The third-order Absorbing Boundary Condition for finite difference modeling of first-order stress-velocity acoustic equation

2015 ◽  
pp. 93-96
Author(s):  
Peng Song ◽  
Jun Tan ◽  
Dongming Xia ◽  
Jing Li ◽  
Zhaolun Liu ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Absorbing Boundary Condition ◽  
Third Order ◽  
Absorbing Boundary ◽  
First Order ◽  
The Third ◽  
Acoustic Equation ◽  
Order Stress

Absorbing boundary condition for the elastic wave equation

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 611-624 ◽  
Author(s):  
C. J. Randall
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Grazing Incidence ◽  
Scalar Fields ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary Condition ◽  
Elastic Wave Equation ◽  
Absorbing Boundary

Extant absorbing boundary conditions for the elastic wave equation are generally effective only for waves nearly normally incident upon the boundary. High reflectivity is exhibited for waves traveling obliquely to the boundary. In this paper, a new and efficient absorbing boundary condition for two‐dimensional and three‐dimensional finite‐difference calculations of elastic wave propagation is presented. Compressional and shear components of the incident vector displacement fields are separated by calculating intermediary scalar potentials, allowing the use of Lindman’s boundary condition for scalar fields, which is highly absorbing for waves incident at any angle. The elastic medium is assumed to be homogeneous in the region immediately adjacent to the boundary. The reflectivity matrix of the resulting absorbing boundary for elastic waves is calculated, including the effects of finite‐difference truncation error. For effectively all angles of incidence, reflectivities are much smaller than those of the commonly employed paraxial absorbing boundaries, and the boundary condition is stable for any physical Poisson’s ratio. The nearly complete absorption predicted by the reflectivity matrix calculations, even at near grazing incidence, is demonstrated in a finite‐difference application.

scholarly journals The fourth-order absorbing boundary condition with optimized coefficients for the simulation of the acoustic equation

2015 ◽  
Vol 12 (6) ◽  
pp. 996-1007 ◽  
Author(s):  
Peng Song ◽  
Zhaolun Liu ◽  
Xiaobo Zhang ◽  
Jun Tan ◽  
Dongming Xia ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Fourth Order ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary ◽  
Acoustic Equation

An optimal absorbing boundary condition for elastic wave modeling

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 296-301 ◽  
Author(s):  
Chengbin Peng ◽  
M. Nafi Toksöz
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Short Note ◽  
Absorbing Boundary Conditions ◽  
Parallel Computer ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary

Absorbing boundary conditions are widely used in numerical modeling of wave propagation in unbounded media to reduce reflections from artificial boundaries (Lindman, 1975; Clayton and Engquist, 1977; Reynolds, 1978; Liao et al., 1984; Cerjan et al., 1985; Randall, 1988; Higdon, 1991). We are interested in a particular absorbing boundary condition that has maximum absorbing ability with a minimum amount of computation and storage. This is practical for 3-D simulation of elastic wave propagation by a finite‐difference method. Peng and Toksöz (1994) developed a method to design a class of optimal absorbing boundary conditions for a given operator length. In this short note, we give a brief introduction to this technique, and we compare the optimal absorbing boundary conditions against those by Reynolds (1978) and Higdon (1991) using examples of 3-D elastic finite‐difference modeling on an nCUBE-2 parallel computer. In the Appendix, we also give explicit formulas for computing coefficients of the optimal absorbing boundary conditions.

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