New curvilinear scheme for elastic wave propagation in presence of curved topography

Tarrass, I.; Giraud, Luc; Thore, P.

doi:10.1111/j.1365-2478.2011.00972.x

Cited by 67 publications

(29 citation statements)

References 57 publications

(79 reference statements)

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“…While this approach is broadly similar to existing methods based on curvilinear coordinates (e.g. Hestholm & Ruud 1994;Komatitsch et al 1996;Zhang & Chen 2006;Tarrass et al 2011;Zhang et al 2012), it is distinct. In these latter methods the various terms in the equations of motion are regarded as tensor fields defined on the equilibrium body.…”

Section: O N C L U S I O N Smentioning

confidence: 96%

“…This is in contrast to methods based on 'tensorial formulations' of the elastic wave equation in general curvilinear coordinates that lead to the introduction of additional terms into the equations of motion (e.g. Hestholm & Ruud 1994;Komatitsch et al 1996;Zhang & Chen 2006;Tarrass et al 2011;Zhang et al 2012).…”

Section: Example 2: Mapping Topography Into Volumetric Heterogeneitymentioning

confidence: 99%

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Particle relabelling transformations in elastodynamics

Al-Attar¹,

Crawford²

2016

Geophys. J. Int.

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S U M M A R YThe motion of a self-gravitating hyperelastic body is described through a time-dependent mapping from a reference body into physical space, and its material properties are determined by a referential density and strain-energy function defined relative to the reference body. Points within the reference body do not have a direct physical meaning, but instead act as particle labels that could be assigned in different ways. We use Hamilton's principle to determine how the referential density and strain-energy functions transform when the particle labels are changed, and describe an associated 'particle relabelling symmetry'. We apply these results to linearized elastic wave propagation and discuss their implications for seismological inverse problems. In particular, we show that the effects of boundary topography on elastic wave propagation can be mapped exactly into volumetric heterogeneity while preserving the form of the equations of motion. Several numerical calculations are presented to illustrate our results.

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Section: O N C L U S I O N Smentioning

confidence: 96%

Section: Example 2: Mapping Topography Into Volumetric Heterogeneitymentioning

confidence: 99%

Particle relabelling transformations in elastodynamics

Al-Attar¹,

Crawford²

2016

Geophys. J. Int.

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“…The free-surface boundary conditions were approximated by second order finite differences, as presented in [91]. Discussion of the boundary conditions approximation for more complex schemes or free-surface topographies can be found in [5,6] and others. Fig.…”

Section: D Statement: Karstic Layermentioning

confidence: 99%

“…Full-scale simulation can be used to study the peculiarities of wave propagation in complex models, such as anisotropic [1,2], viscoelastic [1], and poroelastic models [3,4], and models with irregular topography [5][6][7], etc. Moreover, numerical simulation is an essential element in seismic imaging procedures such as Reverse Time Migration and Full Waveform Inversion [8].…”

Section: Introductionmentioning

confidence: 99%

Local time–space mesh refinement for simulation of elastic wave propagation in multi-scale media

Kostin¹,

Lisitsa

Reshetova

et al. 2015

Journal of Computational Physics

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“…To overcome problems that may arise to handle arbitrary shaped anomalies or topographies using the regular lattice grids, curvilinear schemes for modeling wave propagation have been developed (e.g. Tarrass et al, 2011). Although these schemes can handle arbitrary shaped topography, arrangement of optimal grid for complex velocity models is not straightforward.…”

Section: Introductionmentioning

confidence: 99%

A mesh-free method with arbitrary-order accuracy for acoustic wave propagation

Takekawa¹,

Mikada²,

Imamura³

2015

Computers & Geosciences

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a b s t r a c tIn the present study, we applied a novel mesh-free method to solve acoustic wave equation. Although the conventional finite difference methods determine the coefficients of its operator based on the regular grid alignment, the mesh-free method is not restricted to regular arrangements of calculation points. We derive the mesh-free approach using the multivariable Taylor expansion. The methodology can use arbitrary-order accuracy scheme in space by expanding the influence domain which controls the number of neighboring calculation points. The unique point of the method is that the approach calculates the approximation of derivatives using the differences of spatial variables without parameters as e.g. the weighting functions, basis functions. Dispersion analysis using a plane wave reveals that the choice of the higher-order scheme improves the dispersion property of the method although the scheme for the irregular distribution of the calculation points is more dispersive than that of the regular alignment. In numerical experiments, a model of irregular distribution of the calculation points reproduces acoustic wave propagation in a homogeneous medium same as that of a regular lattice. In an inhomogeneous model which includes low velocity anomalies, partially fine arrangement improves the effectiveness of computational cost without suffering from accuracy reduction. Our result indicates that the method would provide accurate and efficient solutions for acoustic wave propagation using adaptive distribution of the calculation points.

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New curvilinear scheme for elastic wave propagation in presence of curved topography

Cited by 67 publications

References 57 publications

Particle relabelling transformations in elastodynamics

Particle relabelling transformations in elastodynamics

Local time–space mesh refinement for simulation of elastic wave propagation in multi-scale media

A mesh-free method with arbitrary-order accuracy for acoustic wave propagation

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