Optimized explicit finite-difference schemes for spatial derivatives using maximum norm

Zhang, Jinhai; Yao, Zhen‐Xing

doi:10.1016/j.jcp.2013.04.029

Cited by 97 publications

(45 citation statements)

References 23 publications

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“…Numerous approaches have been developed to deal with the numerical dispersion in space. One common way to reduce space dispersion is to use high-order FD schemes (Dablain, 1986;Liu and Sen, 2009), optimized FD operators (Etgen, 2007;Zhou and Zhang, 2011;Zhang and Yao, 2013;Wang et al, 2014), or the flux-corrected transport technique (Yang et al, 2002). The nearly analytical discrete methods (Yang et al, 2006(Yang et al, , 2007Ma et al, 2011) and stereo-modeling method (Tong et al, 2013), which introduce gradients of wave displacement in propagation, are proposed as well to suppress the numerical dispersion.…”

Section: Introductionmentioning

confidence: 99%

Finite-difference time dispersion transforms for wave propagation

Wang¹,

Xu²

2015

GEOPHYSICS

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The finite-difference (FD) wave equation is widely implemented in seismic imaging for oil exploration. But the numerical dispersion due to discretization of time and space derivatives can introduce severe numerical errors. We have investigated time dispersion, which might distort the phase and introduce severe artifacts to the data and images, especially for long-time propagation. We first studied precisely how the time dispersion was produced, and then we developed an efficient approach -the time dispersion transforms -to cope with time dispersion errors in wave propagation. The proposed forward time dispersion transform can predict or simulate the time dispersion errors, and it can be applied to remove time dispersion errors in reverse time migration. The inverse time dispersion transform can be used to eliminate time dispersion errors from synthetic data after modeling. The proposed method is general and works for low-and high-order time FD schemes. By using this method, large time steps were allowed in wave propagation; thus, we can remove the time dispersion errors at a negligible numerical cost, and the efficiency is not affected. To test the effectiveness and robustness of the proposed time dispersion transforms, we used isotropic and anisotropic examples, as well as modeling and imaging examples.

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Section: Introductionmentioning

confidence: 99%

Finite-difference time dispersion transforms for wave propagation

Wang¹,

Xu²

2015

GEOPHYSICS

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“…Essentially, temperature T controls the perturbation range of the optimal solution. High temperature is more likely to make it achieve a wider range (Zhang and Yao, 2013). Because −dE/KT < 0, the range of function P (dE) is (0, 1).…”

Section: Calculate the Coefficients Of The Optimized Implicit Staggermentioning

confidence: 99%

“…In fact, under the given tolerance limit Tolerrance, there will be many different groups of solutions whereas other optimization methods have only one set of solution. Therefore, we can take a further step to choose a set of optimal solutions by balancing between the error and the accurate wave number coverage (Zhang and Yao, 2013). Based on the assumption of discretization, we use the optimized first-order operator to approach the real wave number, and get the coefficients array X = [a; c].…”

Section: Calculate the Coefficients Of The Optimized Implicit Staggermentioning

confidence: 99%

A Global Optimized Implicit Staggered‐Grid Finite‐Difference Scheme for Elastic Wave Modeling

Wang

Liu

Zhang

et al. 2015

Chinese J of Geophysics

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The implicit finite-difference schemes make the process of numerical simulation possess higher accuracy and stability. However, most of the conventional implicit schemes have the limitation of lower computational efficiency because of the requirement of solving large scale matrix equation. In this paper, we first propose an optimized implicit staggered-grid finite-difference scheme based on first order velocity-stress elastic wave equation. Then we transform the new scheme from the time-space domain into the time-wavenumber domain, and construct the objective function by means of the two norm theory. Different from traditional global optimized schemes, we select the simulated annealing algorithm to get optimized coefficients. According to the shot records and wavefield snapshots acquired by homogeneous medium model and complex medium model numerical simulations, the optimized implicit staggered-grid finite-difference scheme not only reduces the calculating amount, but also suppresses the numerical dispersion, thus improves the precision of numerical simulation remarkably.

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“…In contrast, the numerical solver using a uniform grid (e.g., the finite‐difference method and pseudo‐spectral method) has less memory demand and computational cost, since it does not need to store the coordinates of the grid system and the wavefield can be explicitly updated without solving the inverse of the matrix. Thus, the numerical solver in the time domain using a uniform grid is one of the most important methods, and it is popular in various practical applications due to its simplicity and good performance (Etgen and O'Brien, 2007; Liu Y and Sen, 2013; Zhang JH and Yao ZX, 2013; Tan SR and Huang LJ, 2014).…”

Section: Introductionmentioning

confidence: 99%

Exact local refinement using Fourier interpolation for nonuniform-grid modeling

Zhang¹,

Yao²

2017

Earth and Planetary Physics

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Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large‐scale media. It is necessary to use a nonuniform grid, where upsampling the wavefield from the coarse grid to the fine grid is essential for reducing artifacts. In this paper, we suggest a local refinement scheme using the Fourier interpolation, which is superior to traditional interpolation methods since it is theoretically exact if the input wavefield is band limited. Traditional interpolation methods would fail at high upsampling ratios (say 50); in contrast, our scheme still works well in the same situations, and the upsampling ratio can be any positive integer. A high upsampling ratio allows us to greatly reduce the computational burden and memory demand in the presence of tiny structures and large‐scale models, especially for 3D cases.

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Optimized explicit finite-difference schemes for spatial derivatives using maximum norm

Cited by 97 publications

References 23 publications

Finite-difference time dispersion transforms for wave propagation

Finite-difference time dispersion transforms for wave propagation

A Global Optimized Implicit Staggered‐Grid Finite‐Difference Scheme for Elastic Wave Modeling

Exact local refinement using Fourier interpolation for nonuniform-grid modeling

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