bscthesis.bib

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@MASTERSTHESIS{lin08THccl,
  author = {Tim T.Y. Lin},
  title = {Compressed computation of large-scale wavefield extrapolation in inhomogeneous medium},
  school = {University of British Columbia},
  year = {2008},
  type = {masters},
  abstract = {In this work an explicit algorithm for the extrapolation
                  of one-way wavefields is proposed which combines
                  recent developments in information theory and
                  theoretical signal processing with the physics of
                  wave propagation. Because of excessive memory
                  requirements, explicit formulations for wave
                  propagation have proven to be a challenge in 3-D. By
                  using ideas from
                  {\textquoteleft}{\textquoteleft}compressed
                  sensing{\textquoteright}{\textquoteright}, we are
                  able to formulate the (inverse) wavefield
                  extrapolation problem on small subsets of the data
                  volume, thereby reducing the size of the
                  operators. Compressed sensing entails a new paradigm
                  for signal recovery that provides conditions under
                  which signals can be recovered from incomplete
                  samplings by \emph{nonlinear} recovery methods that
                  promote sparsity of the to-be-recovered
                  signal. According to this theory, signals can
                  successfully be recovered when the measurement basis
                  is \emph{incoherent} with the representation in
                  which the wavefield is sparse. In this new approach,
                  the eigenfunctions of the Helmholtz operator are
                  recognized as a basis that is incoherent with
                  sparsity transforms that are known to compress
                  seismic wavefields. By casting the wavefield
                  extrapolation problem in this framework, wavefields
                  can successfully be extrapolated in the modal
                  domain, despite evanescent wave modes. The degree to
                  which the wavefield can be recovered depends on the
                  number of missing (evanescent) wave modes and on the
                  complexity of the wavefield. A proof of principle
                  for the {\textquoteleft}{\textquoteleft}compressed
                  sensing{\textquoteright}{\textquoteright} method is
                  given for inverse wavefield extrapolation in
                  2-D. The results show that our method is stable, has
                  reduced dip limitations and handles evanescent waves
                  in inverse extrapolation.},
  keywords = {BSc, SLIM},
  month = {04},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2008/lin08THccl.pdf}
}