Browsing by Author "Bencomo, Mario Javier"

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    Discontinuous Galerkin and Finite Difference Methods for the Acoustic Equations with Smooth Coefficients
    (2015-04-20) Bencomo, Mario Javier; Symes, William W.; Warburton, Timothy C; Riviere, Beatrice M
    This thesis analyzes the computational efficiency of two types of numerical methods: finite difference (FD) and discontinuous Galerkin (DG) methods, in the context of 2D acoustic equations in pressure-velocity form with smooth coefficients. The acoustic equations model propagation of sound waves in elastic fluids, and are of particular interest to the field of seismic imaging. The ubiquity of smooth trends in real data, and thus in the acoustic coefficients, validates the importance of this novel study. Previous work, from the discontinuous coefficient case of a two-layered media, demonstrates the efficiency of DG over FD methods but does not provide insight for the smooth coefficient case. Floating point operation (FLOPs) counts are compared, relative to a prescribed accuracy, for standard 2-2 and 2-4 staggered grid FD methods, and a myriad of standard DG implementations. This comparison is done in a serial framework, where FD code is implemented in C while DG code is written in Matlab. Results show FD methods considerably outperform DG methods in FLOP count. More interestingly, implementations of quadrature based DG with mesh refinement (for lower velocity zones) yield the best results in the case of highly variable media, relative to other DG methods.
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    Representation and Estimation of Seismic Sources via Multipoles
    (2017-04-17) Bencomo, Mario Javier; Symes, William W
    Accurate representation and estimation of seismic sources are essential to the seismic inversion problem. General sources can be approximated by a truncated series of multipoles depending on the source anisotropy. Most research in the joint inversion of source and medium parameters assumes seismic sources can be modeled as isotropic point-sources resulting in an inability to fit the anisotropy observed in data, ultimately impacting the recovery of medium parameters. In this thesis I lay the groundwork for joint source-medium parameter inversion with potentially anisotropic seismic sources via full waveform inversion through three key contributions: a mathematical and computational framework for the modeling and inversion of sources via multipoles, construction and analysis of discretizations of multipole sources on regular grids, and preconditioners based on fractional time derivative/integral operators for the ill-conditioned source estimation subproblem. As an application of my multipole framework, I also study the efficacy of multipoles in modeling the airgun array source, the most common type of active source in marine seismic surveying. Inversion results recovered a dominating isotropic component of the multipole source model that accounted for 84% of the observed radiation pattern. An extra 10% of the observed output pressure field can be explained when incorporating dipole terms in the source representation, thus motivating the use of multipoles to capture source anisotropy.