Adaptive 9-point frequency-domain finite difference scheme for wavefield modeling of 2D acoustic wave equation

Xu, Wenhao; Gao, Jinghuai

doi:10.1088/1742-2140/aab015

Cited by 19 publications

(6 citation statements)

References 31 publications

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“…Then, the corresponding table of weights is built by minimizing the dispersion for each tabulated G, which are processed separately although some regularization can be implemented to force smooth variations of the weights with G. Then, each row of the impedance matrix is built by picking in the table the weights corresponding to the local wavelength. A similar idea was proposed for the 2D 9-point stencil by Xu & Gao (2018), who concluded from basic 2D simulations that the 9-point adaptive stencil reaches the same accuracy as the 25-point counterpart (Shin & Sohn, 1998). However, this study lacks comprehensive validation of the method against structurally complex and contrasted media.…”

Section: Introductionmentioning

confidence: 96%

Accurate 3D frequency-domain seismic wave modeling with the wavelength-adaptive 27-point finite-difference stencil: a tool for full waveform inversion

Aghamiry¹,

Gholami²,

Combe³

et al. 2021

Preprint

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Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset/wide-azimuth node data can be designed with a few discrete frequencies. However, 3D frequency-domain seismic modeling remains challenging since it requires solving a large and sparse linear indefinite system per frequency. When such systems are solved with direct methods or hybrid direct/iterative solvers, based upon domain decomposition preconditioner, finite-difference stencils on regular Cartesian grids should be designed to conciliate compactness and accuracy, the former being necessary to mitigate the fill-in induced by the Lower-Upper (LU) factorization. Compactness is classically implemented by combining several second-order accurate stencils covering the eight cells surrounding the collocation point, leading to the so-called 27-point stencil. Accuracy is obtained by applying optimal weights on the different stiffness and consistent mass matrices such that numerical dispersion is jointly minimized for several number of grid points per wavelength (G). However, with this approach, the same weights are used at each collocation point, leading to suboptimal accuracy in heterogeneous media. In this study, we propose a straightforward recipe to improve the accuracy of the 27-point stencil. First, we finely tabulate the values of G covering the range of wavelengths spanned by the subsurface model and the frequency. Then, we estimate with a classical dispersion analysis in homogeneous media the corresponding table of optimal weights that minimize dispersion for each G treated separately. We however apply a Tikhonov regularization to guarantee smooth variation of the weights with G. Finally, we build the impedance matrix by selecting the optimal weights at each collocation point according to the local wavelength, hence leading to a wavelength-adaptive stencil. We validate our method against analytical solutions in homogeneous and velocity gradient models and 3D heterogeneous benchmarks with sharp contrasts and complex tectonic pattern. In the latter case, the accuracy of the adaptive stencil is checked with the highly accurate solution of the convergent Born series (CBS). Each benchmark reveals the higher accuracy of the adaptive stencil relative to the non-adaptive one. We also show that, in the presence of sharp contrasts, the adaptive stencil is more accurate than a O(∆t 2 , ∆h 8 ) finite-different time-domain method.

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Section: Introductionmentioning

confidence: 96%

Accurate 3D frequency-domain seismic wave modeling with the wavelength-adaptive 27-point finite-difference stencil: a tool for full waveform inversion

Aghamiry¹,

Gholami²,

Combe³

et al. 2021

Preprint

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“…Accurate acoustic wave propagation is a highly challenging computational problem that is crucial to acoustic modeling, imaging, and inversion. To solve the time-domain or frequency-domain acoustic wave equation in a heterogeneous medium, it is necessary to apply numerical modeling techniques, such as the finite-difference time-domain (FDTD) method [1][2][3][4][5], finite-difference frequency-domain (FDFD) [6,7], finite-element time-domain (FETD) [8][9][10][11], finite-element frequency-domain (FEFD) [12], pseudo-spectral time-domain (PSTD) [13][14][15], and spectral-element time-domain (SETD) methods [16][17][18]. The FDTD method is the most popular numerical scheme for simulating acoustic wave propagation.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Chebyshev Pseudo-Spectral Finite-Difference Time-Domain Method for Numerical Simulation of 2D Acoustic Wave Propagation

