Discontinuous-Grid Finite-Difference Seismic Modeling Including Surface Topography

Hayashi, Koichi

doi:10.1785/0120000024

Cited by 93 publications

(41 citation statements)

References 38 publications

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“…Like in most FD modeling techniques including surface topography, the oblique segments of the topography are approximated by a staircase shape (Hayashi et al, 2001). The primary shortcoming of this approximation is that it needs a fine-grid discretization to reduce the spurious diffractions at the corners of the stairs.…”

Section: An Improved Vacuum Formulation T3mentioning

confidence: 99%

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

et al. 2012

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Rayleigh waves are generated along the free surface and their propagation can be strongly influenced by surface topography. Modeling of Rayleigh waves in the near surface in the presence of topography is fundamental to the study of surface waves in environmental and engineering geophysics. For simulation of Rayleigh waves, the traction-free boundary condition needs to be satisfied on the free surface. A vacuum formulation naturally incorporates surface topography in finite-difference (FD) modeling by treating the surface grid nodes as the internal grid nodes. However, the conventional vacuum formulation does not completely fulfill the free-surface boundary condition and becomes unstable for modeling using high-order FD operators. We developed a stable vacuum formulation that fully satisfies the free-surface boundary condition by choosing an appropriate combination of the staggered-grid form and a parameter-averaging scheme. The elastic parameters on the topographic free surface are updated with exactly the same treatment as internal grid nodes. The improved vacuum formulation can accurately and stably simulate Rayleigh waves along the topographic surface for homogeneous and heterogeneous elastic models with high Poisson's ratios (>0.4). This method requires fewer grid points per wavelength than the stress-image-based methods. Internal discontinuities in a model can be handled without modification of the algorithm. Only minor changes are required to implement the improved vacuum formulation in existing 2D FD modeling codes.

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Section: An Improved Vacuum Formulation T3mentioning

confidence: 99%

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

et al. 2012

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“…In case of more complex topographies, one strategy is to adapt the topography to the grid structure at the expense of numerical dispersion effect (Robertsson, 1996) or to deform the underlying meshing used in the numerical method to the topography (Hestholm, 1999;Hestholm & Ruud, 1998;Tessmer et al, 1992). In the first case, because of stair-case approximation, a local fine sampling is required (Hayashi et al, 2001). …”

Section: Free Surfacementioning

confidence: 99%

Seismic Waves - Research and Analysis

Kanao¹

2012

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“…Therefore, the type of nonuniform grids that have larger grid-spacing for deeper part of the simulation domain are of particular interest for seismic applications. Earlier attempts on finite difference simulation of seismic wave on this type of grids can be found in Hayashi et al (2001); Kristek et al (2010); Zhang et al (2013), etc., and the references therein. Unfortunately, these earlier attempts encounter the so-called long-time instability longfei.gao@kaust.edu.sa † david.ketcheson@kaust.edu.sa ‡ david.keyes@kaust.edu.sa Instability 3…”

Section: Introductionmentioning

confidence: 99%

“…To the knowledge of the authors, the cause of this long-time instability has not yet been fully understood. Various techniques have been devised to control this long-time instability, including spatial averaging (Hayashi et al 2001), spatial filtering (Kristek et al 2010;Zhang et al 2013) and temporal filtering (Gao et al 2016). In this work, we analyze this long-time instability issue from an algebraic perspective and employ the discrete energy method (cf.…”

Section: Introductionmentioning

confidence: 99%

On long-time instabilities in staggered finite difference simulations of the seismic acoustic wave equations on discontinuous grids

Gao¹,

Ketcheson²,

Keyes³

2017

Geophysical Journal International

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SUMMARYWe consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings.Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.

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Discontinuous-Grid Finite-Difference Seismic Modeling Including Surface Topography

Cited by 93 publications

References 38 publications

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

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

Seismic Waves - Research and Analysis

On long-time instabilities in staggered finite difference simulations of the seismic acoustic wave equations on discontinuous grids

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