Attenuating boundary conditions for numerical modeling of acoustic wave propagation

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 231-243 ◽  
Author(s):  
Shunhua Cao ◽  
Stewart Greenhalgh
Keyword(s):  
Boundary Condition ◽  
Numerical Modeling ◽  
Boundary Conditions ◽  
Absorbing Boundary Condition ◽  
Damped Wave Equation ◽  
Acoustic Wave Propagation ◽  
Absorbing Boundary ◽  
Multidimensional Modeling ◽  
Transmitting Boundary ◽  
Wide Zone

Four types of boundary conditions: Dirichlet, Neumann, transmitting, and modified transmitting, are derived by combining the damped wave equation with corresponding boundary conditions. The Dirichlet attenuating boundary condition is the easiest to implement. For an appropriate choice of attenuation parameter, it can achieve a boundary reflection coefficient of a few percent in a one‐wavelength wide zone. The Neumann‐attenuating boundary condition has characteristics similar to the Dirichlet attenuating boundary condition, but it is numerically more difficult to implement. Both the transmitting boundary condition and the modified transmitting boundary condition need an absorbing boundary condition at the termination of the attenuating region. The modified transmitting boundary condition is the most effective in the suppression of boundary reflections. For multidimensional modeling, there is no perfect absorbing boundary condition, and an approximate absorbing boundary condition is used.

An absorbing boundary condition for acoustic-wave propagation using a mesh-free method

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. T145-T154 ◽  
Author(s):  
Junichi Takekawa ◽  
Hitoshi Mikada
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Acoustic Wave ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary Condition ◽  
Acoustic Wave Propagation ◽  
Absorbing Boundary ◽  
Mesh Free ◽  
Mesh Free Method

We have developed an absorbing boundary condition for acoustic-wave propagation using a mesh-free method without sacrificing the flexibility of the mesh-free framework. When we simulate acoustic-wave propagation using a numerical method, artificial reflections from model edges induced by a truncated computational domain should be avoided. Although many absorbing boundary conditions have been developed, most of them have been based on a regular latticed alignment of grids or nodes, and the efficiency of such absorbing boundary conditions for irregular arrangement of grids or nodes has not been examined yet. We have studied the artificial reflections generated at the boundaries of a model for a mesh-free method, and we have proposed a novel approach for suppressing the artifacts. The method uses a hybrid approach with a transition zone, in which the wavefield is estimated by a weighted average of solutions from the one- and two-way wave equations. Numerical experiments indicate that the proposed method can provide good performance in suppression of the artificial edge reflections even for irregular distributions of calculation points in the vicinity of model edges.

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.

Relationship between Liao and Clayton-Engquist absorbing boundary conditions: Acoustic case

1995 ◽  
Vol 85 (3) ◽  
pp. 954-956
Author(s):  
Ningya Cheng ◽  
Chuen Hon Cheng
Keyword(s):  
Boundary Condition ◽  
Reflection Coefficient ◽  
Boundary Conditions ◽  
Closed Form ◽  
Differential Form ◽  
Short Note ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary ◽  
Close Relationship

Abstract In this short note, we derive the differential form of Liao's multi-transmitting formula. The reflection coefficient of the multi-transmitting formula in the acoustic case is obtained in closed form. These formulas are compared with Clayton-Engquist absorbing boundary condition and are shown to have a very close relationship.

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