objective function. By viewing the DSO problem as a perturbation of this dual problem, this method can be shown to be effective. In particular, it is demonstrated that, under suitable assumptions, the DSO method defines a parameterized path of minimizers converging to the desired solution, and that for certain values of the parameter, standard optimization techniques can be used to find a point on the path. The predictions of the theory are motivated and illustrated on two simple model problems for seismic velocity inversion, the plane wave detection problem and the "layer-over-half-space" problem. It is shown that the theory presented in this thesis extends the existing theory for the plane wave detection problem.en_US
dc.format.extent90 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 1994 GOCKENBACHen_US
dc.identifier.citationGockenbach, Mark Steven. "An abstract analysis of differential semblance optimization." (1994) Diss., Rice University. <a href="https://hdl.handle.net/1911/16728">https://hdl.handle.net/1911/16728</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/16728en_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.subjectMathematicsen_US
dc.titleAn abstract analysis of differential semblance optimizationen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
9514177.PDF
Size:
2.28 MB
Format:
Adobe Portable Document Format
Download
Collections
Rice University Theses and Dissertations