Use of Operator Upscaling for Seismic Inversion: Computationally Feasible Forward and Adjoint Calculations

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dc.contributor.advisorMinkoff, Susan E.
dc.contributor.authorGriffith, Sean M.L.
dc.contributor.departmentMathematics and Statistics
dc.contributor.programMathematics
dc.date.accessioned2015-10-14T03:12:52Z
dc.date.available2015-10-14T03:12:52Z
dc.date.issued2008-10-28
dc.description.abstractTo solve seismic inverse problems via the adjoint state method, we must be able to repeatedly solve both the wave equation and its adjoint efficiently. Operator upscaling applied to the wave equation imparts fine scale information to the coarse scale without requiring that we solve the full fine scale problem. We apply the algorithm to the stress-free form of the 3D elastic wave equation. This algorithm has two stages: first, we solve independent subgrid problems on the fine scale; second, we use these subgrid solutions to solve the coarse problem. Because the subgrid problems are independent, they can be solved via an embarrassingly parallel algorithm. Surprisingly, the most expensive part of the coarse grid solve is not assembling the mass matrix (which is time independent) but instead it is calculation of the load vector (which is time dependent). Thus we parallelize the load vector calculation for the coarse problem, as it dominates the time step. The most expensive parts of the algorithm (the subgrid solve and the coarse load vector calculation) exhibit near linear speedup. In the second half of the thesis we discuss using the adjoint state method to solve the seismic inverse problem. As the acoustic wave operator is self-adjoint, we chose to differentiate and then discretize the problem. The result is that the adjoint problem can be solved by the same upscaling method as the standard acoustic wave equation. The forward and adjoint upscaling algorithms differ only in the source terms and in the time stepping order.
dc.formatapplication/pdf
dc.genretheses
dc.identifierdoi:10.13016/M2910S
dc.identifier.other1268
dc.identifier.urihttp://hdl.handle.net/11603/1033
dc.languageen
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Theses and Dissertations Collection
dc.relation.ispartofUMBC Graduate School Collection
dc.relation.ispartofUMBC Student Collection
dc.relation.ispartofUMBC Mathematics and Statistics Department Collection
dc.rightsThis item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu.
dc.sourceOriginal File Name: umi-umbc-1268.pdf
dc.subjectMathematics(0405)
dc.subjectGeophysics(0373)
dc.subjectUpscaling
dc.subjectParallel Computing
dc.subjectInverse Problem
dc.subjectSeismology
dc.subjectMultiscale Methods
dc.subjectWave Propagation
dc.titleUse of Operator Upscaling for Seismic Inversion: Computationally Feasible Forward and Adjoint Calculations
dc.typeText
dcterms.accessRightsAccess limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan through a local library, pending author/copyright holder's permission.

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