Finite Element Methods for Seismic Modelling

Sjoerd Geevers

Research output: ThesisPhD Thesis - Research UT, graduation UTAcademic

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.
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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title = "Finite Element Methods for Seismic Modelling",
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 UTAcademic

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