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.

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.

An optimized wave equation for seismic modeling and reverse time migration

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA153-WCA158 ◽  
Author(s):  
Faqi Liu ◽  
Guanquan Zhang ◽  
Scott A. Morton ◽  
Jacques P. Leveille
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Computational Cost ◽  
Numerical Dispersion ◽  
New Wave ◽  
Acoustic Wave Equation ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration

The acoustic wave equation has been widely used for the modeling and reverse time migration of seismic data. Numerical implementation of this equation via finite-difference techniques has established itself as a valuable approach and has long been a favored choice in the industry. To ensure quality results, accurate approximations are required for spatial and time derivatives. Traditionally, they are achieved numerically by using either relatively very fine computation grids or very long finite-difference operators. Otherwise, the numerical error, known as numerical dispersion, is present in the data and contaminates the signals. However, either approach will result in a considerable increase in the computational cost. A simple and computationally low-cost modification to the standard acoustic wave equation is presented to suppress numerical dispersion. This dispersion attenuator is one analogy of the antialiasing operator widely applied in Kirchhoff migration. When the new wave equation is solved numerically using finite-difference schemes, numerical dispersion in the original wave equation is attenuated significantly, leading to a much more accurate finite-difference scheme with little additional computational cost. Numerical tests on both synthetic and field data sets in both two and three dimensions demonstrate that the optimized wave equation dramatically improves the image quality by successfully attenuating dispersive noise. The adaptive application of this new wave equation only increases the computational cost slightly.

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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