An improved vacuum formulation for 2D finite-difference modeling of Rayleigh waves including surface topography and internal discontinuities

Zeng, Chong; Xia, Jianghai; Miller, Richard D.; Tsoflias, G. P.

doi:10.1190/geo2011-0067.1

Cited by 82 publications

(32 citation statements)

References 32 publications

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“…For elastic wave propagation, Bartel et al (2000) find that some smoothing of the extreme density contrast is required for numerical stability. Boore (1972), Robertsson (1996), Mittet (2002), Bohlen and Saenger (2006), and Zeng et al (2012) consider variants of the vacuum approach. Unfortunately, the loss of accuracy can become significant: Numerical experiments with a higher order finite-difference scheme for the acoustic wave equation indicate that the numerical error increases to only the first order in space (Zhebel et al, 2014) in case of a smoothed density contrast.…”

Section: Introductionmentioning

confidence: 99%

A simple finite-difference scheme for handling topography with the second-order wave equation

Mulder

2017

GEOPHYSICS

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Citation (APA) Mulder, W. A. (2017). A simple finite-difference scheme for handling topography with the second-order wave equation. Geophysics, 82(3), T111-T120. https://doi.org/10.1190/GEO2016-0212.1 Important noteTo cite this publication, please use the final published version (if applicable). Please check the document version above. CopyrightOther than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policyPlease contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. This work is downloaded from Delft University of Technology. For technical reasons the number of authors shown on this cover page is limited to a maximum of 10.A simple finite-difference scheme for handling topography with the second-order wave equation ABSTRACTThe presence of topography poses a challenge for seismic modeling with finite-difference codes. The representation of topography by means of an air layer or vacuum often leads to a substantial loss of numerical accuracy. A suitable modification of the finite-difference weights near the free surface can decrease that error. An existing approach requires extrapolation of interior solution values to the exterior while using the boundary condition at the free surface. However, schemes of this type occasionally become unstable and may be impossible to implement with highly irregular topography. One-dimensional extrapolation along coordinate lines results in a simple and efficient scheme. The stability of the 1D scheme is improved by ignoring the interior point nearest to the boundary during extrapolation in case its distance to the boundary is less than half a grid spacing. The generalization of the 1D scheme to more than one dimension requires a modification if the boundary intersects the finite-difference stencil on both sides of the central evaluation point and if there are not enough interior points to build the finite-difference stencil. Examples for the 2D constant-density acoustic case with a fourth-order finite-difference scheme demonstrate the method's capability. Because the 1D assumption is not valid in two dimensions if the boundary does not follow grid lines, the formal numerical accuracy is not always obtained, but the method can handle highly irregular topography.

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Section: Introductionmentioning

confidence: 99%

A simple finite-difference scheme for handling topography with the second-order wave equation

Mulder

2017

GEOPHYSICS

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“…3). We found that the second-order-accurate [71] and fourth-order-accurate [83] spatial finite difference operators were both stable and suitable for our purposes. We used the second-orderaccurate operator because it is computationally simpler.…”

Section: A the Finite-difference Time-domain (Fdtd) Methods For The Ementioning

confidence: 94%

“…For accuracy and stability, a half-grid-cell-thick fictitious layer of material is added around the structure to ease the transition from the material to vacuum [83]. Fixed BCs are simpler to implement: we force v = 0 on the surface.…”

Section: A the Finite-difference Time-domain (Fdtd) Methods For The Ementioning

confidence: 99%

Rayleigh waves, surface disorder, and phonon localization in nanostructures

2016

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We introduce a technique to calculate thermal conductivity in disordered nanostructures: a finitedifference time-domain (FDTD) solution of the elastic wave equation combined with the Green-Kubo formula. The technique captures phonon wave behavior and scales well to nanostructures that are too large or too surface disordered to simulate with many other techniques. We investigate the role of Rayleigh waves and surface disorder on thermal transport by studying graphenelike nanoribbons with free edges (allowing Rayleigh waves) and fixed edges (prohibiting Rayleigh waves). We find that free edges result in a significantly lower thermal conductivity than fixed ones. Free edges both introduce Rayleigh waves and cause all low-frequency modes (bulk and surface) to become more localized. Increasing surface disorder on free edges draws energy away from the center of the ribbon and toward the disordered edges, where it gets trapped in localized surface modes. These effects are not seen in ribbons with fixed boundary conditions and illustrate the importance of phonon surface modes in nanostructures.

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“…We run the case both with the vacuum formulation (Robertsson, 1996;Zeng et al, 2012) and with the mimetic approach described here.…”

Section: Examplementioning

confidence: 99%

Mimetic Operators for Seismic Exploration

Puente¹,

Rojas²,

Ferrer³

et al. 2016

78th EAGE Conference and Exhibition 2016

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SUMMARYMimetic operators are a kind of discrete operators which, on staggered grids, can accomplish "mimetic" properties analogous to their continuous counterparts. Furthermore, they can attain identical convergence order everywhere in the domain, including at or near the domain's boundaries in non-periodic problems. This property makes mimetic finite difference (MFD) operators attractive whenever high-contrast interfaces or physical boundary conditions are present in our models. In the seismic case, the strongest boundary condition is the interface between Earth and air, the so-called free surface. This surface is typically represented as a traction-free boundary condition and, although it is of critical importance for achieving accurate results, due to its vicinity to the sources and receivers, it is still a problem for current FD implementations. Despite efforts in the past, few FD schemes have attained convergence of order beyond two in results involving the free surface. Here we summarize the properties of mimetic operators applied to the elastic wave equation, as well as the changes required in order to incorporate into current explicit staggered grid codes the mimetic approach of the free-surface condition

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An improved vacuum formulation for 2D finite-difference modeling of Rayleigh waves including surface topography and internal discontinuities

Cited by 82 publications

References 32 publications

A simple finite-difference scheme for handling topography with the second-order wave equation

A simple finite-difference scheme for handling topography with the second-order wave equation

Rayleigh waves, surface disorder, and phonon localization in nanostructures

Mimetic Operators for Seismic Exploration

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