Frequency-domain acoustic-wave modeling with hybrid absorbing boundary conditions

Moreira, Roger Matsumoto; Santos, Marco Antônio Cetale; Martins, Jorge Leonardo; Silva, Denis L. F.; Pessolani, Raul Bernardo Vidal; Filho, Djalma Manoel Soares; Bulcão, André

doi:10.1190/geo2014-0085.1

Cited by 22 publications

(5 citation statements)

References 15 publications

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“…where f = ω/2π and f c = f (3 √ π) is related to the cuttoff frequency f [44]. We solve the problem for three different frequencies, 10, 25, and 50 Hz, by keeping the total number of nodes in the domain as constant (50 × 50).…”

Section: Frequency-domain Visualizationmentioning

confidence: 99%

A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels

Mishra

Fasshauer

Sen

et al. 2019

Computers & Mathematics with Applications

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Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless implementation and is referred to as the radial basis-generated finite difference (RBF-FD) method. In this paper, we propose a stabilized RBF-FD approach with a hybrid kernel, generated through a hybridization of the Gaussian and cubic RBF. This hybrid kernel was found to improve the condition of the system matrix, consequently, the linear system can be solved with direct solvers which leads to a significant reduction in the computational cost as compared to standard RBF-FD methods coupled with present stable algorithms. Unlike other RBF-FD approaches, the eigenvalue spectra of differentiation matrices were found to be stable irrespective of irregularity, and the size of the stencils. As an application, we solve the frequency-domain acoustic wave equation in a 2D half-space. In order to suppress spurious reflections from truncated computational boundaries, absorbing boundary conditions have been effectively implemented. * Corresponding Author

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Section: Frequency-domain Visualizationmentioning

confidence: 99%

A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels

Mishra

Fasshauer

Sen

et al. 2019

Computers & Mathematics with Applications

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“…Combined with the frequency-space domain PML absorbing boundary condition (Berenger, 1994;Zhang et al, 2014;Moreira et al, 2014), we construct the 2D VTI media ADM 9-point frequency-space domain with the PML wave equation (Appendix A). We can perform the VTI media ADM 9-point frequencyspace domain modeling by combining the optimized coefficients of different ratio of the horizontal sampling interval and the vertical sampling interval with the VTI media ADM 9-point PML wave equation.…”

Section: Numerical Modeling and Analysismentioning

confidence: 99%

“…By introducing the PML technique (Berenger, 1994;Moreira et al, 2014), we combine the 2D PML stretch function e x and e z in the frequency-space domain with the frequency-space domain qP wave equation for 2D VTI media (formula (4)) and derive the frequency-space domain qP wave equation for 2D VTI media with the PML absorbing boundary condition:…”

mentioning

confidence: 99%

Forward Modeling of VTI Media in the Frequency‐Space Domain Based on an Average‐Derivative Optimal Method

Zhang

Liu

Tang

et al. 2015

Chinese J of Geophysics

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This paper proposed a new kind of qP wave equation second-order 9-point scheme of two-dimensional vertical transversely isotropic (VTI) media in the frequency-space domain based on an average-derivative optimal method (ADM for short). This scheme represents the finite-difference approximations of the second-order centered spatial-derivative terms of two-dimensional VTI media qP wave equation as the weighted average of 3 grid points in orthogonal directions and the acceleration term as the weighted average of all 9 grid points. Determining the optimal weighting coefficients of the second-order centered spatial-derivative terms and the acceleration term by using the least-square optimal method to minimize numerical dispersion, the number of grid points per wavelength bounded by a phase velocity error range of ±1% is only 3.57. But the VTI conventional 9-point scheme needs approximately 12 grid points per wavelength bounded by the same error range of ±1%, so the ADM method significantly increases the computational accuracy. The numerical example of the complex BP2007 2D VTI ocean standard model also proves the validity and precision of the VTI media ADM 9-point scheme.

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“…) and the finite‐difference method (Moreira et al . ; Doyon and Giroux ). The finite‐difference method is the most popular numerical method due to its simple implementation and good balance between accuracy and computational cost.…”

Section: Introductionmentioning

confidence: 98%

Complex frequency‐shifted multi‐axial perfectly matched layer for frequency‐domain seismic wavefield simulation in anisotropic media

Zhao

Chen

2019

Geophysical Prospecting

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A B S T R A C TSeismic anisotropy has an important influence on seismic data processing and interpretation. Although the frequency-domain seismic wavefield simulation has a problem of solving the large scale linear sparse matrix due to the computational limitations, it has some advantages over the time-domain seismic wavefield simulation including efficient inversion using only a limited number of frequency components and easy implementation of multiple sources. To accurately simulate seismic wave propagation in the frequency domain, we also need to choose the absorbing boundary conditions to absorb artificial reflections from edges of the model as we do in the time domain. Compared with the classical boundary conditions including the perfectly matched layer and complex frequency-shifted perfectly matched layer, the complex frequencyshifted multi-axial perfectly matched layer has been proven to effectively suppress the unwanted reflections at grazing incidence and solve the instability problem in the time-domain seismic numerical modelling in anisotropic elastic media. In this paper, we propose to extend the complex frequency-shifted multi-axial perfectly matched layer absorbing boundary condition to the frequency-domain seismic wavefield simulation in anisotropic elastic media. To test the validity of our proposed algorithm, we compare the results (snapshots and seismograms) of the frequency-domain seismic wavefield simulation with those of the time-domain modelling. The model studies indicate that the complex frequency-shifted multi-axial perfectly matched layer absorbing boundary condition is stable in the frequency-domain seismic wavefield simulation in anisotropic media, and provides better absorbing performance than the complex frequency-shifted perfectly matched layer boundary condition.

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Frequency-domain acoustic-wave modeling with hybrid absorbing boundary conditions

Cited by 22 publications

References 15 publications

A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels

A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels

Forward Modeling of VTI Media in the Frequency‐Space Domain Based on an Average‐Derivative Optimal Method

Complex frequency‐shifted multi‐axial perfectly matched layer for frequency‐domain seismic wavefield simulation in anisotropic media

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