The spectral element method for elastic wave equations: Application to 2D and 3D seismic problems

Komatitsch, Dimitri; Tromp, J.; Vilotte, Jean‐Pierre

doi:10.1190/1.1820185

Cited by 27 publications

(29 citation statements)

References 3 publications

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“…(5)) leading to various types of damping-frequency variations. In addition to the Finite Element Method, the method may be considered in the framework of other numerical methods such as the Spectral Element Method [8,9].…”

Section: Resultsmentioning

confidence: 99%

“…Such methods as finite or spectral elements have strong advantages (for complex geometries [9], nonlinear media [10], etc) but may have such drawbacks as numerical dispersion [4,11,12] for low order finite elements, or spurious reflections at the mesh boundaries [4,13]. The problem of spurious reflections may be dealt with using the Boundary Element Method [5,6,7] or coupling it with other numerical methods [14].…”

mentioning

confidence: 99%

“…Numerical methods for elastic waves in unbounded domains Various numerical methods are available to simulate elastic wave propagation in solids: finite differences [1,2], finite elements [3,4], boundary elements [5,6,7], spectral elements [8,9], etc. Such methods as finite or spectral elements have strong advantages (for complex geometries [9], nonlinear media [10], etc) but may have such drawbacks as numerical dispersion [4,11,12] for low order finite elements, or spurious reflections at the mesh boundaries [4,13].…”

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confidence: 99%

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A simple numerical absorbing layer method in elastodynamics

Semblat

Gandomzadeh

Lenti

2009

Comptes Rendus. Mécanique

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Abstract:The numerical analysis of elastic wave propagation in unbounded media may be difficult to handle due to spurious waves reflected at the model artificial boundaries. Several sophisticated techniques such as nonreflecting boundary conditions, infinite elements or absorbing layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this Note, a simple and efficient absorbing layer method is proposed in the framework of the Finite Element Method. This method considers Rayleigh/Caughey damping in the absorbing layer and its principle is presented first. The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types (surface waves, body waves) and incidences (normal to grazing). The method is shown to be efficient for different types of elastic waves and may thus be used for various elastodynamic problems in unbounded domains.Abstract: La simulation numérique de la propagation d'ondes élastiques en milieux infinis peut s'avérer délicate du fait des réflexions d'ondes parasites sur les frontières du modèle discrétisé. Plusieurs méthodes sophistiquées, telles que les frontières absorbantes, les éléments infinis ou les couches absorbantes (e.g. « Perfectly Matched Layers ») permettent une réduction importante des réflexions parasites. Dans cette note, une méthode de couche absorbante simple et efficace est proposée dans le cadre de la méthode des éléments finis. Cette méthode s'appuie sur une formulation de l'amortissement dans la couche de type Rayleigh/Caughey et ses principes sont d'abord détaillés. L'efficacité de la méthode est alors démontrée grâce à des simulations unidimensionnelles en considérant un amortissement homogène ou variable dans la couche absorbante. Des modèles bidimensionnels permettent ensuite d'apprécier l'efficacité de la méthode de couche absorbante proposée pour différents types d'ondes (ondes de surface, ondes de volume) et des incidences variées (normale à rasante). La méthode s'avère ainsi efficace pour différents types d'ondes élastiques et pourrait être utilisée pour traiter divers problèmes élastodynamiques en milieux non bornés. 1.Numerical methods for elastic waves in unbounded domains Various numerical methods are available to simulate elastic wave propagation in solids: finite differences [1,2], finite elements [3,4], boundary elements [5,6,7], spectral elements [8,9], etc. Such methods as finite or spectral elements have strong advantages (for complex geometries [9], nonlinear media [10], etc) but may have such drawbacks as numerical dispersion [4,11,12] for low order finite elements, or spurious reflections at the mesh boundaries [4,13]. The problem of spurious reflections may be dealt with using the Boundary Element Method [5,6,7] or coupling it with other numerical methods [14]. Domain Reduction Methods are also available in th...

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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A simple numerical absorbing layer method in elastodynamics

Semblat

Gandomzadeh

Lenti

2009

Comptes Rendus. Mécanique

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“…The solution we present is obtained computing just 128 frequencies, while the spectral method is run through 4000 time steps. More details on the model used in the SEM simulation can be found in Komatitsch et al [31]. The two methods give the displacement field in the whole domain, but the number of unknowns they manage differs in orders of magnitude.…”

Section: Examplesmentioning

confidence: 99%

“…The spectral element method will be presented elsewhere (see Komatitsch et al [31]). Some results obtained for the models of Figs.…”

Section: Examplesmentioning

confidence: 99%

Elastic wave propagation in an irregularly layered medium

Vai

Castillo-Covarrubias²,

Sánchez-Sesma

et al. 1999

Soil Dynamics and Earthquake Engineering

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A Coupled Method of Spectral Element and Normal Mode: A Powerful Tool for Modeling the Seismic Waves Propagation in the Anisotropic D″ Region

Zhao

Capdeville

2013

Chinese J of Geophysics

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We extended the coupled mode/spectral element method (CSEM hereafter) to incorporate threedimensional, anisotropic media in the lowest 300 km above the core-mantle boundary, the D area. This extended method was applied to modeling of seismic waves propagation in earth models under the so-called "sandwich" structure, which uses a spherical shell of spectral elements between two modal solutions to represent the D area. Using a spherically symmetric reference model with modified anisotropic parameters in the spherical shell, the CSEM yields waveforms in excellent agreement with that of normal-mode. The two methods match very well for all body wave arrivals with periods greater than 8 s. Besides, the S, ScS, SKS, and SKKS phases in the synthetic seismograms of the transverse isotropic model show obvious arrival time differences between SH and SV components. This proves the capability of the extended CSEM code for modeling S wave splitting caused by the radial anisotropic media in the D area.

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The spectral element method for elastic wave equations: Application to 2D and 3D seismic problems

Cited by 27 publications

References 3 publications

A simple numerical absorbing layer method in elastodynamics

A simple numerical absorbing layer method in elastodynamics

Elastic wave propagation in an irregularly layered medium

A Coupled Method of Spectral Element and Normal Mode: A Powerful Tool for Modeling the Seismic Waves Propagation in the Anisotropic D″ Region

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