A multidomain approach of the Fourier pseudospectral method using discontinuous grid for elastic wave modeling

Wang, Yanbin; Takenaka, Hiroshi

doi:10.1186/bf03352372

Cited by 23 publications

(9 citation statements)

References 29 publications

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“…Moreover, interpolation errors would be aggravated when wavefield are propagating within the media; therefore, the overall accuracy of the discontinuous-grid FD method would decrease. Some efforts have been made to improve the linear interpolation technique Wang and Takenaka, 2001) or to decrease the number of interpolation points using decreasing accurate FD operators toward the border of the fine grid in the transition zones (Kristek et al, 2010). However, neither of these two techniques effectively eliminates the artifacts caused by the interpolation.…”

Section: Introductionmentioning

confidence: 98%

“…This requirement would cause oversampling in high-velocity areas. To lower the storage requirements and reduce computational costs, a nonuniformgrid modeling technique has been widely applied using fine and coarse grids to discretize low-and high-velocity areas, respectively (e.g., Jastram and Tessmer, 1994;Moczo et al, 1996;Wang and Takenaka, 2001;Kang and Baag, 2004a;Wu et al, 2005;Zhang et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

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A discontinuous collocated-grid implementation for high-order finite-difference modeling

et al. 2015

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The discontinuous-grid method can greatly reduce the storage requirements and computational costs of finite-difference (FD) modeling for large-velocity-contrast models. However, traditional discontinuous-grid methods have to use interpolation when refining the wavefield in transition zones and would cause apparent artifacts. We have developed a new discontinuous collocated-grid scheme for highorder FD modeling. We refined the wavefield on a rotated coordinate system, where the interpolation is not required again. The horizontal and vertical spatial derivatives can be accurately converted into diagonal derivatives within the rotated coordinate system; thus, our scheme would be free of artifacts caused by improper interpolation. The ratio from coarse-to fine-grid spacing is restricted to 2 n for our scheme, where n is a positive integer. Numerical experiments demonstrate that the proposed discontinuous collocated-grid scheme reduces the artificial reflections by about two orders of magnitude compared to the interpolation scheme and yields a wavefield that is almost identical to that of the uniform-grid simulation. The rotated FD operator with arbitrary even-order accuracy is applied in the transition zones; thus, it significantly improves the spatial accuracy while saving computational cost.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

A discontinuous collocated-grid implementation for high-order finite-difference modeling

et al. 2015

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“…Its main advantage is that it requires considerably fewer grid points per wavelength to attain any desired accuracy (Fornberg ). To simulate wave propagation in a realistic earth model, many advances have been made to treat the internal interfaces and general boundaries, including the free‐surface and irregular topography, e.g., Fornberg (), Carcione (), Tessmer (), Wang and Takenaka (), and Klin et al . ().…”

Section: Introductionmentioning

confidence: 99%

Pseudo‐spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

Zou

Cheng

2017

Geophysical Prospecting

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A B S T R A C TStaggering grid is a very effective way to reduce the Nyquist errors and to suppress the non-causal ringing artefacts in the pseudo-spectral solution of first-order elastic wave equations. However, the straightforward use of a staggered-grid pseudo-spectral method is problematic for simulating wave propagation when the anisotropy level is greater than orthorhombic or when the anisotropic symmetries are not aligned with the computational grids. Inspired by the idea of rotated staggered-grid finitedifference method, we propose a modified pseudo-spectral method for wave propagation in arbitrary anisotropic media. Compared with an existing remedy of staggeredgrid pseudo-spectral method based on stiffness matrix decomposition and a possible alternative using the Lebedev grids, the rotated staggered-grid-based pseudo-spectral method possesses the best balance between the mitigation of artefacts and efficiency. A 2D example on a transversely isotropic model with tilted symmetry axis verifies its effectiveness to suppress the ringing artefacts. Two 3D examples of increasing anisotropy levels demonstrate that the rotated staggered-grid-based pseudo-spectral method can successfully simulate complex wavefields in such anisotropic formations.Key words: Arbitrary anisotropy, Wave propagation, Pseudo-spectral method, Rotated staggered grid. I N T R O D U C T I O NThe numerical modelling of the seismic wave propagation in realistic media is a key element in earthquake and exploration seismology. Several approaches have been developed with different physical model approximations, different complexity levels of the numerical schemes, and different usage of computational resources; see, for example, Carcione et al. (2002) for an overview. The finite-difference method (FDM) remains the most popular numerical method for seismic modelling because it is robust and relatively simple to implement, and it offers a good balance between accuracy and efficiency (Moczo et al. 2007;Yang et al. 2010;Virieux et al. 2011;Liu 2013). Other methods such as the pseudo-spectral (Kosloff and Baysal 1982;Sun et al. 2016a), finite-element (Eriksson * E-mail: 923458778@qq.com and Johnson 1991), spectral elements (Komatitsech et al. 2000), discontinuous Galerkin (Chung and Engquist 2006;De Basabe et al. 2008), finite-volume (Benjemaa et al. 2007, and grid methods (Zhang and Liu 1999) are used to various extent in the geophysical community. Wave propagation simulation has attracted a renewed interest mainly because the so-called (acoustic or elastic) full-wave equation approaches have become a fundamental tool in seismic migration and waveform inversion, considering the new challenges in exploration, especially anisotropy (Operto et al. 2009;Lisitsa and Vishnevskiy 2010;Bartolo et al. 2015;Cheng et al. 2016).The pseudo-spectral method (PSM) (Kosloff and Baysal 1982) we used here is an attractive alternative to the FDM that exploits the fast Fourier transform (FFT) algorithm for computing the spatial derivatives. Its main advantage is that ...

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“…So far, a number of attempts were made to apply numerical algorithms based on the pseudospectral time-domain methods to simulate various wave phenomena such as electromagnetic, seismic and acoustic waves [1,2,3,4], with various degrees of success. It is accepted that pseudospectral time-domain methods have high spatial resolution that meets the requirements of numerical simulation of aeroacoustic phenomena.…”

Section: Introductionmentioning

confidence: 99%

A Fourier Pseudospectral Method for Some Computational Aeroacoustics Problems

Huang

Zhang

2006

International Journal of Aeroacoustics

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A Fourier pseudospectral time-domain method is applied to wave propagation problems pertinent to computational aeroacoustics. The original algorithm of the Fourier pseudospectral timedomain method works for periodical problems without the interaction with physical boundaries. In this paper we develop a slip wall boundary condition, combined with buffer zone technique to solve some non-periodical problems. For a linear sound propagation problem whose governing equations could be transferred to ordinary differential equations in pseudospectral space, a new algorithm only requiring time stepping is developed and tested. For other wave propagation problems, the original algorithm has to be employed, and the developed slip wall boundary condition still works. The accuracy of the presented numerical algorithm is validated by benchmark problems, and the efficiency is assessed by comparing with high-order finite difference methods. It is indicated that the Fourier pseudospectral time-domain method, time stepping method, slip wall and absorbing boundary conditions combine together to form a fullyfledged computational algorithm.

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A multidomain approach of the Fourier pseudospectral method using discontinuous grid for elastic wave modeling

Cited by 23 publications

References 29 publications

A discontinuous collocated-grid implementation for high-order finite-difference modeling

A discontinuous collocated-grid implementation for high-order finite-difference modeling

Pseudo‐spectral method using rotated staggered grid for elastic wave propagation in 3D arbitrary anisotropic media

A Fourier Pseudospectral Method for Some Computational Aeroacoustics Problems

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