An optimal finite-difference method based on the elongated stencil for 2D frequency-domain acoustic wave modeling

Geophysics ◽  
2021 ◽  
pp. 1-62
Author(s):  
Shizhong Li ◽  
Chengyu Sun ◽  
Han Wu ◽  
Ruiqian Cai ◽  
Ning Xu
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Frequency Domain ◽  
Directional Derivative ◽  
Finite Difference Methods ◽  
Computational Cost ◽  
Grid Spacing ◽  
Wave Modeling ◽  
Spacing Ratio ◽  
Derivative Method

Frequency-domain finite-difference (FDFD) modeling plays an important role in exploration seismology. However, a major disadvantage of FDFD modeling is the computational cost, especially for large-scale models. By compactly distributing nonzero strips, the elongated stencil helps to generate a narrow-bandwidth impedance matrix, improving computational efficiency without sacrificing numerical accuracy. To further improve the accuracy and efficiency of modeling, we have developed an optimal FDFD method with an elongated stencil for 2D acoustic-wave modeling. The Laplacian term is approximated using the directional-derivative method and the average-derivative method. The dispersion analysis indicates that this elongated-stencil-based method (ESM) achieves higher accuracy than other finite-difference methods with the elongated stencil, and it is more suitable for large grid-spacing ratios. To keep the phase-velocity error within 1%, 15-point and 21-point schemes in the ESM only require approximately 2.28 and 2.19 grid points per wavelength, respectively, when the grid-spacing ratio, namely, the ratio of directional sampling intervals, is not less than 1.5. Moreover, we also adopt a variable-stencil-length scheme, in which the stencil length varies with the velocity, to further reduce the computational cost in frequency-domain modeling. Several numerical examples are presented to demonstrate the effectiveness of our ESM.

A generalized average-derivative optimal finite-difference scheme for 2D frequency-domain acoustic-wave modeling on continuous nonuniform grids

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. T265-T279
Author(s):  
Quanli Li ◽  
Xiaofeng Jia
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Frequency Domain ◽  
Computational Cost ◽  
Numerical Dispersion ◽  
Grid Spacing ◽  
Wave Modeling ◽  
Nonuniform Grids ◽  
Optimal Scheme ◽  
Average Derivative

The frequency-domain finite-difference (FDFD) method is an effective tool for implementing frequency-domain seismic modeling, inversion, and migration. However, the computational cost for the FDFD method dealing with large models is prohibitive, limiting its application. As a common strategy to improve the computational efficiency, a nonuniform grid is usually adopted in the time-domain finite-difference method instead of the FDFD method. We have developed a generalized average-derivative optimal scheme (GADOS) that can perform frequency-domain acoustic-wave modeling on continuous nonuniform grids in the vertical and horizontal directions. Before we begin the calculations, we optimize numerous stencils in which the grid spacing ratios are different to obtain a large dictionary composed of many groups of optimal coefficients. We consider the continuous nonuniform grids as a gathering of nonuniform nine-point stencils (i.e., the stencil of the GADOS) and select the proper weighted coefficients for every stencil to ensure that the numerical dispersion is minimal in the global area. All the phase-velocity errors of the GADOS for different grid spacing ratios are less than [Formula: see text] even if the number of grid points per wavelength is as small as four after the weighted coefficients are optimized by minimizing the numerical dispersion. Compared with the average-derivative optimal scheme (ADOS), simulating seismic waves with the GADOS on nonuniform grids reduce the computational cost with the premise of ensuring sufficient accuracy. Several numerical examples are presented to illustrate the feasibility and efficiency of the GADOS on continuous nonuniform grids.

A discontinuous-grid finite-difference scheme for frequency-domain 2D scalar wave modeling

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. T235-T244 ◽  
Author(s):  
Na Fan ◽  
Lian-Feng Zhao ◽  
Xiao-Bi Xie ◽  
Zhen-Xing Yao
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Frequency Domain ◽  
Transition Zone ◽  
Time Domain ◽  
Finite Difference Scheme ◽  
Grid Method ◽  
Scalar Wave ◽  
Wave Modeling ◽  
Spacing Ratio

The discontinuous-grid method can greatly reduce the storage requirement and computational cost in finite-difference modeling, especially for models with large velocity contrasts. However, this technique is mostly applied to time-domain methods. We have developed a discontinuous-grid finite-difference scheme for frequency-domain 2D scalar wave modeling. Special frequency-domain finite-difference stencils are designed in the fine-coarse grid transition zone. The coarse-to-fine-grid spacing ratio is restricted to [Formula: see text], where [Formula: see text] is a positive integer. Optimization equations are formulated to obtain expansion coefficients for irregular stencils in the transition zone. The proposed method works well when teamed with commonly used 9- and 25-point schemes. Compared with the conventional frequency-domain finite-difference method, the proposed discontinuous-grid method can largely reduce the size of the impedance matrix and number of nonzero elements. Numerical experiments demonstrated that the proposed discontinuous-grid scheme can significantly reduce memory and computational costs, while still yielding almost identical results compared with those from conventional uniform-grid simulations. When tested for a very long elapsed time, the frequency-domain discontinuous-grid method does not show instability problems as its time-domain counterpart usually does.

Efficient Two-dimensional Acoustic Wave Finite-Difference Numerical Simulation in Strongly Heterogeneous Media Using the Adaptive Mesh Refinement (AMR) Technique

Geophysics ◽  
2021 ◽  
pp. 1-76
Author(s):  
Chunli Zhang ◽  
Wei Zhang
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Adaptive Mesh Refinement ◽  
Heterogeneous Media ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Grid Spacing ◽  
Time Step ◽  
Velocity Models ◽  
The Stability

The finite-difference method (FDM) is one of the most popular numerical methods to simulate seismic wave propagation in complex velocity models. If a uniform grid is applied in the FDM for heterogeneous models, the grid spacing is determined by the global minimum velocity to suppress dispersion and dissipation errors in the numerical scheme, resulting in spatial oversampling in higher-velocity zones. Then, the small grid spacing dictates a small time step due to the stability condition of explicit numerical schemes. The spatial oversampling and reduced time step will cause unnecessarily inefficient use of memory and computational resources in simulations for strongly heterogeneous media. To overcome this problem, we propose to use the adaptive mesh refinement (AMR) technique in the FDM to flexibly adjust the grid spacing following velocity variations. AMR is rarely utilized in acoustic wave simulations with the FDM due to the increased complexity of implementation, including its data management, grid generation and computational load balancing on high-performance computing platforms. We implement AMR for 2D acoustic wave simulation in strongly heterogeneous media based on the patch approach with the FDM. The AMR grid can be automatically generated for given velocity models. To simplify the implementation, we employ a well-developed AMR framework, AMReX, to carry out the complex grid management. Numerical tests demonstrate the stability, accuracy level and efficiency of the AMR scheme. The computation time is approximately proportional to the number of grid points, and the overhead due to the wavefield exchange and data structure is small.

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