Finite Element Methods for Seismic Modelling

Sjoerd Geevers

    Research output: ThesisPhD Thesis - Research UT, graduation UT

    188 Downloads (Pure)

    Abstract

    In this dissertation, new and more efficient finite element methods for modelling seismic wave propagation are presented and analysed.

    Seismic modelling is a useful tool for better understanding seismic behaviour in complex rock structures, but it is also a key aspect of full waveform inversion, which is a powerful technique for imaging the structure of the earth's subsurface. The great advantage of finite element methods over other wave modelling methods, like the popular finite difference method, is that it accurately captures the effect of complex topographies, such as mountainous areas and rough seabeds, without refining the grid resolution. Even so, these methods require a huge amount of computational power and making them more efficient is of great value in many industrial applications.

    Topics addressed in this dissertation include: new and sharper bounds for the penalty term and time step size of the Discontinuous Galerkin method, new and significantly more efficient mass-lumped tetrahedral elements, new and efficient quadrature rules for evaluating the stiffness matrix of these mass-lumped elements, stability properties of a basic local time-stepping algorithm, and a dispersion analysis and comparison of multiple finite element methods.

    Overall, the finite element methods and algorithms presented in this dissertation allow for a much faster modelling of seismic waves. This is especially true for the new mass-lumped finite elements, which in some cases result in a speed of a factor 10 compared to other finite element methods. These improvements make the use of finite element methods much more attractive for geophysical applications or other industrial applications that involve solving wave propagation problems.
    Original languageEnglish
    Awarding Institution
    • University of Twente
    Supervisors/Advisors
    • van der Vegt, Jacobus J.W., Supervisor
    Thesis sponsors
    Award date21 Sep 2018
    Place of PublicationEnschede
    Publisher
    Print ISBNs978-90-365-4613-3
    Electronic ISBNs978-90-365-4613-3
    DOIs
    Publication statusPublished - 2018

    Fingerprint

    Finite Element Method
    Finite element method
    Computer simulation
    Modeling
    Seismic Waves
    Seismic waves
    Industrial Application
    Wave propagation
    Wave Propagation
    Industrial applications
    Discontinuous Galerkin Method
    Sharp Bound
    Quadrature Rules
    Local Time
    Stiffness matrix
    Time Stepping
    Galerkin methods
    Topography
    Stiffness Matrix
    Modeling Method

    Keywords

    • Finite Element Method
    • Wave Equation
    • Seismic Modelling

    Cite this

    Geevers, Sjoerd . / Finite Element Methods for Seismic Modelling. Enschede : University of Twente, 2018. 178 p.
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    abstract = "In this dissertation, new and more efficient finite element methods for modelling seismic wave propagation are presented and analysed. Seismic modelling is a useful tool for better understanding seismic behaviour in complex rock structures, but it is also a key aspect of full waveform inversion, which is a powerful technique for imaging the structure of the earth's subsurface. The great advantage of finite element methods over other wave modelling methods, like the popular finite difference method, is that it accurately captures the effect of complex topographies, such as mountainous areas and rough seabeds, without refining the grid resolution. Even so, these methods require a huge amount of computational power and making them more efficient is of great value in many industrial applications.Topics addressed in this dissertation include: new and sharper bounds for the penalty term and time step size of the Discontinuous Galerkin method, new and significantly more efficient mass-lumped tetrahedral elements, new and efficient quadrature rules for evaluating the stiffness matrix of these mass-lumped elements, stability properties of a basic local time-stepping algorithm, and a dispersion analysis and comparison of multiple finite element methods.Overall, the finite element methods and algorithms presented in this dissertation allow for a much faster modelling of seismic waves. This is especially true for the new mass-lumped finite elements, which in some cases result in a speed of a factor 10 compared to other finite element methods. These improvements make the use of finite element methods much more attractive for geophysical applications or other industrial applications that involve solving wave propagation problems.",
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    Finite Element Methods for Seismic Modelling. / Geevers, Sjoerd .

    Enschede : University of Twente, 2018. 178 p.

    Research output: ThesisPhD Thesis - Research UT, graduation UT

    TY - THES

    T1 - Finite Element Methods for Seismic Modelling

    AU - Geevers, Sjoerd

    PY - 2018

    Y1 - 2018

    N2 - In this dissertation, new and more efficient finite element methods for modelling seismic wave propagation are presented and analysed. Seismic modelling is a useful tool for better understanding seismic behaviour in complex rock structures, but it is also a key aspect of full waveform inversion, which is a powerful technique for imaging the structure of the earth's subsurface. The great advantage of finite element methods over other wave modelling methods, like the popular finite difference method, is that it accurately captures the effect of complex topographies, such as mountainous areas and rough seabeds, without refining the grid resolution. Even so, these methods require a huge amount of computational power and making them more efficient is of great value in many industrial applications.Topics addressed in this dissertation include: new and sharper bounds for the penalty term and time step size of the Discontinuous Galerkin method, new and significantly more efficient mass-lumped tetrahedral elements, new and efficient quadrature rules for evaluating the stiffness matrix of these mass-lumped elements, stability properties of a basic local time-stepping algorithm, and a dispersion analysis and comparison of multiple finite element methods.Overall, the finite element methods and algorithms presented in this dissertation allow for a much faster modelling of seismic waves. This is especially true for the new mass-lumped finite elements, which in some cases result in a speed of a factor 10 compared to other finite element methods. These improvements make the use of finite element methods much more attractive for geophysical applications or other industrial applications that involve solving wave propagation problems.

    AB - In this dissertation, new and more efficient finite element methods for modelling seismic wave propagation are presented and analysed. Seismic modelling is a useful tool for better understanding seismic behaviour in complex rock structures, but it is also a key aspect of full waveform inversion, which is a powerful technique for imaging the structure of the earth's subsurface. The great advantage of finite element methods over other wave modelling methods, like the popular finite difference method, is that it accurately captures the effect of complex topographies, such as mountainous areas and rough seabeds, without refining the grid resolution. Even so, these methods require a huge amount of computational power and making them more efficient is of great value in many industrial applications.Topics addressed in this dissertation include: new and sharper bounds for the penalty term and time step size of the Discontinuous Galerkin method, new and significantly more efficient mass-lumped tetrahedral elements, new and efficient quadrature rules for evaluating the stiffness matrix of these mass-lumped elements, stability properties of a basic local time-stepping algorithm, and a dispersion analysis and comparison of multiple finite element methods.Overall, the finite element methods and algorithms presented in this dissertation allow for a much faster modelling of seismic waves. This is especially true for the new mass-lumped finite elements, which in some cases result in a speed of a factor 10 compared to other finite element methods. These improvements make the use of finite element methods much more attractive for geophysical applications or other industrial applications that involve solving wave propagation problems.

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    KW - Seismic Modelling

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    SN - 978-90-365-4613-3

    PB - University of Twente

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    Geevers S. Finite Element Methods for Seismic Modelling. Enschede: University of Twente, 2018. 178 p. https://doi.org/10.3990/1.9789036546133