scholarly journals Optimized Finite Difference Methods for Seismic Acoustic Wave Modeling

2018 ◽  
Author(s):  
Yanfei Wang ◽  
Wenquan Liang
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Finite Difference Methods ◽  
Wave Modeling ◽  
Difference Methods

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.

Biharmonic navigation using radial basis functions

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Real World ◽  
Biharmonic Equation ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Large Size ◽  
Radial Basis ◽  
Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

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