Tong,

Sun

2023

Mathematics

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In this study, a hybrid Chebyshev pseudo-spectral finite-difference time-domain (CPS-FDTD) algorithm is proposed for simulating 2D acoustic wave propagation in heterogeneous media, which is different from the other traditional numerical schemes such as finite element and finite difference. This proposed hybrid method integrates the efficiency of the FDTD approach in the time domain and the high accuracy of the CPS technique in the spatial domain. We present the calculation formulas of this novel approach and conduct simulation experiments to test it. The biconjugate gradient is solved by combining the large symmetric sparse systems stabilized algorithm with an incomplete LU factorization. Three numerical experiments are further presented to illustrate the accuracy, efficiency, and flexibility of the hybrid CPS-FDTD algorithm.

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“…Since forward modeling of the wave equation consumes most computational time in the RTM and FWI processes (Jing et al, 2019;Xu et al, 2021b;Liu et al, 2021), how to achieve the improvement of efficiency and the reduction of memory usage without a significant decrease of accuracy for 3D large-scale modeling is a key problem of seismic modeling. The finite-difference (FD) method has been regarded as one of the most popular wave modeling methods for its easy implementation and high-computational efficiency (Antunes et al, 2014;Abreu et al, 2015;Xu and Gao, 2018;Robertsson and Blanch, 2020). However, the numerical dispersion of the traditional FD method leads to the use of fine grids or high-order operators (Dablain, 1986;Liu and Sen, 2011b), which inevitably affects the efficiency of simulation.…”

Section: Introductionmentioning

confidence: 99%

Trapezoid-Grid Finite-Difference Time-Domain Method for 3D Seismic Wavefield Modeling Using CPML Absorbing Boundary Condition

Tan

et al. 2022

Front. Earth Sci.

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The large computational memory requirement is an important issue in 3D large-scale wave modeling, especially for GPU calculation. Based on the observation that wave propagation velocity tends to gradually increase with depth, we propose a 3D trapezoid-grid finite-difference time-domain (FDTD) method to achieve the reduction of memory usage without a significant increase of computational time or a decrease of modeling accuracy. It adopts the size-increasing trapezoid-grid mesh to fit the increasing trend of seismic wave velocity in depth, which can significantly reduce the oversampling in the high-velocity region. The trapezoid coordinate transformation is used to alleviate the difficulty of processing ununiform grids. We derive the 3D acoustic equation in the new trapezoid coordinate system and adopt the corresponding trapezoid-grid convolutional perfectly matched layer (CPML) absorbing boundary condition to eliminate the artificial boundary reflection. Stability analysis is given to generate stable modeling results. Numerical tests on the 3D homogenous model verify the effectiveness of our method and the trapezoid-grid CPML absorbing boundary condition, while numerical tests on the SEG/EAGE overthrust model indicate that for comparable computational time and accuracy, our method can achieve about 50% reduction on memory usage compared with those on the uniform-grid FDTD method.

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Adaptive 9-point frequency-domain finite difference scheme for wavefield modeling of 2D acoustic wave equation

Cited by 19 publications

References 31 publications

Accurate 3D frequency-domain seismic wave modeling with the wavelength-adaptive 27-point finite-difference stencil: a tool for full waveform inversion

Accurate 3D frequency-domain seismic wave modeling with the wavelength-adaptive 27-point finite-difference stencil: a tool for full waveform inversion

A Hybrid Chebyshev Pseudo-Spectral Finite-Difference Time-Domain Method for Numerical Simulation of 2D Acoustic Wave Propagation

Trapezoid-Grid Finite-Difference Time-Domain Method for 3D Seismic Wavefield Modeling Using CPML Absorbing Boundary Condition

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