3D Heterogeneous Staggered-Grid Finite-Difference Modeling of Seismic Motion with Volume Harmonic and Arithmetic Averaging of Elastic Moduli and Densities

Moczo, Peter; Kristek, Jozef; Vavryčuk, Václav; Archuleta, Ralph J.; Halada, Ladislav

doi:10.1785/0120010167

Cited by 386 publications

(239 citation statements)

References 41 publications

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“…The semiellipsoidal surface of the canyon and the surrounding portion of free surface lying inside a disk of radius D > a, b are discretized using boundary elements. Such a configuration is representative of a "topographic site effect" in seismology and has been the subject of numerous studies, see [13,28,29,57] and [7,26,34,40,49] where diffraction of waves by surface heterogeneities is considered.…”

Section: Diffraction Of An Incident P Plane Wave By a Semi-ellipsoidamentioning

confidence: 99%

A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain

Chaillat

Bonnet

Semblat

2008

Computer Methods in Applied Mechanics and Engineering

104

144

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To reduce computational complexity and memory requirement for 3-D elastodynamics using the boundary element method (BEM), a multi-level fast multipole BEM (FM-BEM) is proposed. The diagonal form for the expansion of the elastodynamic fundamental solution is used, with a truncation parameter adjusted to the subdivision level, a feature necessary for achieving optimal computational efficiency. Both the single-level and multi-level forms of the elastodynamic FM-BEM are considered, with emphasis on the latter. Crucial implementation issues, including the truncation of the multipole expansion, the optimal number of levels, the direct and inverse extrapolation steps are examined in detail with the backing of numerical experiments. A complexity analysis for both the single-level and multi-level versions is conducted. The correctness and computational performances of the proposed elastodynamic FMM are demonstrated on numerical examples, featuring up to O(10 6 ) DOFs run on a single-processor PC and including the diffraction of an incident P plane wave by a semi-spherical or semi-ellipsoidal canyon, representative of topographic site effects.Keywords: Fast multipole method; Boundary element method; 3-D elastodynamics; Topographic site effects IntroductionThe boundary element method (BEM), pioneered in the sixties [6,41], is a mesh reduction method, subject to restrictive constitutive assumptions but yielding highly accurate solutions. It is in particular well suited to deal with unbounded-domain idealizations commonly used in e.g. acoustics [50], electromagnetics [35,39] or seismology [7,22]. In contrast with domain discretization methods, artificial boundary conditions [18] are not needed for dealing with the radiation conditions, and grid dispersion cumulative effects are absent [24,51].However, in traditional boundary element (BE) implementations, the dimensional advantage with respect to domain discretization methods is offset by the fully-populated nature of the BEM coefficient matrix, with set-up and solution times rapidly increasing with the problem size N . It is thus essential to develop alternative, faster strategies that allow to still exploit the known advantages of BEMs when large N prohibit the use of traditional implementations. Fast BEMs, i.e. BEMs of complexity lower than that of traditional BEMs, appeared around 1985 with an iterative integral-equation [19,20], in the context of many-particle simulations. The FMM then naturally led to fast multipole boundary element methods (FM-BEMs), whose scope and capabilities have rapidly progressed, especially in connection with application in electromagnetics [21,31,32,53], but also in other fields including acoustics [14,36,48] and computational mechanics [30]. Many of these investigations are summarized in a review article by Nishimura [37]. The FMM, as well as other fast BEM approaches [23,27,55,56], intrinsically relies upon an iterative solution approach for the linear system of discretized BEM equations, with solution times typically of order O(N lo...

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Section: Diffraction Of An Incident P Plane Wave By a Semi-ellipsoidamentioning

confidence: 99%

A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain

Chaillat

Bonnet

Semblat

2008

Computer Methods in Applied Mechanics and Engineering

104

144

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“…A similar argument was introduced in the context of heterogeneous finite-difference methods by Boore (1972) and further developed by Zahradnik et al (1993) and Moczo et al (2002). In more recent developments of homogenization theory (e.g.…”

Section: Oa R S E -G R a I N E D M E M O Ry Va R I A B L E Smentioning

confidence: 84%

Optimized viscoelastic wave propagation for weakly dissipative media

Driel

Nissen‐Meyer

2014

Geophysical Journal International

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S U M M A R YThe representation of viscoelastic media in the time domain becomes more challenging with greater bandwidth of the propagating waves and number of travelled wavelengths. With the continuously increasing computational power, more extreme parameter regimes become accessible, which requires the reassessment and improvement of the standard 'memory variable' methods to implement attenuation in time-domain seismic wave-propagation methods. In this paper, we propose a method to minimize the error in the wavefield for a fixed complexity of the anelastic medium. This method consists of defining an appropriate misfit criterion based on a first-order analysis of how errors in the discretized medium propagate into errors in the wavefield and a simulated annealing optimization scheme to find the globally optimal parametrization. Furthermore, we derive an analytical time-stepping scheme for the memory variables that encode the strain history of the medium. Then we develop the coarse grained memory variable approach for the spectral element method (SEM) and benchmark it using the 2.5-D code AxiSEM for global body waves up to 1 Hz. Showing very good agreement with a reference solution, it also leads to a speedup of a factor of 5 in the anelastic part of the code (factor 2 in total) in this 2.5-D approach. A factor of ≈15 (3 in total) can be expected for the 3-D case compared to conventional implementations.

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“…For the homogeneously damped case (bottom), when compared to the amplitudes of the undamped case, the first reflections are not significant at time 2 t (only the incident wavefield is present in this plot) and no reflection at all can be identified at time 3 t .…”

Section: Efficiency Of the Homogeneous Absorbing Layersmentioning

confidence: 95%

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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3D Heterogeneous Staggered-Grid Finite-Difference Modeling of Seismic Motion with Volume Harmonic and Arithmetic Averaging of Elastic Moduli and Densities

Cited by 386 publications

References 41 publications

A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain

A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain

Optimized viscoelastic wave propagation for weakly dissipative media

A simple numerical absorbing layer method in elastodynamics

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